Fitting Cox's proportional hazards model using grouped survival data

Cox's proportional hazard model is often fit to grouped survival data (i.e., occurrence and exposure data over various specified time-intervals and covariate bins), as opposed to continuous data. The practical limits to using such data for inference in the Cox model are investigated. A large sample theory, allowing the bins and time-intervals to shrink as the sample size increase, is developed. It turns out that the usual estimator of the regression parameter is asymptotically biased under optimal rates of convergence. The asymptotic bias is found, and an assessment of the effect on inference is given.