In some clinical trials, the primary outcome of interest may only be measured in a subset of subjects where the subset is identified by a post-randomization event. For example, in prophylactic vaccination studies a primary objective may be to assess the effect of a vaccine on an outcome that is measured only in subjects who become infected with disease. Formulating causal effects in subgroups selected by post-randomization events can be challenging due to the potential of selection bias compounded by other limitations of clinical trials where certain subjects do not have outcomes measured. Principal stratification is a common approach that can be used to tackle selection bias in this context; however, causal treatment effects using principal stratification cannot be identified from the observed data with standard assumptions made in randomized trials. Currently published methods using principal stratification to identify the average causal effect of treatment in subsets selected after randomization do adjust for such unmeasured selection bias, but they are limited by various assumptions, including that the treatment or vaccine is not harmful (i.e., monotonicity) and that missing outcome data are missing completely at random (MCAR). In this dissertation, we describe a non-parametric approach to assess an average causal effect (ACE) of treatment in a subset selected post-randomization that resolves some limitations of current causal approaches. We first derive bounds of the ACE without assuming monotonicity and develop testing procedures for these bounds. We further propose estimation and testing procedures that utilize logistic regression models to reflect intermediate degrees of selective effects and describe applying these models to assess the ACE through a sensitivity analysis. Simulation is used to demonstrate the value of our methods. Finally, we develop a robust multiple imputation based approach to estimate and test the ACE using principal stratification in the presence of missing outcome data when MCAR is untenable and an ignorable missing data mechanism is plausible. We compare our approach with other recently published methods to handle ignorable missing data in this context via simulation. Throughout, we use two HIV vaccination trials to motivate our work and apply the new methods.