This thesis is comprised of three parts. The first part (Chapter 2) develops nonparametric statistical inference methods for partial area under ROC curves (PAUC) that can be applied to genomic studies. ROC curves are used to analyze the performance of a diagnostic test while the areas or partial areas under ROC curves are used to judge how accurately the test results can discriminate between two groups (for example, diseased and non-diseased groups).The third part of this thesis (Chapter 4) presents a novel weighted nonparametric method for estimating ROC curves. We model the probability of the disease status for a given test result by logistic regression models and we connect logistic regression and ROC curves by a weighted nonparametric method. The ROC curves fitted by this method are smoother than ROC curves produced purely by traditional nonparametric methods. More importantly, the method can be used to correct for verification bias.The second part (Chapter 3) develops methods for PAUC when results of the applicable gold standard test are incomplete, situations also referred to as data with incomplete verification or with verification bias. The true (disease) status is the 'gold standard' against which a given diagnostic test should be measured. However, there are many diseases for which the definitive diagnosis is expensive or difficult to obtain for an entire sample. We have developed a method based on the nonparametric approach for estimating partial area and its variance and tested the method by simulation studies under various situations.