(Quantitative Analysis of Dose-Response Data Obtained With Three Carcino- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 genic Hydrocarbons in Strain C3H Male Mice By W. RAY BRYAN, biologist, and MICHAEL B. SHIMKIN, passed assistant surgeon, National Cancer Institute, National Institute of Health, United States Public Health Service In a previous communication (1) analy- of the hydrocarbons so that the unit volume ses were made of published data dealing of solvent containing the quantity of with the responses of mice to measured hydrocarbon injected was 0.25 cc., except quantities of several carcinogenic hydro- in two dose groups, noted in the tables, carbons. Certain conclusions were reached where 0.5 cc. of solvent was used. The regarding the nature of the latent-period suspensions containing the higher con- and percentage response curves obtained centrations were prepared by weighing with such agents. This paper deals with separate batches of the hydrocarbons for investigations carried out to test further each dose and adding the desired amount these conclusions and to compare the of solvent. results obtained in simultaneous studies The doses were spaced logarithmically of 20-methylcholanthrene, 1, 2, 5, 6-dibenz- over a wide range (0.00024 to 8.0 mg.) anthracene, and 3, 4-benzpyrene.' The in order to include extreme responses and former conclusions are substantiated, and thus obtain information regarding the estimates are made of the relative carcino- range of doses within which both the inci- genic potencies of the above-named dence and the latent period of tumor re- materials. sponse are correlated with dose. The test animals were 1,004 male mice EXPERIMENTAL PROCEDURE of strain C3H, which were obtained from The corrected melting points of the three the Roscoe B. Jackson Memorial Labora- hydrocarbons used were: methylcholan- tory, Bar Harbor, Maine, and which were threne, 179.7 ° -180.2 ° C.; dibenzanthra- received in varying lots during the first cene, 267.3 ° -267.7 ° ; benzpyrene, 178.2 ° - 3 months of 1941. Each lot was divided 178.9 0 2 The same batches of the . at random into 3 groups for injection with chemicals were used throughout the in- the respective hydrocarbons. Subdivi- vestigation. sion of the groups according to the various The hydrocarbons were dissolved in doses of the 3 chemicals was also carried a tricaprylin with melting point of 8.3 ° out. The mice were 1.5 to 3 months old, ° . The various solutions used for in-9.0 and most of them weighed 20 to 24 gm. jection were prepared by making appro- at the time of injection. They were main- priate dilutions of standard stock solutions tained on unlimited supplies of water and i Hereinafter referred to as methylcholanthrene, di- Purina dog chow, and were individually benzanthracene, and óenzpyrene. identified. 2 The hydrocarbons and the solvent were supplied by Dr. J. I. Hartwell, of the National Cancer Institute. All injections were made into the sub- 503 504JOURNAL OF THE NATIONAL CANCER INSTITUTE cutaneous tissues of the right axilla. In final analysis of results. Forty-seven ani- order to prevent leakage, a long needle was mals were listed as missing or dead and inserted just above the tail in the dorsal autolyzed before small nodules were con- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 region and passed diagonally through clusively diagnosed as tumors and were the subcutaneous tissues into the right discarded from the results. axillary space. The volumes injected were A total of 433 tumors I at the site of in- measured with tuberculin syringes of 0.5- jection was observed in the 957 mice. cc. capacity. The morphology of 415 tumors that were Examination, by palpation, of each examined histologically is described and individual mouse for subcutaneous tumor analyzed in another publication (4). Of was carried out every fourth or fifth day the 415 tumors, 411 (99 percent) were beginning 4 weeks after injection. Mice spindle-cell sarcomas, 2 were carcinomas, with subcutaneous nodules thought to be and 2 consisted of mixed sarcoma and early tumors were isolated at each exami- carcinoma elements. The 18 tumors that nation, and the growth of the nodules was have been included, in the absence of followed every second day by measure- histologic examination, grew rapidly to a ment until the growth had reached a mean fairly large size (10 to 20 mm. in diameter) diameter of about 20 mm. unless death but were lost for microscopic studies be- intervened. Sections through several cause of death and autolysis or because planes were taken of the tumor tissue they were devoured by other mice. at necropsy for microscopic examination. A progressively growing tumor when RESULTS proved by subsequent growth and histo- The results for the different hydrocar- logic appearance to be a malignant neo- bons are summarized in tables 1, 4, and 7, plasm, was listed as having appeared on respectively, which give as much infor- the date on which the nodule was first re- mation as is practicable concerning the corded. The interval between injection actual data. Detailed information in re- and appearance of the tumor was con- gard to individual latent periods for the sidered the latent period. respective hydrocarbons is given in the Two factors may complicate the first scatter diagrams of figures 1, 9, and 18. detection of a tumor nodule. The first Analyses were made to determine the is the formation of cysts containing the variability of the biologic responses and injected solvent. These cysts are ruptured to determine the trends of the various by slight pressure and can be ruled out group responses with dose of hydrocarbon. easily (2). The second factor is the thick- In addition, certain statistics were calcu- ening of the subcutaneous tissue which lated to facilitate comparison between the occurs with higher concentrations of the results obtained with the various carcino- hydrocarbons (3). Occasionally the thick- genic agents as well as with data from the ening may be nodular because of small literature. For simplicity, graphic presen- encapsulated areas of necrosis or oil. tation of the analyses is given where prac- This reaction appears fairly soon after ticable. Most of the biomathematical injection and usually subsides before the procedures involved in these analyses are appearance of a progressively growing discussed in detail by Bliss (5, 6, 7) and malignant process. 3 A few mice developed multiple tumors, but only the Of the 1,004 strain C3H male mice first tumor occurring in a given animal is considered in originally employed, 957 contributed to the this report. DOSE RESPONSE W1T1-I THREE CARCINOGENIC HYDROCARBONS 505 Irwin (8). Where tests for statistical sig- METHYLCHOLANTHRENE nificance were carried out, the results are The results with methylcholanthrene are indicated in the text as follows: statistically Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 summarized in table 1. The upper limit, significant, when P is less than 0.01; not 1.0 mg., of the dose range (0.00024 to 1.0 statistically significant, when P is greater mg.) was selected because previous studies than 0.05; probably significant when P (9), in which methylcholanthrene had been administered to similar test animals under is between 0.01 and 0.05. Values pre- similar conditions, had showed that the ceded by a ± sign represent standard incidence of tumors was 100 percent at all errors. Limits of error corresponding to a doses above 0.25 mg. Furthermore, above probability of 0.05 are designated where this dose level the latent period was con- included. stant and unrelated to dose. TABLE 1.-Summarized results on latent period of tumors and tumor incidence of mice injected with methylcholanthrene Latent period Tumor incidence Dose Mice in- Mice with --- jected tumors Mean Stand- Weight "Cor- Mice Weight latent and de- of obser- rected with Probits 4 of obser- period 2 viation 2 vation 3 total" tumors vations Mg. Log mg. Number Number Months Months Number Percent 1.0 0.000 20 20 2.40 0.40 20 20 100 0.5 -.301 21 21 2.57 .40 21 21 100 5 8.484 0.063 0.25------------------.602 21 21 2.77 .61 7.64 21 100 5 7.860 .441 0.125-----------------.903 21 21 3.32 .92 3.72 21 100 5 7.268 1.911 0.062-----------------1.204 21 17 3.92 1.01 1.78 19.7 86.3 6.094 7.98 0.031 -1.505 20 13 5.24 1.87 .90 19.9 65.3 5.393 11.96 0.0156----------------1.806 18 6 4.59 .96 .29 16.5 36.4 4.652 9.97 0.0078______________ -2.107 17 3 6.97 4.64 .11 15.8 19.0 4.122 7.55 0.0039______________ -2.408 19 0 ----___-__-___-----_ -_---___-_14.6 0 5 2.893 1.372 0.00195------------- -2.709 19 0 ----_______-__----__ -___-_____16.6 0 52.319 .578 0.00098---------------3.010 41 0 __________ __________ __________ 6 29.2 0 5 1.695 .175 0.00024---------------3.612 79 0 --------- -------- ---------33.6 0 ---------- --------- I The volume of solvent used for each injection was 0.5 cc. at dose 1.0 mg.; 0.25 cc. at all other doses. 2 Months=Days /30. a See text. 4 See Bliss (5, 7). 5 Estimated probits for 0- and 100-percent responses. Provisional values determined by extrapolation. Latent Period prior to the times indicated along the Standard deviation.-The latent periods are ordinate (fig. 1). For example, the top shown graphically in figure 1, in which line of the figure shows for any given dose they have been plotted against the loga- the time at which 99 percent of the mice rithm of dose. The graph shows the that are going to develop tumors would be variation of the latent periods at successive expected to have developed them. The dose levels, i.e., the vertical spread of the derivation of the calculated lines is dis- plotted points. The horizontal and cussed later (p. 509). oblique lines represent calculated values In figure 1 it will be noted that the latent and are for the purpose of showing periods are most stable at the two highest the estimated vertical distribution at con- doses (0.5 and 1.0 mg.), but that their tinuous dose levels. They are in terms variability increases as the dose becomes of accumulative percentages of mice smaller. (within the tumor population only) which The standard deviation of individual would be expected to develop tumors at or latent periods about their respective group 506 JOURNAL OF THE NATIONAL CANCER INSTITUTE o e =0.584-0.950 (X+0.519) (1) where a e is the calculated standard devia- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 tion in months (days /30) and X the dosage in log milligrams. The curved lines 4 show the limits of error of the calculated regression line corresponding to P =0.05. n The wide range of variation coupled with a low incidence of tumors at the low dose levels make estimates of the standard N deviation in this region of little practical z 0 importance unless very large numbers of animals are used. The standard errors W I- of the estimates for the two lowest- doses (0.015 and 0.0078 mg.) are so large that the information which they contribute with respect to the true nature of the trend is of no consequence. The regression in this region is therefore indicated as a DOSE IN LOG MILLIGRAMS FIGURE 1.