Over the last few decades, shape constrained methods have increasingly gathered importance in statistical inference as attractive alternatives to traditional nonparametric methods which often require tuning parameters and restrictive smoothness assumptions. This talk focuses on application of shape-constraints like unimodality and log-concavity in comparing the outcome of two HIV vaccine trials. To this end, we develop shape-constrained tests of stochastic dominance, and shape-constrained plug-in estimator of the Hellinger distance between two densities. Our techniques are either tuning parameter free, or rely on only one tuning parameter, but their performance is comparable with nonparametric methods. We also show that our tests and estimators have desirable asymptotic properties.