A novel estimand to adjust for rescue treatment in randomized clinical trials.

The interpretation of randomized clinical trial results is often complicated by intercurrent events. For instance, rescue medication is sometimes given to patients in response to worsening of their disease, either in addition to the randomized treatment or in its place. The use of such medication complicates the interpretation of the intention-to-treat analysis. In view of this, we propose a novel estimand defined as the intention-to-treat effect that would have been observed, had patients on the active arm been switched to rescue medication if and only if they would have been switched when randomized to control. This enables us to disentangle the treatment effect from the effect of rescue medication on a patient's outcome, while tempering the strong extrapolations that are typically needed when inferring what the intention-to-treat effect would have been in the absence of rescue medication. We propose a novel inverse probability weighting method for estimating this effect in settings where the decision to initiate rescue medication is made at one prespecified time point. This estimator relies on specific untestable assumptions, in view of which we propose a sensitivity analysis. We use the method for the analysis of a clinical trial conducted by Janssen Pharmaceuticals, in which patients with type 2 diabetes mellitus can switch to rescue medication for ethical reasons. Monte Carlo simulations confirm that the proposed estimator is unbiased in moderate sample sizes.

Doubly robust and multiple-imputation-based generalized estimating equations.

Generalized estimating equations (GEE), proposed by Liang and Zeger (1986), provide a popular method to analyze correlated non-Gaussian data. When data are incomplete, the GEE method suffers from its frequentist nature and inferences under this method are valid only under the strong assumption that the missing data are missing completely at random. When response data are missing at random, two modifications of GEE can be considered, based on inverse-probability weighting or on multiple imputation. The weighted GEE (WGEE) method involves weighting observations by the inverse of their probability of being observed. Imputation methods involve filling in missing observations with values predicted by an assumed imputation model, multiple times. The so-called doubly robust (DR) methods involve both a model for the weights and a predictive model for the missing observations given the observed ones. To yield consistent estimates, WGEE needs correct specification of the dropout model while imputation-based methodology needs a correctly specified imputation model. DR methods need correct specification of either the weight or the predictive model, but not necessarily both. Focusing on incomplete binary repeated measures, we study the relative performance of the singly robust and doubly robust versions of GEE in a variety of correctly and incorrectly specified models using simulation studies. Data from a clinical trial in onychomycosis further illustrate the method.