— Latent periods of tumors induced with broken line which should be considered methylcholanthrene. The solid circles repre- only as a provisional estimate and not as sent individual observations plotted to avoid definite information regarding the exact superposition of points at given doses. The nature of the trend. oblique and horizontal lines show the calculated On a basis of previous studies (9) in variation at continuous dose levels. which the value of the minimal standard means are given in table 1 and shown deviation was identical with that reported graphically in figure 2. Their regression here, 0.4 months (days /30), the standard on log dose is statistically significant and deviation is considered to have reached its minimal level at about dose 0.5 mg. U) ( -0.301 log mg.). That the standard 5 deviation of individual latent periods a 4. would not be decreased below this level by F- 3• larger doses of methylcholanthrene is fur- á ther indicated by the breaks in the trends of results shown in figures 1 and 2. Relative weights of latent-period observations -2.4 -1.8 LOG MILLIGRAMS -12 -0.6 0 at different dose levels.—The reliability of a FIGURE 2.— Standard deviation of latent periods latent-period response, such as a group with successive doses of methylcholanthrene. mean, is dependent upon the variability Circles: Observed standard deviations; Solid line: Calculated regression line; as well as upon the total number of indi- Curved dash lines: Limits of error of calcu- vidual observations employed in its der- lated regression line for P=0.05. ivation. In the following analyses, the may be adequately represented as linear 4 The curved lines of this and subsequent figures rep- within the limits indicated by the solid resent the limits within which the relation between dose oblique line. The equation to the re- and response has been established. They apply to the calculated regression line and not to the distribution of gression line is: points about the calculated line. DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 507 reciprocal of variance (1/v 2) was used as a may also be used as a basis for estimating weighting factor for adjusting the weights the numbers of unit observations required of responses at different dose levels with to give results possessing the same degree Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 respect to the variability factor. 5 of reliability at different levels of dosage. Table 2, column 5, shows the relative Column 6 shows the relative numbers weights when the number of observations when 10 are considered at the dose level (mice with tumors) is constant and when where the weight is at its maximum. It the maximum weight for any one dose should be emphasized that the relative group is considered as unity. The maxi- numbers in this column refer to individual mum weight is reached with those doses latent-period determinations and that they that yield the minimal standard devia- represent, therefore, only mice that actu- tion. The relative weights may be em- ally develop tumors. The incidence of ployed as weighting coefficients, and they tumors decreases with the dose of methyl- cholanthrene, and it is necessary to in- 5 This procedure was suggested by Dr. Harold F. Dorn, Division of Public Health Methods, National crease accordingly the total number of Institute of Health, to compensate for the correlation injected mice to produce the desired num- between standard deviation and dose. In the present analyses, the calculated standard deviations, derived bers with tumors indicated by column 6. from equation (1), were used rather than the observed (See section entitled "Joint Use of Latent standard deviations. The maximum value of 1/o, 2 was considered as unity for determining the relative weights, Period and Tumor Incidence Data," also or weighting coefficients, used in the analyses. columns 7 and 8 of table 2.) TABLE 2.-Relative weights of latent-period observations and numbers of mice required for observations of equal weight at various doses of methrlcholanthrene Total inject- Expected Mice with ed mice re- Expected Reciprocal Relative tumors re- Expected in- quired for Dose (in milligrams) mean latent standard of variance weight quired for cidence of latent period period deviation (l/o ,) (weighting responses of tumors responses (o^) coefficient) equal weight of equal weight Months Months Number Percent Number 1.0_____________________ 2.48 0.40 6.25 1.0 10 100.0 it 0.5_____________________ 2.48 .40 6.25 1.0 10 100.0 it 0.25____________________ 2.73 .66 2.27 .364 27 99.6 21 0.125------------------- 3.40 .95 1.11 .178 56 97.3 59 0.0625__________________ 4.07 1.23 .656 .105 95 88.1 10£ 0.0312__________________ 4.74 1.52 .432 .069 145 66.8 211 0.0156 5.42 '1.81 3 .306 3 .049 3 204 37.9 '531 0.0078------------------ - 6.09 3 2.09 3.228 3.036 3 278 14.6 3 1.904 0.0039__________________ 6.76 Í 32.38 3.177 3.028 3357 3.6 Months= Days/30. a See text. 3 Provisional values determined by extrapolation. 508 JOURNAL OF THE NATIONAL CANCER INSTITUTE latent period in days /30 and X the dosage in log milligrams. The latent period is considered to have Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 x6 reached a minimal level with the two I.- 0 highest doses, 0.5 and 1.0 mg. ( -0.3 and z4 0 log mg.). This is indicated by the bi apparent break in the trend of responses I- at this dose level (figs. 1 and 3) and by the results of a previous study (9) in which the established minimal latent period, 2.27 days /30, was very nearly the same as -2R -1.6 -1.2 -0.6 0 DOSE IN LOG MILLIGRAMS that found here, 2.48 days /30. FIGURE 3. —Dose response curve for methylchol- Frequency distribution of individual .latent- anthrene showing regression of mean latent period on log dose. period observations.—Exact information re- Circles: Observed mean latent periods; garding the distribution of individual latent Solid line: Calculated regression line; Curved dash lines: Limits of error of calcu- periods about the true response curve for lated regression line for P=0.05. methylcholanthrene cannot be derived from data available at the present time. Mean latent period.— Statistical analyses 6 However, an approximation made from indicate that the regression of mean latent the distribution of observed latent periods period on log dose is significant when about their respective group means may dosages of methylcholanthrene smaller be of value for certain practical purposes than 0.5 mg. ( -0.301 log mg.) are used. such as the weighting of animals that die The regression (below dose —0.3 log without tumors, and estimation of the mg.) is adequately represented by the time-tumor frequency relationship at oblique line of figure 3, the equation to various dose levels. which is: In a previous communication (1) the frequency relationships of the normal curve Y=3.274-2.233 (X+0.846) (2) were used for weighting animals that died where Y is the estimated value of the mean without tumors.' It would be more desir- able, however, to use the actual frequency 6 The finding in a previous section of a significant distribution if this were known. Figure 4 correlation between the standard deviation of individual shows the distribution of latent periods ob- latent periods and the logarithm of dose necessitates a modification of the statistical procedures described by tained by compiling the data of the present Irwin (8) for analyses involving the continuous type of experiments and those of Shimkin (11) to variate. Irwin treated only the condition in which the standard deviation is the same at all dose levels but give a total of 198 unit observations suit- pointed out that, if this were not the case, special pro- able for the analysis. Combination of the cedures would have to be introduced. It is beyond the scope of the present investigation to deal with statistical data for various doses and the different ex- techniques, and no attempt was made to work out special periments was made possible by expressing procedures for the latent period data. An approximate method, which employed as the standard error of estimate the individual latent periods as deviations the over-all average value for the standard deviation of from their group means in standard devia- group responses about the calculated regression line, was used in determining the limits of error and in making tion units. tests of significance. It is apparent from figure 4 that the fre- In computing the regression equation the variation in standard deviation with log dose was compensated for quency distribution is fundamentally by weighting the latent-period observations with respect skew ed, indicating an excess of values in to the reciprocal of variance (see footnote 5) as well as in accordance with the number of observations. 7 The data treated were those of Lettinga (10). DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 509 defect of the mean and a tendency to "tail out" toward the higher latent-period values. A better approximation to the observed fre- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 quencies would result, therefore, from use of the empirically established skew curve than from the relationships of a normal E1 curve. More suitable for present use is the ac- cumulative form of the frequency curve shown in figure 5. The relationships be- -2 -I0 +I tween accumulative frequency and devi- +2 +3 DEVIATIONSFROM GROUP MEANS - IN STANDARD DEVIATION UNITS ate represented by the curve of figure 5 are FIGURE 5. —Accumulative frequency curve of shown in actual time units (days /30) for latent-period responses obtained with methyl- the various dose levels by the solid (calcu- cholanthrene, expressed as deviations from group means. The smoothed curve was drawn lated) lines of figure 1. The transforma- by sight. tion to actual time units was accomplished Solid circles: Present data; by adding (or subtracting) appropriate Open circles: Data of Shimkin (11). multiples of the expected standard devia- tion to (or from) the expected mean latent skewness with dose could not be investi- period for a given dose. The expected gated with the limited data available. values were derived from the respective re- The above frequency distribution, there- gression lines. (See figs. 2 and 3, or equa- fore, represents an over-all average. It tions 1 and 2.) Accumulative percent- has been used to express the results over ages corresponding to various multiples the entire dose range pending the accumu- of the standard deviation are shown along lation of sufficient data for a more detailed the ordinate (fig. 5). analysis. Another question of importance The analysis of the frequency distribu- concerns the character of the frequency tion was, of necessity, based on the com- curve in the dose range where the latent- bined data of all dose groups, and the period response curve is flat, i. e., above possibility of a variation in degree of 0.5 mg. ( -0.301 log mg.). It is possible that the distribution at this dose level will be entirely different from that represented- here (see analysis of dibenzanthracene data), but the available data are not sufficient for a separate analysis of this dose range. Tumor Incidence The incidence of tumors, in percent, was -Z -I0 +i .2 +3 DEVIATIONS FROM GROUP MEANS - IN STANDANDARD DEVIATION UNITS determined from the "corrected totals" FIGURE 4.— Frequency distribution of latent- (table 1). The procedures for estimating period responses obtained with methylchol- the corrected totals have been discussed anthrene, expressed as deviations from group in detail previously (1). Briefly, the means. The smoothed curve was drawn by sight. method is that animals that die without Solid circles: Present data; tumors are weighted with respect to the Open circles: Data of Shimkin (11). proportion of animals in the tumor popu- 510 JOURNAL OF THE NATIONAL CANCER INSTITUTE centage response may be used for quanti- tative studies. Without taking into con- 8 sideration the limits of error of the esti- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 mated curve, the useful dose range is seen á6 to be from about 0.0045 mg., the dose cal- w 22 , N a culated to give tumors in 5 percent of the mice (TD 5 ), to about 0.096 mg., the dose which would be expected to yield a 95- percent incidence of tumors (TD 95 ). Be- -3.6 -3.0 -2A -1.8 -42 -0.6 0 yond these limits the responses rapidly DOSE IN LOG MILLIGRAMS approach 0 and 100 percent, respectively, FIGURE 6.