The simulation, fitting, and testing of a stochastic cellular proliferation model.
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Biomedical subjects
Publications and source records attributed to D G Hoel.
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Formation of the BCR-ABL chromosomal translocation t(9;22)(q34;q11) is essential to the genesis of chronic myeloid leukemia (CML). An interest in the dose-response of radiation induced CML therefore leads naturally to an interest in the dose-response of BCR-ABL formation. To predict the BCR-ABL dose-response to low-linear energy transfer (LET) ionizing radiation, three models valid over three different dose ranges are examined: the first for doses greater than 80 Gy, the second for doses less than 5 Gy and the third for doses greater than 2 Gy. The first of the models, due to Holley and Chatterjee, ignores the accidental binary eurejoining of DNA double-strand break (DSB) free ends ('eurejoining' refers to the accidental restitution of DSB free ends with their own proper mates). As a result, the model is valid only in the limit of high doses. The second model is derived directly from cytogenetic data. This model has the attractive feature that it implicitly accounts for single-track effects at low doses. The third model, based on the Sax-Markov binary eurejoining/misrejoining (SMBE) algorithm, does not account for single-track effects and is therefore limited to moderate doses greater than approximately 2 Gy. Comparing the second model to lifetime excess CML risks expected after 1 Gy, estimates of the number of hematopoietic stem cells capable of causing CML were obtained for male and female atomic bomb survivors in Hiroshima and Nagasaki. The stem cell number estimates lie in the range of 5 x 10(7)-3 x 10(8) cells.
The ED01 study is an experiment conducted by the National Center for Toxicological Research (NCTR) of the FDA in which over 24,000 mice were exposed to the known carcinogen 2-acetylaminofluorene. The details of the experiment and analysis of the results by NCTR are documented in Staffa and Mehlman (1979). The analysis by the ED01 task force of the Society of Toxicology is in disagreement with NCTR on several issues, and is reported in Fundam. Appl. Toxicol. 1:26-128. The results given in this paper are from a separate analysis aimed at adequately and parsimoniously representing the functional relationship of dose and time to the carcinogenic response. A very general non-parametric approach is applied to the data on sacrificed animals, which eliminates any complications due to a change in protocol and avoids the difficulties in combining sacrifice and non-sacrifice data. It is shown that for either liver neoplasms or bladder neoplasms as the toxicological endpoint, any model which has a factorable hazard function (one that can be factored into the product of a function of dose exclusively and a function of time exclusively) is too simplistic to accurately describe the response over the entire experimental range of dose and time. The lack of fit of the liver neoplasm data to a time-dose product model is due to data at the highest time (month 33). If these data are excluded then a factorable hazard function fits the data well, with the function of dose following a J-shaped curve and the function of time being either a simple power of time or a polynomial in time. For a power of time, the resultant probability distribution is Weibull over time with dose affecting the scale parameter, and this result is consistent with the empirical equation of Druckrey (1967). Both of the functional forms described fit the data significantly better than the previously suggested Hartley-Sielken model which utilized polynomials in both dose and time. The lack of fit of bladder neoplasms to a model with a factorable hazard function is not due to just the data at month 33 or the data at months 24 and 33 combined. Unfortunately, from the viewpoint of model fitting, the response of bladder neoplasms is fairly insensitive to changes in time and dose, except at the high extremes. This leaves only a small number of observations which are actually very useful in model validation and comparison, which means that one could only hope to discriminate between gross differences of fit.(ABSTRACT TRUNCATED AT 400 WORDS)
The ED01 study is a large-scale experiment in which mice were exposed to the known carcinogen 2-acetylaminofluorene (2-AAF). The dosing was continuous until time of death for most of the mice. However, for some mice, dosing was terminated at specified intervals prior to sacrifice time. Exploratory model fitting of the continuous dosing data of sacrificed mice using liver neoplasms as the endpoint was conducted by Brown and Hoel (1982). They report that the multistage model of Armitage and Doll (1954) fits the data moderately well, however a much improved fit with fewer parameters is attainable by a modified multistage model. These two models, with parameter estimates obtained from the data on continuous dosing, are referred to in this paper as Model 1 and Model 2, respectively. Models 1 and 2 are extended to provide for termination of dosing prior to time of sacrifice. The resultant equations are used to predict cancer responses in the serial dosing part of the ED01 study, and then are compared to the actual observed tumor frequencies. The objective is to evaluate the change in cancer risk over time after dosing is terminated, and to establish which stages in the multistage process are affected by dose. The predictive capabilities of the two models are compared and contrasted. Model 1, which presumes four stages of which two are affected by dose, predicts only moderately well and is inconclusive as to which two of the stages are the ones affected. Model 2, which differs from the multistage model by using a "J-shaped" curve instead of a polynomial for the dose metameter, provides an improvement over Model 1.(ABSTRACT TRUNCATED AT 250 WORDS)
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This paper discusses some of the statistical and biological problems that are likely to be encountered when an indirect or ecological approach is used to assess the possible public health impact of general population exposures to environmental agents. For purposes of illustration, the potential association between various site-specific cancer mortality rates and chloroform levels in public drinking water supplies was considered. The analyses that were performed demonstrated that, for the data sets under consideration, there were some definite associations between chloroform levels and cancer mortality for specific sites such as the rectum-intestine and bladder. However, the marked extent to which these results were dependent on (1) the weighting scheme adopted in the analysis, (2) the presumed appropriateness of the data, and (3) the characteristics of the statistical model was also clearly illustrated. Because of these dependencies the quantitative, causal interpretation of results generated from an indirect study would appear to be a very tenuous and questionable practice in most instances.
This paper considers certain statistical aspects of the problem of among-strain differences in cancer susceptibilities and how these differences may affect the design of toxicity assays. First, in order to investigate the magnitude of within-study, between-strain differences in tumor induction, the data of Innes et al. (1969) were examined. It was found that although there was a very high overall association between mouse strains with respect to the induction of hepatomas, several compounds showed evidence of strain-to-strain variability. Next, a number of long-term carcinogenicity studies with DDT were considered, and among-strain differences in cancer susceptibility for this compound were noted. Finally, it was shown that if susceptible subgroups do exist and certain simplifying assumptions are made, then in many cases tumor increases can be detected more readily by using several inbred mouse strains for study rather than a single outbread stock.
A number of animal carcinogenesis experiments have demonstrated that the time from initial exposure to first detection of tumors increases with decreasing dose. This observation has led to some speculation that at very low doses tumors would take so long to develop that life would end before tumors appeared. We show that the apparent increase in tumor development time can be easily seen as nothing more than a manifestation of the mathematical fact that decreasing the incidence necessarily increases the first time-to-tumor. No physical increase in tumor growth time need be postulated to explain the observations. Existing methods of low-dose risk extrapolation implicitly account for the increase in time-to-tumor statistics insofar as they account for the decrease in tumor incidence.