The estimation of the unknown parameters in the stratified Cox's proportional hazard model is a typical example of the trade-off between bias and precision. The stratified partial likelihood estimator is unbiased when the number of strata is large but suffer from being unstable when many strata are non-informative about the unknown parameters. The estimator obtained by ignoring the heterogeneity among strata, on the other hand, increases the precision of estimates although pays the price for being biased. An estimating procedure, based on the asymptotic properties of the above two estimators, serving to compromise between bias and precision is proposed. Two examples in a radiosurgery for brain metastases study provide some interesting demonstration of such applications.