—Dose response curve for methylchol- and there is no further correlation between anthrene showing the regression of probits on log dose. dose and tumor incidence. Circles: Empirical probits corresponding to Median tumor dose (TD 50).—The dose of observed percentages; methylcholanthrene which would be ex- Circles with arrows: Estimated probit val- pected on a basis of the present data to ues for 0- and 100-percent responses; produce tumors in 50 percent of the test Solid line: Calculated regression line; Curved dash lines: Limits of error of calcu- animals is —1.681+0.063 log mg., or lated regression line for P= 0.05. +0.0032 m 0.021 The limits of error cor- 0.0028g' — lation that would be expected to have responding to P=0.05 are +0.123 log mg., developed tumors at or prior to the time of +0.0068 or death of the animal under consideration. —0.0051 mg. Tumor incidence in relation to dose. —For a Standard deviation of the logarithms of indi- statistical evaluation of the data, the per- vidual effective doses about log TD 50 .—Gad- centage values were converted into probits dum (12) has shown that the S-shaped (table 1), and the doses to logarithms dose-response curve may be considered as (table 1, log milligrams). The regression an integrated frequency curve of individual of probits on log dose is adequately de- effective doses and that the standard de- scribed by a straight line (deviations of the DOSE IN MILLIGRAMS observed values from a straight line are not statistically significant) thus indicating that the logarithms of individual effective doses of methylcholanthrene are normally distributed. The relations are shown in figure 6. The regression equation is: w Y=5.098+2.474 (X+1.641) (3) where Yis the estimated probit correspond- I- ing to dose X in log milligrams. The percentage equivalents of the -2.4 -1.8 -I.2 -0.6 0 DOSE IN LOG MILLIGRAMS observed and calculated probits are given FIGURE 7.—Dose response curve for methylchol- in figure 7. The S-shaped curve of this anthrene showing relation of tumor incidence figure permits a better visualization of the in percent to log dose. Transformed from data practical dose limits within which the per- of figure 6. DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 511 viation, X, of the logarithms of individual responses of equal weight, with respect to effective doses about the median effective estimates of potency (table 3), are those dose may be estimated from this curve or which would be required if 10 were used Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 from its counterpart in probability units, at the 50 -percent level. e. g., probits (5), or normal equivalent TABLE 3. Relative weights of tumor-incidence obser- deviations (12). In the instance of methyl- vations and numbers of mice required for observations cholanthrene, the value of X estimated of equal weight at various doses of methylcholanthrene from probit data is 0.40+0.06. The Mice re- limits of error corresponding to P=0.05 Dose (in Expected Expected Weighting quired coef- for equal are ±0.13. milligrams) probit percent ficient 1 weight The statistic X has been widely used in --- responses recent years for comparing the biologic Number actions of various drugs. It has also been 1.0_____ __________ 9.158 100.0 0.000 0.5 ---------------- 8.413 99.97 .004 1,667 0.25 --------------- 7.669 99.62 .032 200 used for comparing the responses of differ- 0.125_____________ 6.924 97.3 .148 43 0.062_____________ 6.179 88.1 .378 17 ent types of test animals to a common ma- 0.031 -------------- 5.435 66.8 .594 11 0.0156 ------------- 4.690 37.9 .614 10 terial. Thus, Boyland and Warren (13) 0.0078____________ 3.945 14.6 .420 15 0.0039 ------------- 3.201 3.6 .180 35 reported X values of 0.58 and 0.73, respec- 0.00195___________ 2.456 .55 .045 141 0.00098___________ 1.711 .05 .006 1,111 tively, for mice of strains CBA and Simp- 0.000244__________ .222 0 .000 son which were injected subcutaneously I From Bliss (5, table III). with a lard solution of methylcholanthrene. The present estimate of the standard Joint Use of Latent-Period and Tumor- deviation, 0.40, is less than the values Incidence Data found by Boyland and Warren, but it is still within the limits for "normal drug Total numbers of injected mice required to action" as quoted by these authors, i. e., give latent period responses of equal weight at 0.37 to 0.91. It would appear, then, various dose levels.-The numbers of mice that the action of tricaprylin solutions of with tumors that would be required to methycholanthrene in C3H male mice is produce latent-period responses of equal less variable than that of lard solutions in weight are given in table 2. It has been CBA and Simpson strain mice. shown that the frequency of tumors among Relative weights of tumor-incidence responses injected animals decreases progressively at different dose levels.-The reliability of a with the dose of methylcholanthrene (figs. dosage, or potency, estimate inferred 6 and 7). In order, therefore, to obtain a from a percentage (or probit) response desired number of mice with tumors at a varies according to the magnitude of the given dose level, it would be necessary to response itself, as well as with the number increase the total number injected to allow of unit observations on which it is based. for those that fail to develop tumors. The Weighting coefficients for use with per- expected tumor frequencies and the total centage (or probit) responses of various numbers of injected mice based thereon magnitudes have been published by Gad- are also given in table 2. The total num- dum (12, fag. 9) and by Bliss (5, table III). bers (column 8) represent approximations The appropriate values corresponding to only, since the relations on which they are the expected percentage responses for based are subject to variation. Account methylcholanthrene are given in table 3, has not been taken of mice that die during column 4. The relative numbers of mice the course of the experiment. that would be required to give percentage Spec(/lc induction time.-The specific induc- 512 JOURNAL OF THE NATIONAL CANCER INSTITUTE tion time was previously defined (1) as the a time when most of the tumors have ap- time required, on an average, for the pro- peared, e. g., 9 months, but several months duction of tumors with dose TIJ 50 . The before full opportunity has been allowed Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 value of this measure for comparing the for the extreme cases to develop, e. g., relative rates of action of different carcino- 12 to 18 months. On the other hand, genic hydrocarbons has already been em- quantitative determinations of the po- phasized (1). The specific induction time tency relationships between various prepa- for methylcholanthrene is 5.14±0.55 rations of a carcinogenic agent are simplest months (days/30).$ The limits of error when a maximum time has been allowed corresponding to P=0.05 are 1.05 months for tumors to appear and when the esti- (days/30). mates are based on final percentage ob- Time-tumor frequency relationships at suc- servations, i. e., on observations which are cessive dose levels. —Time-frequency curves no longer changing with time. Potency have been widely used in presenting the relationships may, nevertheless, be estab- results obtained with single doses of car- lished from observations made during the cinogenic hydrocarbons or in comparing period when tumors are still appearing the results obtained with two or more provided the time-frequency relationship preparations of such materials. This pro- is known for successive levels of potency cedure gives detailed information regard- (or dosage) and a series of standard curves ing the latent periods of individual animals is available for comparison. Such a series of a group and offers the advantage that of standard curves may be constructed the responses to various preparations may from the latent-period and tumor-inci- be compared on a common basis at any dence relationships presented previously. particular time during the course of an For example, the percentage of mice in experiment. Thus, the essential informa- the tumor population which would be ex- tion of an experiment may be obtained at pected to develop tumors at, or prior to, a given time is shown for various levels of dosage by the calculated lines of figure 1. These percentages may be converted to percentages of the total injected population, and the time frequency relationship ex- pressed in terms of the total numbers of injected mice in each dose group. The time-frequency curves for the vari- I- ous doses of methylcholanthrene are shown in figure 8. Although this series of curves 0.0034 illustrates the nature of the time-frequency 4 6 B 1D TIME IN. MONTHS (DAYS/3O) 14 results to be expected at different levels of dosage and while it may be profitably FIGURE 8.-Time-frequency curves for succes- sive doses of methylcholanthrene showing the used in the planning of future experiments calculated incidence of tumors at successive periods. under the present conditions, it cannot at present be considered as a standard for e The value 5.14 was obtained by substituting —1.681, quantitative comparison. For the latter log TD 5Di for X in equation 2 and solving for Y, the expected latent period at this dose level. The limits of usage it would be necessary to prove (1) error were estimated by taking into consideration the that this estimate is fairly close to the true error of estimate of log TD 59 as well as the error of the latent period regression equation. results that would be obtained with very DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 513 large numbers of observations, and (2) dose is decreased. Furthermore, the tnat the animal population remains rela- curves asymptote at various levels below tively stable over long periods of time. No 100 percent as the dose is decreased below Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 attempt has been made to set the limits of about 0.5 mg., and an incidence of 100 error of the curves of figure 8, since in- percent would never be reached at these volved in their estimation are errors of low doses regardless of the length of time the latent-period response curve, errors of the observations are continued. the probit response curve, errors of the standard-deviation regression line, and DIBENZANTHRACENE finally errors of estimate of the latent- period frequency distribution. The summarized results obtained with In spite of wide possible limits of error dibenzanthracene in doses of 0.00195 to of the curves of figure 8, some information 8.0 mg. are presented in table 4. The dis- concerning their nature has been gained. cussion concerning analytical procedures For example, it is apparent that tumors in the section on methylcholanthrene is may occur practically as early with the applicable also to dibenzanthracene, and lower doses as with the higher doses of the reader is referred to that section for methylcholanthrene although the proba- explanation of the methods of presentation bility of early tumors becomes less as the and the purposes of the various analyses. TABLE 4.