Clinical trials have many different aspects to them, and here three topics will be explored: Bayesian sensitivity analysis in survival models, ROC methods in the presence of verification bias, and non-parametric adjustment of covariates in randomized clinical trial with and without missing data. The aim of the first paper is to develop several Bayesian influence measures to assess the influence of the prior, the sampling distribution, and individual observations in survival analysis with the presence of missing covariate data and describe these changes in a modified likelihood model (the perturbation model). We construct a Bayesian perturbation manifold to the perturbation model and calculate its associated geometric quantities and influence measures based on several objective functions to quantify the degree of various perturbations to statistical models. We carry out several simulation studies and analyze a real data set to illustrate the finite sample performance of our Bayesian influence method. While clinical trials concerned with survival track how long people will live given that they have the disease, some trials are concerned with using screeners to predict disease in the first place. Chronic obstructive pulmonary disease (COPD) affects 5% of the adult population in the United States, but a general screener has not been evaluated for the disease at a large scale. In this paper a COPD screener is evaluated using an innovative application of sampling weights. With these sampling weights, which help us adjust for verification bias, we explore the different variables to use in the screener. The optimal variable on the pocket screener was forced expiratory volume in 1 second as compared to peak expiratory flow. While screeners can help predict disease, mainly clinical trials are designed to evaluate treatments that cure disease or improve health outcomes. Non-parametric adjustment of covariates is an attractive methodology in the regulatory setting as it requires few assumptions. We develop methodology to estimate the treatment effect in a longitudinal logistic randomized trial after non-parametrically adjusting for covariates. We also develop methodology to estimate treatment effect when the outcome is ordinal (with more than two groups) instead of binary, when there is missing data among the baseline covariates, and when there are multiple treatment groups to be evaluated. This methodology and it’s extensions are applied to a data set evaluating Cushing’s disease and another data set evaluating multiple doses of a neurological disorder medication.