Stratified Data

In clinical studies when survival changes with important prognostic factors, stratification on different level of those factors is often done either at the design stage to ensure treatment balance in each stratum, or at the analysis stage. The ordinary logrank test, ignoring strata effect, is conservative and is biased when there is treatment imbalance in each prognostic subgroup. The stratified logrank test, on the other hand, is unbiased and retains high efficiency as long as the number of strata is small. However, when the number of strata gets large, the stratified test can become very inefficient unless there is a large strata effect. Shih and Fay (1999) have developed a versatile test based on the DPT framework which combines the advantages of both the ordinary and stratified logrank tests. That is, when the number of observations in each stratum is large or when the within-strata variance is small relative to the between-strata variance, the test weights each stratum approximately equally and performs like the stratified logrank test. Conversely, when the within-strata variance is large relative to the between-strata variance, the test weights each stratum proportional to the stratum size and performs like the ordinary logrank test. For cases between these two extremes, the versatile test is a compromise between the ordinary logrank and stratified logrank tests. The attractive feature of the proposed method is that we do not need to choose in advance whether to do a stratified analysis or not and hope that the correct decision was made; the method automatically does this primarily based on the estimated within- and between-strata variances.

The DPT setup is the same as above, but now we choose an appropriate estimator for C,, i = 1, . . . , n, when n >1. Once chosen, this estimator is inserted in (1) to calculate the scores Cj and then the test statistic (2).

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