- Summarized results obtained on latent period of tumors and tumor incidence of mice injected with dibenzanthracene Latent period Tumor incidence Mice Mice Dose I with Mean Stand- Weight Weight injected tumors of ob- "Cor- Mice of ob - latent and de- serva- rected with Probits 4 serva- period 2 viation 2 tion 3 total" 3 tumors tion Mg. Log mg. Number Number Months Months Number Percent 8.0__________________ +0.903 21 16 3.75 0.32 16.0 16.0 100.0 4.0___________ ______ +602 20 17 3.83 .62 17.0 18.6 91.5 6.372 2.0________________ +.301 19 19 3.69 .64 19.0 19.0 100.0 1.0 ------------------ -0 22 22 3.60 .54 22.0 22.0 100.0 _ __________ 0.5____________ ______ -.301 21 20 3.76 .56 15.4 20.1 99.5 __________ __________ 0.25 ------------------ --.602 21 19 4.01 1.16 7.11 20.0 95.0 6.645 __________ 0.125 ----------------- --.903 23 21 4.47 1.48 4.62 21.9 95.9 6.739 4.58 0.062 ----------------- -- 1.204 20 20 5.10 1.91 2.90 20.0 100.0 6.726 8.46 0.031 1.505 21 16 6.31 1.67 1.63 19.8 80.8 5.870 11.44 0.0156 ---------------- -1.806 19 6 5.94 1.41 .46 15.8 38.0 4.694 10.05 0.0078 -2.107 40 6 8.78 2.61 .35 32.1 18.7 4.111 17.30 0.00195_________ _____ -2.709 79 2 9.48 2.40 .08 61.9 3.2 3.148 10.27 1 The volume of solvent used for each injection was 0.5 cc. at dose 8.0 mg.; 0.25 cc. at all other doses. 2 Months=Days /30. 3 See text. 4 See Bliss (5, 7). 5 Estimated probity for the 100 -percent response. Latent Period lions of individual latent periods obtained Standard deviation.-Inspection of figure with different doses are listed in table 4 9 reveals that above dose 0.5 mg. the and are shown graphically in figure 10. variability of individual latent periods is The regression of standard deviation on relatively stable whereas below this dose log dose is probably significant in the range variability increases progressively as the 0.00195 to 0.5 mg., but there is no corre- dose is decreased. The standard devia- lation between standard deviation and 523119 -43-5 514 JOURNAL OF THE NATIONAL CANCER INSTITUTE .0039 .0156 .0625 .25 1.0 4.0 of the standard deviation in months T6 (days/30) and X the dose in log milli- 99' grams. It is apparent that at about dose Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 95 ^^ I4 0.5 mg. (-0.301 log mg.) the standard deviation reaches a minimal level below 90 12 which it is not further reduced in spite of o so . progressive increases in dosage. On the 70 other hand, with doses of dibenzanthra- cene smaller than 0.5 mg. the standard = 50 i 8 á 30 deviation becomes progressively greater i p 2D ° D as the dosage is decreased. = 6 Relative weights of latent period responses at t4 different dose levels.-The relative weights ., ^• of latent-period observations when equal ------------- numbers of tumorous mice are available 2 for the successive doses of dibenzanthra- cene are shown in table 5. They repre- DOSE IN LOG MILLIGRAMS sent the relative weights when the maxi- FIGURE 9-Latent periods of tumors induced with dibenzanthracene. Solid circles represent mum weight is considered as unity. individual observations plotted to avoid super- T 111111 position of points at given doses. The oblique and horizontal lines show the calculated varia- I5 tion at continuous dose levels. w3 ^ `• dose in the range 1.0 to 8.0 mg. The re- gression in the lower dose region may be represented as linear as shown by the ob- lique line (fig. 10). The equation to this DOSE IN LOG MILLIGRAMS line is: FIGURE 1 0.-Standard deviation of latent periods with successive doses of dibenzanthracene. Circles: Observed standard deviations; Q e =0.935-0.894 (X+0.649) (4) Solid line: Calculated regression line; Curved dash lines: Limits of error of calcu- where v, represents the calculated value lated regression line for P=0.05 TABLE 5.-Relative weights of latent-period observations and numbers of mice required for observations of equal weight at various doses of dibenzanthracene Mice with Total in- Expected Expected Reciprocal Relative tumors re- Ex cted jected mice Dose (in milligrams) mean latent standard of variance weight. quired for inci ence of required for deviation , (1^QO2) (weighting, responses of tumors latent period period (o^) coef&eient)' responses of equal weight equal weight Months Months Number Percent Number 8.0--------------------- - 3.72 0.544 3.38 1.0 10 90 to 100 10 or]! 4.0 --------------------- 3.72 .544 3.38 1.0 10 90 to 100 10 or 11 2.0_____________________ 3.72 .544 3.38 1.0 10 90 to 100 10 or 11 1.0_____________________ 3.72 .544 3.38 1.0 10 90 to 100 10 or 11 0.5_____________________ 3.72 .624 2.57 .760 13 90 to 100 13 or 14 0.25-------------------- - 3.88 .893 1.25 .370 27 90 to 100 27 to 29 0.125------------------- - 4.61 1.16 .743 .220 45 90 to 100 45 to 48 0.062___________________ 5.34 1.43 .489 .145 69 91.2 76 0.031___________________ 6.08 1.70 .346 .102 98 74.8 131 0.0156__________________ 6.81 1.97 .258 .076 132 49.4 267 0.0078__________________ 7.54 2.24 .199 .059 169 24.2 698 0.0039__________________ 8.27 2.51 .159 .047 213 8.3 2,566 0.00195_________________ 9.00 2.78 .129 .038 263 1.9 I Months=Days/30. See text. DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 515 The relative numbers of mice with tumors required to give latent-period re- sponses of equal weight when 10 are used Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 at the level of maximum weight are shown in table 5, also the total numbers required to give the desired numbers with tumors. 11 (See section entitled "Joint Use of Latent G Period and Tumor-Incidence Data.") DEVIATIONS FROM GROUP MEANS IN STANDARD DEVIATION UNITS Mean latent period. —The mean latent FIGURE 12.— Frequency distributions of latent- periods for the various doses of dibenzan- period responses obtained with dibenzanthra- thracene are listed in table 4, colum 5; cene, expressed as deviations from group means. The smoothed curves were drawn by sight. their trend with log dose is shown graph- Solid circles: Data of dose groups 0.5 to ically in figure 11. There is a statistically 8.0 mg.; significant regression of mean latent peri- Open circles: Data of dose groups 0.00195 ods on log dose within the dose range to 0.25 mg. 0.00195 to 0.25 but not within the range The regression of mean latent periods 0.5 to 8.0 mg. The responses within the in the dose range 0.00195 to 0.25 mg. is latter dose limits undoubtedly represent represented by the oblique line (fig. 11), the minimal limiting level of the latent the equation to which is period for dibenzanthracene under the present condition. The average value for Y=4.709-2.427 (X+0.942) (5) the minimal latent period, represented by the horizontal line (fig. 11) is 3.72 where Y represents the estimated value of months (days /30) which is identical with the mean latent period in months (days /30) that found for dibenzanthracene in previ- and X the dosage in log milligrams. ous analyses (1) of the data of Lettinga (10). Frequency distribution of individual latent- period observations. —In order to obtain suffiicient data for an analysis of the fre- quency distribution, it was necessary to combine the data of the various dose i groups. For this purpose the variates were 'expressed as deviations from group means in standard deviation units. Since it was found that the trend of the mean responses could be divided into two com- ponents, the data corresponding to the oblique and horizontal components of the response curve of figure 11 were compiled in separate lots. The frequency distri- DOSE IN LOG MILLIGRAMS bution curve obtained with the combined FIGURE 11. —Dose response curve for dibenzan- data of dose groups 0.00195 to 0.25 mg. is thracene, showing regression of mean latent shown by the broken curve of figure 12. period on log dose. The solid curve shows the distribution for Circles: Observed mean latent periods; Solid line: Calculated regression line; dose groups 0.5 to 8.0 mg. The accumu- Curved dash lines: Limits of error of calcu- lative forms of the frequency curves are lated regression line for P=0.05. shown in like manner in figure 13. 516 JOURNAL OF THE NATIONAL CANCER INSTITUTE steeper than the apparent trend (dash line). The procedure of curve fitting developed by Bliss (7) for application to Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 data on small numbers of animals, or data that are relatively variable about the smoothed trend, involves a series of approx- imations, using for each new approx- 2 imation the preceding computed curve for correcting the probit values and their f U }I02 }3 }4 DEVIATIONS FROM GROUP MEANS IN STANDARD DEVIATION UNITS relative weights. In the present analysis FIGURE 13. —Accumulative frequency curves of a series of such approximations was carried latent-period responses obtained with dibenz- out, and with each new approximation anthracene, expressed as deviations from the corrected probit for dose 0.25 mg. group means. The smoothed curves were drawn by sight. ( -0.602 log mg.) decreased progressively Solid circles: Data of dose groups 0.5 to whereas the corrected values for the other 8.0 mg.; empirical probits became practically iden- Open circles: Data of dose groups 0.00195 tical with the empirical values themselves. to 0.25 mg. Also with each new approximation, the estimated weight of the response to dose The relations between accumulative 0.25 mg., as estimated from the computed frequency in percent, and deviate in stand- regression line, grew smaller, and the ard deviation units, obtained by reference slope of the regression line became steeper, to the smoothed curves of figure 13, were approaching the oblique line shown in employed in determining the expected figure 15. The low corrected probit for accumulative frequency levels indicated dose 0.25 mg when considered together by the calculated lines of figure 9. (See with the discordant result previously men- discussion of similar determinations with tioned for dose 4.0 mg. indicated that the methylcholanthrene. ) Tumor Incidence The corrected totals and the tumor- incidence responses obtained with dibenz- 0. anthracene are given in table 4. The I empirical probits corresponding to the per- centage estimates are also listed. The response to dose 4.0 mg. (0.6 log mg.) is Z considerably out of line.with the trend of the remainder of the data when plotted in probability units (probits) (fig. 14). A DOSE IN LOG MILLIGRAMS similar phenomenon was noted in an FIGURE 14. — Probit-dose relations obtained with dibenzanthracene. earlier analysis (1) of the data of Lettinga Circles: Empirical probits corresponding to (10), and, following the same procedure of observed percentages; Circles with arrows: Estimated probit values analysis, this apparent discordant result corresponding to 100-percent responses; was omitted in making the first approxi- Dash line: Provisional regression line, drawn by sight; mation to the trend of the results. The Solid line: First calculated approximation computed regression line (solid line) is to regression line. DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 517 probit-dose relationship for the higher DOSE IN MILLIGRAMS .0039 .0156 .0625 .25 1.0 4.0 doses of dibenzanthracene might actually be different from that obtained with lower Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 doses. This was further indicated by the findings of Shimkin and Andervont (9) 60 who studied the dose range 0.25 to 3.0 mg. under conditions similar to those of the 40 ^ present experiments. Their results all fell between 90 and 95 percent and were not 20 1^' correlated with dose. Additional evi- dence of erratic results with higher doses -2.4 -1.8 -1.2 -0.6 0 +0.6 of dibenzanthracene is contained in the DOSE IN LOG MILLIGRAMS results of Lettinga (10), previously dis- FIGURE 16.