This Is AuburnElectronic Theses and Dissertations

Survival, Count and Discrete Mixture Models for Analyzing Tumor Latency and Multiplicity in Carcinogenesis and Chemoprevention




Zhang, Rong

Type of Degree



Mathematics and Statistics


Since the chemicals, including Bisphenol A (BPA), Bis(2-ethylhexyl) phthalate (DEHP), have been reported for potential carcinogens separately and genistein is an controversial chemopreventive isoflavone, animal experiment was designed and conducted for solving the following questions of interest: i) Can the compounds like BPA, DEHP and their combinations accelerate the carcinogenic process? ii) If yes, which one has significant stronger effect? iii) Does genistein have chemopreventive effect on those rats? And iv) What are the patterns when genistein was fed as a diet interacted with those treated compounds together? Tumor latency, burden and multiplicity, analyzed univariately, were three issues of interests. The first two were survival time, and were analyzed by survivor functions estimated by nonparametric methods as well as parametrical survival regression analysis. Nonparametric methods did not detect any difference across ten groups while Weibull model fitted both of them better than Proportional hazards model. Tumor multiplicity was count data and analyzed by Poisson regression, negative binomial regression and their corresponding Zero-inflated models due to the problems of over-dispersion and excess zeros. The zero-inflated Poisson model reflected the multiplicity best yet negative binomial distribution fitted the data best among the four models. The survival analysis and generalized linear modeling indicated that BPA, DEHP and their combinations decreased the time to first tumor but did not have significant effects on tumor burden and multiplicity. Genistein did not show any chemopreventive effect in this study no matter solo or combined with other carcinogens. In application, this study indicates that early exposure to plastic consumer products which contain BPA and DEHP may increase the risk of breast cancer, while drinking soymilk may not help.