Semiparametric Regression Inference for Tumor Progression in Cross-sectional Cancer Studies

In cancer studies, to develop better treatment and screening programs, it is of great interest to understand the natural history of the disease and what factors affect its progression. Methods for assessing covariate effects on the joint response of age and stage of cancer at diagnosis are our main focus. We address this question through a semiparametric regression model for stage-specific cancer incidence. Such data structure requires a joint model for correlated survival and binary data. Constructed through a series of semiparametric regression models with time-dependent covariates, our model can be represented as a transformation model induced by a complex non-proportional frailty. We develop maximum likelihood estimation and inference procedures. The methodology is illustrated by simulation studies and real prostate cancer data from the Surveillance, Epidemiology and End Results (SEER) program.