Semi-/non-parametric statistical inference in survival analysis

Estimating subject-specific survival function under accelerated failure time model. The semi-parametric accelerated failure time model relates the logarithm of the survival time linearly to its covariates without specifying a parametric distribution for the error term. In this article, we are interested in utilizing this model to predict the survival function and its related quantities for future subjects with a given set of covariates. Specifically, we derive the large-sample distribution for the subject-specific cumulative hazard function estimate. We then propose a simple resampling technique to construct point-wise confidence intervals and simultaneous bands for the corresponding survival function and its quantile function over a properly selected time interval.;Identifying subjects benefiting most from the new treatment in a comparative clinical study. An important follow-up question arises after comparative clinical studies that include the collection of a set of baseline covariates or the predictors: How do we use these covariates to identify future patients who would benefit most/least from the new treatment compared to the standard treatment? To answer this question, we present "point" and "interval" estimates for the set of covariate or predictor vectors associated with a certain degree of benefit from the new treatment compared to that from the standard treatment. These estimates can be easily displayed on a two-dimensional plane, even for high-dimensional covariate vectors. The simple numerical and graphical procedures we present provide useful tools for patient management and/or the design of future studies, both key issues in pharmacogenomics studies with genetic markers. The new proposals are illustrated with data from chronic hepatitis C and breast cancer clinical trials.;One- and two-sample nonparametric inference procedures in the presence of dependent censoring. In survival analysis, the event time T is often subject to dependent censorship. Without assuming a parametric model between the failure and censoring times, the parameter theta of interest, for example, the survival function of T, is generally not identifiable. On the other hand, the collection O of all attainable values for theta may be well-defined. In this article, we present non-parametric inference procedures for S2 in the presence of a mixture of dependent and independent censoring variables. By varying the criteria of classifying censoring to the dependent or independent category, our proposals can be quite useful for the so-called sensitivity analysis of censored failure times. The case that the failure time is subject to dependent interval censorship is also discussed in this article. The new proposals are illustrated with data from two clinical studies on HIV-related diseases. (Abstract shortened by UMI.)...