On fitting Cox's proportional hazards models to survey data

Binder (1992) proposed a method of fitting Cox's proportional hazards model s to survey data with complex sampling designs. He defined the regression p arameter of interest as the solution to the partial likelihood score equati on based on all the data values of the survey population under study, and d eveloped heuristically a procedure to estimate the regression parameter and the corresponding variance. In this paper, we provide a formal justificati on of Binder's method. Furthermore, we present an alternative approach whic h regards the survey population as a random sample from an infinite univers e and accounts for this randomness in the statistical inference. Under the alternative approach, the regression parameter retains its original interpr etation as the log hazard ratio, and the statistical conclusion applies to other populations. The related problem of survival function estimation is a lso studied.