The spontaneous occurrence of cancer in humans, or induced occurrence in laboratory animals, reflects the interplay of many variables. Also multivariate in nature are the factors influencing survival times or remission times of individuals with cancer, whether treated or left untreated. The multivariate statistical problems which arise may relate to identifying individually important variables which may be causative, making prognoses of survival or other predictions for cancer patients with a specified multivariate vector and seeking to identify optimal therapeutic procedures for such patients. Data available for such analyses may be prospective or retrospective in nature, and for the prospective case will generally involve incomplete observation. Recent developments in mathematical models and statistical approaches for relating response to multivariate regressors, specifically models involving hazard functions and generalized logistic regression, open the way to handling such problems, and it is the effective use of such models and approaches that I plan to study. In instances these approaches may bear modification as, say, using a classification approach when data are abundant but variables to be studied few in number. I anticipate that tie-ins with other problems of cancer epidemiology will develop. Related, or variant methods, may be appropriate in the study of potential environmental carcinogens. Methods for safety evaluation of such agents represent a preventive epidemiology approach.