In HIV-1 clinical trials the interest is often to compare how well treatments suppress the HIV-1 RNA viral load. The current practice in statistical analysis of such trials is to define a single ad hoc composite event which combines information about both the viral load suppression and the subsequent viral rebound, and then analyze the data using standard univariate survival analysis techniques. The main weakness of this approach is that the results of the analysis can be easily influenced by minor details in the definition of the composite event. We propose a straightforward alternative endpoint based on the probability of being suppressed over time, and suggest that treatment differences be summarized using the restricted mean time a patient spends in the state of viral suppression. A nonparametric analysis is based on methods for multiple endpoint studies. We demonstrate the utility of our analytic strategy using a recent therapeutic trial, in which the protocol specified a primary analysis using a composite endpoint approach.