Noninferiority testing with censoring when the event rate is low

The PREDICT TB trial tests noninferiority of an abbreviated treatment regimen (arm A) vs a conventional treatment regimen (arm C). Treatment trials of drug-susceptible tuberculosis are expected to have low event rates (ie, relapse probabilities around 3-5%). We examine the question of what is the "best" way to test for noninferiority in a setting with low event rates. In a series of simulations supported by theoretical arguments, we examine operating characteristics of five tests, including normal approximation, exact, and simulation-based tests. Two of these tests are constructed from Kaplan-Meier based-estimators, which account for variable follow-up time (and those lost to follow-up). We evaluate the effect of loss to follow-up via simulations. We also examine the results of the five tests on a data set similar to PREDICT TB, the REMoxTB trial. We find that the normal approximation tests perform well, albeit with small type I error rate inflation. We also find that the Kaplan-Meier methods generally have larger power than the other tests, especially when there is between 10-30% loss to follow-up.