—Dose response curve for dibenzan- thracene, showing relation of tumor incidence cussed in this connection (1), as well as in in percent to log dose. Transformed from data some unpublished data of Shear. 9 In view of figure 15. The dotted extension of the S-shaped curve shows the relations that would of these findings it seemed advisable to con- be expected to hold if the responses to the higher doses had followed the same trend as those of the lower doses. response curve for dibenzanthracene was e recalculated by using only the data of dose _ TTT T groups 0.00195 to 0.125 mg. The curve á 6 is shown in figure 15. The regression equation is: ^ 2 I T=4.919+2.272 (X+1.835) (6) where Y is the expected incidence of tumors in probits and X is the dosage in -2.4 -1.8 -12 -0.6 0 .0.6 log milligrams. The relations of figure 15 DOSE IN LOG MILLIGRAMS are shown in terms of percent in figure 16. FIGURE 15.—Dose response curve for dibenzan- thracene showing the regression of probits on The horizontal line, indicating a break at log dose. about dose 0.25 mg., shows the average Circles: Empirical probits corresponding to observed percentages; level of the erratic responses. Circle with arrow: Estimated probit value The significant dose range for dibenz- for 100-percent response; Arrows: Arrows designate doses that gave anthracene is from about 0.003 mg. 100-percent responses in the region where (dose TD 5) to about 0.084 mg. (dose the results were erratic; Solid line: Calculated regression line for TD 95 ). The break in the probit response dose range 0.00195 to 0.125 mg.; curve does not alter appreciably the use- Curved dash lines: Limits of error of calcu- lated regression line for P=0.05; ful dose range. Horizontal dash line: Average level of Median tumor dose (TD 50).—The dose of erratic responses in dose region 0.25 to 8.0 mg. dibenzanthracene that would be expected to produce tumors in 50 percent of the Sider 0.125 mg. as the upper limit of the sig- injected animals was estimated from the nificant dose range and to determine the present data to be —1.799±0.056 log probit-dose relationship only in the dose mg. The limits of error of the estimate region below this level. Accordingly, the corresponding to P=0.05 are ±0.11. 9 Personal communication. In terms of milligrams, TD 50 is, therefore, 518 JOURNAL OF THE NATIONAL CANCER INSTITUTE +0.0022 The last column shows the total numbers 0.016 - 0.0019'and the limits correspond- p of mice that would have to be injected in + 0.0046 order to obtain the desired numbers with ing to P=0.05 are 0.0035' Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 tumors indicated by column 6. Standard deviation of logarithms of indi- vidual effective doses about log TD 50 .-The TABLE 6.-Relative weights of tumor-incidence ob- servations and numbers of mice required for observa- standard deviation, X, of the logarithms of tions of equal weight at various doses of dibenzan- individual effective doses found from thracene the present studies on dibenzanthracene, Mice Ex- eight- is 0.44 ±0.05. The limits of error for Dose (in milli- pected Ex- pected ing required for equal grams) co'% P=0.05 are ± 0.094. This value does not probit percent eient weight responses differ significantly from tnat for methyl- Number cholanthrene in the preceding section, 8.0 to 0. 125___._ -_6.282 or 90 to 100 greater. 0.40. 0.0625___ -______ 6.353 91.2 0.318 20 0.0312__________ 5.669 74.8 .540 12 Relative weights of tumor-incidence responses 0.0116 ------------- 4.985 49.4 .636 10 0.00781 ------------ 4.301 24.2 .532 12 at different dose levels.--Table 6 gives the 0.00390______ --_ 3.617 8.3 .302 21 0.00195_______ -___ 2.933 1.9 .117 54 expected probits and their equivalents in percent, for the various doses of dibenz- anthracene. The values were computed Specific induction time.-The specific in- from equation 6. The weighting coef- duction time is 6.79±0.45 months (days/ ficients were determined by reference to 30). The limits of error corresponding the tabled values published by Bliss. to P=0.05 are ± 1.06. They represent the relative weights of the The value 6.79 is identical with a previous various percentage responses when the estimate (1) of the specific induction time number of animals is the same in each made from Lettinga's data on dibenz- dose group. The relative numbers of anthracene (10). mice required to give responses of equal Time-tumor frequency relationships at suc- weight when 10 are used at the level of cessive dose levels.-The time-frequency the 50-percent response (at dose TD 50 ) are curves for various doses of dibenzanthra- presented in the last column of table 6. cene are shown in figure 17. They were derived, as described in the section on Joint Use of Latent-Period and Tumor- methylcholanthrene, by joint use of the Incidence Data calculated regression lines for both the Total numbers of injected mice required to latent-period and tumor-incidence types give latent-period responses of equal weight at various dose levels.-The relative numbers of mice with tumors required for obser- vations of equal weight have been dis- cussed in a preceding section. They are listed in table 5. The decreasing inci- dence of tumor-bearing mice with succes- sively smaller doses of dibenzanthracene is shown in column 7 of table 5. The TIME IN MONTHS (OATS /3O) values represented are the expected per- FIGURE 17. -Time frequency curves for successive centages derived from the dose-response doses of dibenzanthracene showing the calcu- relationships developed (figs. 15 and 16). lated incidence of tumors of successive periods. DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 519 of responses as well as the estimated ac- Latent Period cumulative frequency curves of figure 13. Standard deviation.-As in the case of the As pointed out in the previous section, Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 other hydrocarbons, the results with benz- the curves are presented as rough approxi- pyrene show a statistically significant mations only, but they may serve as a correlation between dose and the stand- guide in the planning of future experi- ard deviation of individual latent periods ments under these same conditions. at all doses below a certain level, but a lack of correlation in the higher dose BENZPYRENE range. The spread of the individual The methods of presentation and the latent-period observations is illustrated in purposes of the analyses of benzpyrene figure 18. The standard deviations are data are similar to those in the preceding shown in table 7 and their regression on sections on methylcholanthrene and dibenz- log dose in figure 19. The relatively low anthracene. Table 7 shows the summa- value observed for dose 0.00195 mg. rized results obtained with doses ranging (-2.709 log mg.), was based on only from 0.00195 to 8.0 mg. of the hydro- two tumors and hence does not represent carbon. a satisfactory estimate. The extension TABLE 7.-Summarized results obtained on latent period of tumors and tumor incidence of mice injected with benzpyrene Latent period Tumor incidence Mice Mice Inci- Dose 1 in- jetted with tumors e Mean riod period 2 Stand- Weight and de- of ob- "Corrected deuce servo- via ion z tion 3 total" 3 of tumors Probits ° Weight of ob - serva- tion Mg. Log mg. Number Number Months Months Number Percent 8.0_________________ +0.903 21 20 2.96 0.34 20 20.1 99.5 5 8.558 0.141 4.0___ + .602 19 16 3.02 .28 16 16.0 100.0 '8084 .432 2.0------------------ + .301 19 19 3.09 .39 14.33 19.0 100.0 5 7.626 1.615 1.0_________________ 0 20 18 3.32 .62 5.38 19.0 94.7 6.616 3.838 0.5_________________ - .301 19 19 3.86 .83 3.02 19.0 100.0 5 6.796 7.011 0.25________________ - .602 21 14 4.41 1.15 1.39 21.0 66.7 5.432 11.235 0.125___ - .903 19 15 5.11 1.49 1.00 18.0 83.3 5.966 11.322 0.062_______________ -1.204 20 4 5.79 1.80 .20 19.8 20.2 4.165 12.038 0.031_______________ -1.505 16 0 _ -- 0 53.428 7.326 0.0156______________ -1.806 19 0 ------- ---------- --------- _ -- - -- - 17.1 0 5 3073 5.250 0.0078______________ -2.107 40 0 __________ ____-___-- __--__---_ 34.4 0 5 2.660 5.298 0.00195-------------- -2.709 81 2 8.7 1. 6.0 69.6 2.87 3.102 1.183 1 Volume of solvent used for each injection was 0.25 cc. at all doses. 2 Months=Days/30. 3 See text. 4 See Bliss (5, 7). 5 Estimated probits for 0- and 100-percent responses. 6 Provisional value. of the regression line to this low dose level reached at about 2.0 mg. (0.3 log mg.). must therefore be considered as provi- The average minimal standard deviation sional. The extension is shown in figure was 0.343 months (days/30). 19 as a broken line. The regression equa- Relative weights of latent period observations tion is: at different dose levels.-The relative weights of latent-period observations with benz- v e =0.584-0.771 (X-0.056) (7) pyrene represent the relative weights when where a, is the estimated standard devia- the maximum weight is considered as tion in days/30 and X the dose in log unity and when the number of mice with milligrams. tumors is the same at all dose levels. The The minimal standard deviation was data are given in table 8. 520 JOURNAL OF THE NATIONAL CANCER INSTITUTE TABLE 8.-Relative weights of latent-period observations and numbers of mice required for observations of equal weight at various doses of benzpyrene Total in- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 Expected Relative Mice with Expected Reciprocal tumors th Expected Jetted mice Dose (in milligrams) mean latent standard of variance weight quired for incidence required for period deviation I (1/0 2) oe i cie n t) 2 responses of of tumors latent period (o) coefficient) equal weight responses of equal weight Months Months Number Percent . Number 8.0_____________________ 3.02 0.343 8.50 1.0 10 100.0 10 4.0_____________________ 3.02 .343 8.50 1.0 10 99.7 10 2.0 3.02 .395 6.41 .754 13 98.8 13 1.0 --------------------- - -3.30 .627 2.54 .299 33 96.0 34 0.5________ _____________ 3.89 .859 1.35 .159 63 88.8 71 0.25____________________ 4.47 1.09 .840 .099 101 75.6. 134 0.125___________________ 5.05 1.32 .571 .067 149 56.5 264 0.062 5.63 1.56 .413 .049 204 35.8 570 0.031___________________ 26.21 21.79 2.313 2.037 2270 18.6 21,452 0.0156 ------------------ - 2 6.79 22.02 2.245 2.029 2345 7.8 ______________ 0.0078__________________ 27.37 22.25 2.197 2.023 2435 .7 ______________ 0.0039__________________ 27.95 22.48 2.162 2.019 2526 .1 ______________ 0.00195_________________ 28.54 22.72 2.135 2.016 2625 0 _____ --- _____- I Months=Days/30. 2 Provisional values. UUSE IN MILLIGRAMS .0039 .0156 .0625 .25 10 4.0 o r 4 r 99 S 2 -2.4 -I.6 95 \ 009E IN LOG MILLIGRAMS FIGURE 19.- Standard deviation of latent periods 90 \ \ \ with successive doses of benzpy 5.5. 5. - 60\ Circles: Observed standard deviations; \ \\ Solid line: Calculated regression line; ó 70, \\ \\ \\ Curved dash lines: Limits of error of calcu- a y S0A \ 60\ ` \\\ ^ • \ 40 \ ^^\ lated regression line for P=0.05. of injected mice required to give the desired numbers with tumors (table 8) are dis- cussed later in the section, Joint Use of Latent-Period and Tumor-Incidence Data. -2A -Le -1.2 -0.6 0 ♦0.6 Mean latent period.-In the dose region DOSE IN LOG MILLIGRAMS below 2.0 mg. the mean latent period in- FIGURE 18.