Confidence bands for survival curves from outcome-dependent stratified samples

We consider the construction of confidence bands for survival curves under the outcome-dependent stratified sampling. A main challenge of this design is that data are a biased dependent sample due to stratification and sampling without replacement. Most literature on regression approximates this design by Bernoulli sampling but variance is generally overestimated. Even with this approximation, the limiting distribution of the inverse probability weighted Kaplan-Meier estimator involves a general Gaussian process, and hence quantiles of its supremum is not analytically available. In this paper, we provide a rigorous asymptotic theory for the weighted Kaplan-Meier estimator accounting for dependence in the sample. We propose the novel hybrid method to both simulate and bootstrap parts of the limiting process to compute confidence bands with asymptotically correct coverage probability. Simulation study indicates that the proposed bands are appropriate for practical use. A Wilms tumor example is presented.