Semiparametric Regression Inference for Age-Stage at Diagnosis Relationship in Cancer Studies
*Chen Hu, Department of Biostatistics, University of Michigan 
Alex Tsodikov, Department of Biostatistics, University of Michigan 

Keywords: Survival Analysis, Semiparametric Regression Model, Cancer Studies

In cancer studies, it is of great interest to understand the relationship between disease progression (from non-metastasis to metastasis) and time-to-diagnosis, as well as what factors affect such relationship. In many observational studies and cancer registry datasets, age and stage at cancer diagnosis are often jointly observed but contain only partial information of interest due to cross-sectional data structure. Joint modeling such composite response of survival and binary outcome may provide more efficient results than using either component alone. We address this problem through a semiparametric regression model for stage-specific cancer incidence. Constructed through a series of Cox relative risk models with time-dependent covariates, our model can be represented as a transformation model induced by a complex non-proportional frailty. We propose an estimating equation based estimation approach and a nonparametric maximum likelihood estimation approach for such transformation models. The estimation procedure and asymptotic variance of proposed estimator can be easily implemented and obtained numerically. The methodology is illustrated by Monte Carlo simulation studies and real prostate cancer incidence data from the Surveillance, Epidemiology and End Results (SEER) program.