Simple adjustments for randomized trials with nonrandomly missing or censored outcomes arising from informative covariates

In randomized trials with missing or censored outcomes, standard maximum likelihood estimates of the effect of intervention on outcome are based on the assumption that the missing-data mechanism is ignorable. This assumption is violated if there is an unobserved baseline covariate that is informative, namely a baseline covariate associated with both outcome and the probability that the outcome is missing or censored. Incorporating informative covariates in the analysis has the desirable result of ameliorating the violation of this assumption. Although this idea of including informative covariates is recognized in the statistics literature, it is not appreciated in the literature on randomized trials. Moreover, to our knowledge, there has been no discussion on how to incorporate informative covariates into a general likelihood-based analysis with partially missing outcomes to estimate the quantities of interest. Our contribution is a simple likelihood-based approach for using informative covariates to estimate the effect of intervention on a partially missing outcome in a randomized trial. The first step is to create a propensity-to-be-missing score for each randomization group and divide the scores into a small number of strata based on quantiles. The second step is to compute stratum-specific estimates of outcome derived from a likelihood-analysis conditional on the informative covariates, so that the missing-data mechanism is ignorable. The third step is to average the stratum-specific estimates and compute the estimated effect of interventionon outcome. We discuss the computations for univariate, survival, and longitudinal outcomes, and present an application involving a randomized study of dual versus triple combinations of HIV-1 reverse transcriptase inhibitors.