Large scale simultaneous testing procedures & semiparametric interval censored data modeling

The first part of this dissertation is concerned with large scale multiple testing. When drawing large scale simultaneous inferences, such as in genomics and imaging problems, multiplicity adjustments should be made in order to avoid inflated type I error. Numerous methods are available to estimate the proportion of true null hypotheses, among a large number of hypotheses tested. Many methods implicitly assume that the proportion of true null hypotheses is close to 1. However, in practice, mid-range values are frequently encountered and many of the widely-used methods tend to produce highly variable or biased estimates. As a remedy in such situations, we propose a hierarchical Bayesian model that produces an estimator of the proportion of true null hypotheses that exhibits considerably less bias and is more stable. Furthermore, when data are obtained from heterogeneous sources, we may encounter a natural stratification occurred among the hypotheses to be tested. A natural way to deal with the stratification is to conduct the testing separately within each stratum. However, by doing so, there is no automatic way to choose the desired false discover rate level within a stratum. We provide the stratified testing procedure where we control the overall false discovery rate at a pre-chosen level and minimize the false negative rate.;The second half of this thesis is dedicated to developing a semi-parametric modeling approach for three types of interval censored data frequently encountered in cancer trials or AIDS studies. Many existing modeling methods are computationally intensive and usually require numerous assumptions that could be unrealistic or difficult to verify in practice. We propose a novel, flexible and computationally efficient modeling strategy based on pseudo-observations obtained via the leave-one-out jackknife. The pseudo-observations constructed through nonparametric maximum likelihood estimators of the survival function are employed as outcomes in an equivalent, yet simpler regression model that produces consistent covariate effect estimates. Hence, instead of operating in the interval censored data context, the problem is translated into the realm of generalized linear models, where numerous options are available. Moreover, the methods developed are not limited to these settings and have broader applicability. We discuss the usefulness of the proposed modeling approach via extensive simulation studies and practical examples.