Clinical trial AIN503/A5217 investigates whether a period of early treatment with antiretroviral therapy might lower the viral setpoint in subjects recently infected with HIV-1. We consider two statistical issues. First, even under the null hypothesis control arm subjects are more likely than treatment arm subjects to be missing final outcome data because of disease progression. The analysis must adjust for this missing data, or it may be unacceptably biased. Second, comparing outcomes between treatment and control arms at identical times post-randomization gives different information than comparing outcomes at the same amount of time off-therapy, as measured post-randomization. This may make interpretation of results problematic. We formulate the null hypothesis of the study as exchangeability under a time-shift between arms, which we call "time delay" between the study arms. This captures clinically relevant information, and allows us to formalize a two-stage hypothesis test in which stage one is a comparison between arms at identical times post-randomization, and stage two is a comparison between arms at identical times off-therapy, as measured post-randomization. Importantly, within this framework we can show that the two-stage test can be adjusted for the missing data using a simple worst-rank substitution.