Nonparametric methods for inference after variable selection, comparisons of survival distributions, and random effects meta-analysis, and reporting of subgroup analyses

The chapters of this thesis focus on developing novel statistical methodologies to address issues arising from clinical trials and other association studies. In the first chapter, we develop testing and interval estimation methods for parameters reflecting the marginal association between the selected covariates and response variable, based on the same data set used for variable selection. We provide theoretical justification for the proposed methods, present results to guide their implementation, use simulations to assess and compare their performance to a sample-splitting approach, and illustrate the methods with data from a recent AIDS study. The second chapter addresses two-group comparisons with a time-to-event endpoint when sample sizes are small and censoring rates may differ between the two groups. We propose two approximate tests, based on first imputing survival and censoring times and then applying permutation methods, that have good properties over a range of settings. Furthermore, the new approaches can be used to obtain point and interval estimates of the parameter characterizing the treatment difference in a semi-parametric accelerated failure model. The proposed methods are shown to yield confidence intervals with better coverage than the approach in Jin et al. (2003) in small sample sizes settings, and are illustrated with a cancer dataset. In the third chapter we consider meta-analysis methods in which the random effect distribution of treatment effects is completely unspecified. We propose a non-parametric interval estimation procedure for the percentiles of this distribution. Regardless of the number of studies involved, the new proposal is valid provided that the individual study sample sizes are large. The approach is illustrated with the data from a recent meta analysis investigating the treatment-related toxicity from erythropiesis-stimulating agents. Subgroup analyses can provide useful information about the heterogeneity of treatment differences among the levels of baseline characteristics. However, misinterpretation can often occur when the methods and results are not clearly reported. The last chapter outlines and illustrates the challenges in conducting and reporting subgroup analyses, summarizes the quality of subgroup analysis reporting over one year period in the New England Journal of Medicine, and proposed guidelines for subgroup analysis reporting.