- Latent periods of tumors induced with benzpyrene. The solid circles represent creased significantly as the dose was de- individual observations plotted to avoid super- creased. The observed results gave an position of points at given doses. The oblique excellent fit to a straight line when plotted and horizontal lines show the calculated varia- against the logarithm of dose (fig. 20). tion at continuous dose levels. The mean latent period for dose 0.00195 The relative numbers of mice with mg. was based on only two unit observa- tumors required to give latent-period tions and therefore does not represent a responses of equal weight are those which reliable estimate. It is fortuitous that it pertain when 10 are employed at the level falls so close to the computed regression of maximum weight. The total numbers line which has been extended as a broken DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 521 DOSE IN MILLIGRAMS .0039 .0156 .0625 .25 1.0 4.0 Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 1 I DEVIATIONS FROM GROUP MEANS IN STANDARD DEVIATION UNITS FIGURE 21.—Frequency distribution of latent- period responses obtained with benzpyrene, ex- -2.4 -1.6 -1.2 -0.6 0 r0.6 DOSE IN LOG MILLIGRAMS pressed as deviations from group means. The FIGURE 20.—Dose response curve for benzpyrene, circles represent observed frequencies. The showing regression of mean latent period on smoothed curve was drawn by sight. log dose. determined from the combined data of all Circles: Observed mean latent periods; Solid line: Calculated regression line; dose groups. Sufficient data were not Curved dash lines: Limits of error of calcu- available for a separate analysis of the dose lated regression line for P=0.05. groups corresponding to the horizontal component of the response curve. As in line to the low dose region. 1 ° The regres- the previous analyses, combination of the sion equation is: data was made possible by conversion of r=3.826-1.931 (X+0.270) (8) the individual variates to deviations from group means in standard deviation units. where Jr represents the calculated value of The frequency distribution based on the the mean latent period in months (days/ combined data is shown in figure 21, and 30) and X the dose in log milligrams. the accumulative frequency curve in As already noted, the mean latent period figure 22. The curve of figure 22 was used was not correlated with dose in the region (as described in section on methylcholan- 2.0 to 8.0 mg. This is shown by the break threne) for deriving the calculated lines of in the plotted results in figures 18 and 20. figure 18. The average value of the minimal latent period was 3.02 months (days/30). It is shown graphically by the horizontal com- 6D ponent of the response curve of figure 20. Frequency distribution of individual latent- 60 period observations.—As in the case of methylcholanthrene, the frequency dis- 40 tribution of individual latent periods was 10 The standard deviation of the mean latent periods 20 about the calculated regression line (the error of estimate used for purposes of statistical analysis (see footnote 6)) was much less for benzpyrene than for the other hydro- -z -I 0 ♦ I 42- ^3 DEVIATIONS FROM GROUP MEANS IN STANDARD DEVIATION. UNITS carbons. That this result is fortuitous is indicated by the fact that figurei 1, 9, and 18 show a similar degree FIGURE 22.—Accumulative frequency curve of of scatter of the individual latent periods. It was de- latent-period responses obtained with benzpy- cided, therefore, to use as the error of estimate for the benzpyrene data the average of the values found for all rene, expressed as deviations from group means. three materials rather than the lower value calculated The circles represent observed frequencies. from the benzpyrene results alone. The smoothed curve was drawn by sight. 523119-43-6 522 JOURNAL OF THE NATIONAL CANCER INSTITUTE UU^ .0039 .0156 .0625 .25 I.0 4.0 vised (5, 6, 7) for their statistical analysis. Whether the present results are character- istic of benzpyrene or whether they are Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 99. } !9 fortuitous and are to be expected with Ó 690 •" 96 methylcholanthrene and dibenzanthracene 70 60 as well cannot be said at the present time. 30 It is possible, however, that larger numbers . 3 of animals in the various dose groups would E .I yield more consistent percentage responses. The heterogeneity of the benzpyrene -y1 -1.6 -IS DOSE IN L00 MILLIGRAMS -016 0 .0.6 data makes it impossible to draw definite FIGURE 23, —Dose response curve for benzpyrene conclusions regarding the true nature of showing the regression of probits on log dose. the dose response curve for this material Circles: Empirical probits corresponding to and renders useless certain of the analyses observed percentages; that were made of the other hydrocarbons. Circles with arrows: Estimated probit values However, other useful information may be for 0– and 100– percent responses; obtained from the benzpyrene results, and Solid line: Calculated regression line; Curved dash lines: Limits of error of cal- the relation between dose and response culated regression line for P=0.05. may be determined within broad limits of error. Tumor Incidence The curved lines of figure 23 show the The summarized tumor-incidence re- limits of error of the calculated regression sults are presented in table 7. The ob- line corresponding to P=0.05. They were served percentages were converted to determined by methods applicable to the probits for the purpose of statistical analysis of heterogeneous data (7). The analysis. The probit values given in table equation to the regression line is: 7 are graphically represented by the solid circles of figure 23. The solid line of Y - 4.971+1.753 (X+1.013) (9) figure 23 represents the third computed approximation derived by the method of where Y is the calculated probit value and Bliss (7). It will be noted that two of the X the dose in log milligrams. plotted points deviate considerably from the trend of the remainder of the data. The percentage equivalents of the probit These deviations are statistically sig- results are shown in figure 24. As judged nificant, and the plotted points cannot be from the S- shaped percentage curve with- said to fall consistently about the best out considering the limits of possible error, straight line drawn through them. Since the useful dose range for benzpyrene is there is no apparent break or curvature in from about 0.012 mg. (TD5 ) to about 0.875 the trend of the results but rather a wide mg. (TD95 ) . variation of the plotted points about any Median tumor dose (TD 50 ) .—Although single line that can be drawn, the con- subject to relatively large errors of esti- clusion is that there is a significant degree mate, TD 50 can be determined within of heterogeneity in the animal responses. known limits. By appropriate procedures Such results are not infrequently en- (7) log TD50 is found to be —0.996 + 0.16. countered in dose-response investigations The limits of error corresponding to. with drugs, and methods have been de- P=0.05 are f 0.37. Thus, TD 50 is DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 523 COMPARISON OF RESULTS OBTAINED WITH .0039 .0156 .0623 .2S ID THE THREE HYDROCARBONS Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 60 ^' Tumor Incidence GO The probit-dose response curves for methylcholanthrene, dibenzanthracene, and benzpyrene are plotted in figure 25. The curves for methylcholanthrene 2G 4V and dibenzanthracene (disregarding in the latter instance the higher dose -n ♦ -I.6 -l2 -0.6 0 .0.6 range within which response is not cor- DOSE IN LOG MILLIGRAMS related with dose) are fairly close together FIGURE 24.—Dose response curve for benzpyrene showing relation of tumor incidence in percent on the common dose scale, and the slopes to log dose. Transformed from data of figure of the two curves are essentially parallel. 23. The curve for benzpyrene, however, differs +0.046 from the others in both position and slope. 0.101 mg ., the limits of error Analyses were made to determine whether —0.032 g'' these differences were significant or whether for P=0.05 are +0.135 — 0.058 they could have occurred by chance under the condition of the experiment. Joint Use of Latent-Period and Tumor- Incidence Data Comparison of tumor-incidence response curves.—Statistical analyses show that the Total number of injected mice required to differences in slope are not significant as give latent-period responses of equal weight at compared with their errors of estimate. various dose levels.—The total number of This fact indicates that variations in slope mice that must be injected to give the de- of the magnitudes observed could have sired number of tumors (table 8) will de- been due to chance under present condi- pend upon the expected incidence of tumors at each dose level. Although the .0039 .0156 .0625 25 TTr I.0 60 curve of expected percentages in figure 24 cannot be considered as being very ac- curately established, it may be used as an approximation in the absence of better i 6 í information for judging the numbers of r^ animals to be used in future experiments ó ^ í ^ involving the latent period type of re- sponse. The expected percentages are ? 2 given in table 8, as well as the total num- bers of mice required for observations of -2.4 -1.6 -1.2 -U.S u tUe DOSE IN LOG MILLIGRAMS equal weight when 10 are used at the FIGURE 25.—Calculated probit-dose response level of maximum weight. curves for three carcinogenic hydrocarbons Specific induction time.—The specific in- showing their relative positions on an absolute dose scale. duction time for benzpyrene is 5.23+0.59 Solid line: Methylcholanthrene; months (days/30). The limits of error Dash line: Benzpyrene; Dash-dot line: Dibenzanthracene; corresponding to P=0.05 are +1.51 Circles on lines: Means of experimental months. observations. 524 JOURNAL OF THE NATIONAL CANCER INSTITUTE tions. Caution should be exercised, how- fore, the apparent potencies of the respec- ever, in considering the slope to be actu- tive hydrocarbons under the prescribed ally the same for the three materials since conditions of the experiment. Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 the errors of the estimates are relatively The logarithms of the potency ratios large, particularly in the instance of benz- were derived by obtaining the differences pyrene, and it is possible that larger num- between the respective values for log bers of observations might show significant TD 50 • The antilogs of the differences differences not detectable under present represent the potency ratio, which is conditions. 6.3 : 4.8 : 1, in the order dibenzanthracene : In spite of the wide range of error methyIcholanthrene benzpyrene. 11 associated with the benzpyrene data, In terms of relative quantities required to the response curve obtained with this produce the sarrie , biologic response (50- material differs significantly, with respect percent tumors), the ratio is 0.16: 0.21:1. to position, from' those of the other two The difference between the relative poten- compounds which do not differ signifi- cies of methylcholanthrene and dibenz- cantly from each other. anthracene is not statistically significant, Estimation of the relative carcinogenic poten- but both of these materials differ signifi- cies of the threehydrocarbons.