Estimation of the odds ratio in a proportional odds model with censored time-lagged outcome in a randomized clinical trial

In many randomized clinical trials of therapeutics for COVID-19, the primary outcome is an ordinal categorical variable, and interest focuses on the odds ratio (active agent vs. control) under the assumption of a proportional odds model. Although at the final analysis the outcome will be determined for all subjects, at an interim analysis, the status of some participants may not yet be determined, e.g., because ascertainment of the outcome may not be possible until some pre-specified follow-up time. Accordingly, the outcome from these subjects can be viewed as censored. A valid interim analysis can be based on data only from those subjects with full follow up; however, this approach is inefficient, as it does not exploit additional information that may be available on those for whom the outcome is not yet available at the time of the interim analysis. Appealing to the theory of semiparametrics, we propose an estimator for the odds ratio in a proportional odds model with censored, time-lagged categorical outcome that incorporates additional baseline and time-dependent covariate information and demonstrate that it can result in considerable gains in efficiency relative to simpler approaches. A byproduct of the approach is a covariate-adjusted estimator for the odds ratio based on the full data that would be available at a final analysis.