Models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters. Estimates of the parameters can be obtained by means of iteratively reweighted least squares (IRLS). When the events of interest follow the Poisson distribution, the IRLS algorithm is equivalent to using the method of scoring to obtain maximum likelihood (ML) estimates. The general Poisson regression models include log-linear, quasilinear and intrinsically nonlinear models. The approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model. Standard statistical packages that support IRLS can then be used to obtain ML estimates, their asymptotic covariance matrix, and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space. Applications of these methods to epidemiologic follow-up studies with the data organized into a life-table type of format are discussed. The method is illustrated by using a nonlinear model, derived from the multistage theory of carcinogenesis, to analyze lung cancer death rates among British physicians who were regular cigarette smokers.

Summarizing relative risk estimates across strata of a covariate is commonly done in comparative epidemiologic studies of incidence or mortality. Conventional Mantel-Haenszel and rate standardization techniques used for this purpose are strictly suitable only when there is no interaction between relative risk and the covariate, and tests for interaction typically are limited to examination for departures from linearity. Poisson regression modeling offers an alternative technique which can be used for summarizing relative risk and for evaluating complex interactions with covariates. A more general application of Poisson regression is its utility in modeling disease rates according to postulated etiologic mechanisms of exposures or according to disease expression characteristics in the population. The applications of Poisson regression analysis to problems of summarizing relative risk and disease rate modeling are illustrated with examples of cancer incidence and mortality data, including an example of a nonlinear model predicted by the multistage theory of carcinogenesis.

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We employed cytochalasin B to block cytokinesis in human lymphocytes exposed to 220 kV X-radiation. When 3 micrograms/ml of cytochalasin B was used, most cells escaped the block whereas at 6 micrograms/ml greater than 90% of the mitogen-responsive cells became binucleate. Using the higher concentration of cytochalasin B, we observed a linear-quadratic (i.e. Y = gamma + alpha D + beta D2) dose dependency for X-ray-induced micronuclei (MN) in preparations from three donors. When dose-response parameters were compared with those for total acentrics scored in first division metaphases, we observed no significant differences in estimates of the background (gamma) or linear (alpha) coefficients, but a 2-fold reduction in the beta coefficient for MN. We interpret our data as providing evidence that radiation-induced micronuclei are derived from acentric fragments (AF); that virtually all AF are recovered as MN in binucleate interphase daughter cells at low radiation doses; and that for our data, the relative proportion of AF that will be observed as independent MN decreases by a constant factor of approximately one-half as radiation dose increases.