-The term "po- cantly from benzpyrene. tency "as used here refers simply to the rela- The magnitude of this difference in tive quantities of the various hydrocarbons potency, however, cannot be stated with required to produce a common biologic certainty in view of the wide limits of response. It is recognized that many error associated with the results with factors would have to be considered in an benzpyrene. ,The values given represent attempt to estimate the absolute potency the best estimates derived from present relationship, e. g., differential solubilities, data. It ha~ not been established that relative rates of elimination from the they represent exact values for the true body, relative rates of detoxification, etc. potency ratios. The potency ratios given represent, there- Latent Period DOSE IN MILLIGRAMS .003' .DISS .OUS .2S 1.1' Comparison on an absolute dose scale (dose in miIHgrams).-The latent-period response Curves for the three hydrocarbons are plotted in figure 26. The curves for methylcholanthrene and dibenzanthra- cene ate essentially parallel, while that for benzpyrene has a somewhat flatter slope. II Shimkln (11) suggested the use oj molecutur weights' 'rather' ·than absolute weights for comparing -2.4 -I.' -1.2 -0.6 .0.6 relative .potencies, "especially if the compared chemicals cess 1N) ,LOG MILLIGRAMS differ considerably in their molecular weights." The FIGURE 26.-Calculated latent period-dose re- materials used in the present investigation do not differ sponse curves for three carcinogenic hydro- appreciably in molecular weights. When their potencies carbons showing their respective positions 'on an absolute dose 'scale. are compared on such a basis, the ratio is 6.8: 5.2 : 1, in the order dibenranihracen» (molecular weight 268): Solid: Methylcholanthrene; Dash: Benzpyrene; methylcholanthrene (molecular weight 268): benzpyrene Dash-dot: Dibenzanthracene. (molecular weight 252). DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 525 Whereas the probit curves (fig. 25) for true when the comparison is made on a methylcholanthrene and dibenzanthracene basis of equal quantities, e. g., milligrams, are close together, the latent-period of the respective materials. Equal quan- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 curves for these materials (fig. 26) are tities of the hydrocarbons, however, did widely separated. The benzpyrene curve not have the same carcinogenic potency as of figure 26 is nearest the dibenzanthra- measured by the tumor-incidence response; cene curve which it crosses in the oblique, benzpyrene acted as if it were significantly and again in the horizontal segment. less potent than the other materials. The horizontal portions of the curves If the latent-period data are considered in the range where response does not alone, there is no point on the abscissa vary with dose are excluded from this and (dose) scale which could be chosen in the following analysis. Tests of statistical preference to all others for comparing the significance show that the variations in relative speeds of action, i. e., the respective slope are no greater than could have latent-period responses, and satisfactory occurred due to chance alone under the comparison could be made only if the conditions of the experiment. (See dis- various response curves were parallel. cussion of similar findings with respect Since the difference between the slopes was to the probit curves on p. 524.) not found to be significant in the present The benzpyrene and dibenzanthracene instance, the curves were compared on a response curves do not differ significantly basis of a common slope (the compound from each other in relative position, but slope). If the differences in slope should be they both differ significantly from the found upon further experimentation to curve for methylcholanthrene. represent real differences, the present con- Estimation of the relative speeds of ac- clusions regarding speeds of action will not tion of the three hydrocarbons.—It has be strictly respresentative, since the relative already been pointed out (1) that latent- speeds of action will vary at different levels period responses are unsatisfactory for of dosage. comparing the relative carcinogenic poten- The average differences between speeds cies of different hydrocarbons 12 since there of action when the materials were consid- is no point on the latent-period response ered in terms of equal quantities were 1.22 curve which is definitely known to have a months (days/30) for methylcholanthrene common significance for different com- and dibenzanthracene, 1.86 months for pounds. Nevertheless, it is of value to methylcholanthrene and benzpyrene, and know the relative speeds of action of dif- 0.64 months for dibenzanthracene and ferent carcinogenic hydrocarbons when benzpyrene. The materials in order of they are administered under similar con- rapidity of action were methylcholan- ditions to similar test animals. threne, dibenzanthracene, and benzpy- The curves of figure 26 indicate that rene. It is obvious from figure 26 that this on an average given quantities of dibenz- order of relative speeds of action applies anthracene and benzpyrene require con- only to the oblique components of the siderably longer periods of time for the respective curves. production of tumors than do similar Although the crossing of the oblique quantities of methylcholanthrene. This is segments of the benzpyrene and dibenzan- thracene curves could be fortuitous, there 12 The latent-period response may, however, be used for determining relative Potencies of different preparation is little doubt that the horizontal segment of a given hydrocarbon. of the dibenzanthracene curve crosses the 526 JOURNAL OF THE NATIONAL CANCER INSTITUTE oblique segment of the benzpyrene curve unit in each instance, the respective dose since the horizontal segment of the latter is scales were converted to carcinogenic significantly lower than that of the former. units by expressing the actual quantities of Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 The relative speeds of action of these two hydrocarbon as fractions or multiples of materials are therefore reversed when the TD B . higher doses are used. The percentage and latent-period re- In view of these findings, it would seem sponse curves for the three hydrocarbons undesirable to make single dose compari- are plotted in figure 27. The lower ab- sons between benzpyrene and dibenzan- scissa scale represents log carcinogenic thracene with respect to the mean latent units, the upper abscissa scale, the relative period. The comparison would have to doses in carcinogenic units. It will be be made over a wide range of doses since noted that the 50 -percent points on the there is one dose, and possibly two, at percentage response curves are superim- which the mean latent period will be ex- posed at one carcinogenic unit. The actly the same for the two materials. At respective points on the latent-period other doses the latent period for one ma- curves corresponding to this same dosage terial may be greater or less than for the represent the specific induction times other, depending upon the magnitude of referred to. the dose employed. When compared on a basis of similar Comparison on a relative dose scale (dose in tumor producing doses, the latent-period carcinogenic units). —Since the quantity of curve for benzpyrene falls much closer to hydrocarbon composing one carcinogenic the methylcholanthrene curve than to the unit (1) was found to differ among the one for dibenzanthracene (fig. 27). This various materials, it would be of interest is in contrast with the findings when ab- to know their relative rates of action when solute dosages were employed (fig. 26). quantities possessing the same number of The slopes of the respective response curves carcinogenic units are compared. Con- were not altered by conversion of the sidering dose TD 50 as one carcinogenic dosages to carcinogenic units. The posi- tions were merely changed so that the respective values of TD 50 coincided. d The analysis of slopes presented in the á i 6 preceding section is applicable to the present series of curves. It may be re- iterated, therefore, that the slopes were not shown to be significantly different. When measured with respect to average position for each curve and on the basis of L06 6202IN06E010 UNITS FIGURE 27. — Calculated response curves for three a common slope, the oblique components carcinogenic hydrocarbons showing incidence of of the response curves for benzpyrene and tumors in percent and latent periods in months methylcholanthrene do not differ signifi- on a relative dose scale (carcinogenic units). cantly from each other. Both of these S- shaped curves: Incidence data; curves, however, differ significantly from Linear curves: Latent-period data; that for dibenzanthracene. The horizon- Solid: Methylcholanthrene; Dash: Benzpyrene; tal components of the respective response Dash-dot: Dibenzanthracene. curves differ significantly among them- DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 527 selves, that for benzpyrene being inter- action while the speed of action of diben- mediate to the others in position. zanthracene was slower by 1.65 and 1.56 Estimation of the relative speeds of ac- months, respectively, when compared with Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 tion of equal carcinogenic units of the the other materials. These results are in three hydrocarbons.—Comparison of the contrast with the differences between min- oblique segments of the curves of figure 27 imal latent periods noted previously. with respect to their average positions and DISCUSSION on the basis of a common slope indicates that tumors produced with dibenzanthra- One of the primary purposes of this study cene appeared on an average 1.49 months was to supply additional data on the nature later than with methylcholanthrene, and of the relationship between dose of sub- 1.22 months later than with benzpyrene. cutaneously injected carcinogenic hydro- Tumors induced with benzpyrene ap- carbons and the local tumor responses which peared 0.27 months later than did those they elicit in test mice. It is necessary to induced with methylcholanthrene. know the nature of the dose-response With doses greater than 16 carcinogenic relationship in order that appropriate units (1.2 log carcinogenic units), the statistical procedures may be employed latent-period response of all materials was in analyses of the biologic results and minimal. In the region of the minimal in testing the significance of differences responses tumors were produced with obtained under various experimental Con- dibenzanthracene 1.24 months later than ditions. In a previous report (1) it was with methylcholanthrene, and 0.7 months pointed out that statistical analysis of later than with benzpyrene. The tumors dose-response data is simplest when the induced with benzpyrene appeared 0.54 relationship between dose and response is months later than did those induced with linear and that statistical methods are methylcholanthrene. available for the analysis of data that fol- If response curves are not parallel, the low this type of relationship. Attempts differences in respective speeds of action were made (1) to find appropriate units for will vary at different levels of dosage, and expressing both dose and response so that as already pointed out it would be difficult the relationship between them would be to select a point of reference on the basis of linear. It was found that certain units latent-period data alone. In conjunction which were applicable in the instance of with the percentage data, however, it most drugs were also applicable in the in- would be possible to compare relative stance of carcinogenic hydrocarbons. speeds of action at doses giving a common The findings of the previous study are percentage response and thus to have substantiated by the present results. They points of reference which possess a common are summarized as follows: (1) The mean significance in the instance of different latent period of tumors appearing in a hydrocarbons. The use of dose TD 50 as group of mice, all of which have received a point of reference for comparing relative the same dose of hydrocarbon, bears a speeds of action has already been described linear relationship to the logarithm of the (specific induction time (1)). If the dose. This relationship is limited, how- present results are compared on a basis of ever, owing to the fact that there is a their specific induction times, methylchol- minimal time below which tumors do not anthrene and benzpyrene differed by only appear with further increases in dose. 0.09 months in their respective speeds of The minimal latent period appears to be 528 JOURNAL OF THE NATIONAL CANCER INSTITUTE characteristic for a given hydrocarbon un- statistically significant and the two may be der constant experimental conditions. (2) exactly the same, or either may be slightly The tumor-incidence responses, in percent, more potent than the other to a degree not Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 follow a symmetrical S- shaped curve pos- detectable in the present experiment. In sessing the characteristics of an integrated any event, it would not be surprising if normal curve when plotted against loga- the order were reversed in a subsequent rithm of dose. Such S- shaped curves may experiment under the same conditions. be converted to a straight line by trans- There seems to be no doubt, however, that forming the percentages to probability larger quantities of benzpyrene were re- units (probits (5), or normal equivalent quired to produce a 50 -percent response deviation (12)) and plotting them against than of either dibenzanthracene or methyl- the logarithm of dose. cholanthrene and that the apparent po- The conclusions regarding the mean tency of benzpyrene is comparatively less latent period-dose relationship are sub- under the conditions of these experiments. stantiated by the results with all three of The order of potency here is the same as the compounds employed. Additional that found by Andervont and Shimkin evidence of a linear relationship between (17) with regard to the induction of pul- the mean latent period and the logarithm monary tumors. Their results showed of dose was obtained by Gottschalk (15) in that dibenzanthracene produced the great- studies with benzpyrene. est number of pulmonary tumors, with The percentage-dose relationship was methylcholanthrene next in potency. Benz- confirmed by the results obtained with pyrene produced only one-tenth as many methylcholanthrene and dibenzanthra- pulmonary tumors as did methylcholan- cene, but the data obtained with benz- threne and only one-sixteenth as many pyrene proved to be heterogeneous and as dibenzanthracene when the materials not strictly definable by the relations of a were injected subcutaneously in equal normal curve. It is possible, however, quantities (17, table 3). This order of that percentage responses to benzpyrene relative potencies of the three compounds based on larger numbers of mice will give is apparently contradictory to that usu- more homogeneous results. (See data of ally given in the literature for the materials Leiter and Shear (16).) when subcutaneously injected. However, A second objective of this study was to it should be pointed out that, to our compare the relative carcinogenic poten- knowledge, no previous comparative stud- cies and the relative speeds of action of ies have been made in which the lower methylcholanthrene, dibenzanthracene, doses were used. Under the conditions and benzpyrene. Attempts were not made of the present experiments doses of dibenz- to estimate absolute potencies but rather anthracene greater than about 0.1 mg. the relative actions, or the "apparent poten- might be expected to give aberrant per- cies, of the three materials- when adminis- centage results which, in the absence of tered under identical test conditions. For a complete dose response curve, might the conditions of the present experiments, be interpreted as indicating a lower car- the carcinogenic potencies were in the cinogenic potency for dibenzanthracene order dibenzanthracene, methylcholan- (fig. 25). threne, benzpyrene; the ratio was 6.3:4.8:1. The most rapidly acting of the three The potency difference between dibenzan- compounds was methylcholanthrene, irre- thracene and methylcholanthrene was not specti've of whether comparisons were DOSE RESPONSE WITH THREE CARCINOGENIC HYDROCARBONS 529 made on an absolute dose basis (in terms other hand doses smaller than TD 50 pro- of milligrams) or in terms of equal tumor- duce tumors in less than half of the inducing doses (carcinogenic units). By injected mice, and the range of variation Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 using the latter comparison, the speeds of in the latent periods is so great that the action were in the order methylcholan- numbers of mice required for reliable threne, benzpyrene, dibenzahthracene. group responses are too large to be When comparisons were made on an practical. The dose range within which absolute dose basis, the conclusions regard- the latent period might be effectively used ing the respective speeds of action of is therefore from about dose TD 50 to the dibenzanthracene and benzpyrene de- maximum effective dose. pended on the dose level at which the Another point of interest is the apparent comparisons were made. common significance of the maximum In addition to the primary objectives of effective dose of all three hydrocarbons. the experiments other useful information The maximum effective dose was defined was obtained. For example, with all by Fieser (14) as the dose that just produces three hydrocarbons there was a significant the minimal latent-period response. Fieser correlation between the standard deviation noted that at this dosage the percentage of individual latent periods and the loga- response "approaches 100 percent." In rithm of dose. The range of variation of previous work (1), the present authors individual latent periods was strikingly questioned the use of the maximum effec- large, especially in the region of the lower tive dose for comparing the relative poten- doses (figs. 1, 9, and 18). In the present cies of different carcinogenic agents be- experiments the . various dose groups cause of the lack of proof that this criterion were made up by the addition of animals possessed the same significance, with re- over a period of about 3 months, and it is spect to potency, for different agents. possible that a wider range has been However, the present findings indicate observed under these conditions than that it does have a common significance, would have been obtained if the sampling at least for the three hydrocarbons used. had been made from a single lot of Reference to figure 27 reveals that the animals. The present results are probably dose opposite the point of junction of the more representative, however, of the oblique and horizontal components of the variations to be expected in the population latent-period response curve (the maxi- as a whole. The increasing range of mum effective dose) corresponds to the variation of the latent period as the dose point on - the corresponding percentage is decreased, coupled with the coincident curve at which, for practical purposes, the progressive decrease in the percentage of latter just reaches 100 percent. Actually mice with tumors, limits the usefulness of the approach to 100 percent is asymptotic, the latent-period response in quantitative and the expression "just reaches 100 per- studies to a very narrow dose range. For cent" is theoretically meaningless. How- example, above the maximum effective ever, as Foster (18) points out, the dose dose, that which just produces the mini- which gives a 99-percent response may for mal latent period (14), there is no correla- practical purposes be considered as that tion between dose and response, and the which just produces 100 percent. latent period cannot be used as a criterion The percentages corresponding to the of quantitative biologic activity. On the maximum effective doses were calculated 530 JOURNAL OF THE NATIONAL CANCER INSTITUTE from the probit regression equations to be which just gives the maximum (99 -percent) 99.8 and 97.8 for methylcholanthrene, and tumor incidence (19, fig. 8). benzpyrene, respectively. The dibenzan- Downloaded from https://academic.oup.com/jnci/article-abstract/3/5/503/954849 by university of winnipeg user on 10 November 2019 thracene percentage response curve did SUMMARY not continue to 100 percent (fig. 16), but the results became erratic with doses The quantitative relations between dose greater than 0.125 mg. If the trend of and tumor response are studied for the the responses at the lower doses is con- following carcinogenic hydrocarbons and tinued, however (see dotted extension of dosages: 20 -methylcholanthrene in serial dibenzanthracene percentage curves of twofold doses of from 0.00024 to 1.0 mg., figures 16 and 27), the percentage re- and 1, 2, 5, 6 -dibenzanthracene and 3, sponse corresponding to the maximum. 4 -benzpyrene both in serial twofold doses effective dose is 99.8. The average per- ranging from 0.00195 to 8.0 mg. centage response corresponding to the break Both the tumor-incidence and latent- in the latent period curve is 99.1; the differ- period types of response are analyzed in ences between the values for the various their relations to dose, by using appro- hydrocarbons are much less than the priate biomathematical procedures. errors associated with the respective esti- The relative carcinogenic potencies and mates. It is clear, then, that the dose the relative speeds of action of the three which just produces the minimum latent- materials are determined for the condi- period response is also that which just tions of the experiment. produces the maximum percentage re- Useful relations between dose and re- sponse and that the maximum effective sponse are presented in graphic form, and dose (based on latent periods) may be con- some implications of the various findings sidered as equivalent to about dose TD 99 . are discussed. For the three hydrocarbons under con- The computed values of certain of the sideration, the maximum effective dose most useful data are as follows (for limits is approximately 16 times the dose that of error of the various estimates, see text) : produces 50 -percent tumors (TD5o). Minimal latent period (average, in months Although the relationship between tumor- (days /30)): dibenzanthracene 3.72, meth- incidence response and maximum effective cholanthrene 2.48, and benzpyrene 3.02. dose was essentially the same for the three Median tumor dose (TD bo : dibenzan- )) materials in the present investigation, thracene 0.016 mg., methylcholanthrene further study is necessary before the maxi- 0.021 mg., and benzpyrene 0.101 mg. 95- mum effective dose (based on latent- Percent tumor dose (TD95 ): dibenzan- period data alone) can be considered as a thracene 0.084 mg., methylcholanthrene satisfactory criterion for the comparison of 0.096 mg., and benzpyrene 08.75 mg. 5- carcinogenic hydrocarbons in general. Percent tumor dose (TD 5 dibenzanthra- ): This criterion is definitely not applicable to cene 0.003 mg., methylcholanthrene 0.0045 another type of tumor-producing agent, mg., and benzpyrene 0.012 mg. 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