Pattern-mixture sensitivity analysis in longitudinaltrials with drop-out

Abstract

The occurrence of missing data due to protocol deviations is inevitable in clinical trials. When missing data exist, analyses rely on assumptions about the behaviour of the individuals after dropping out. As a result, sensitivity analysis, which is now advocated by regulatory bodies, should be performed to explore the robustness of the inference to those assumptions. These assumptions should be relevant to the estimand of the study and be practically accessible by all parties. The aim of this document is twofold: to assess the statistical validity of a new method for sensitivity analysis, and apply this method to a published Alzheimer’s study. At the beginning of the thesis, a description of the Alzheimer’s study and issues with missing data encountered therein, take place. This study was mainly set up to investigate the effect rosiglitazone, as an adjunct therapy in Alzheimer’s patients. Two different doses of the drug were compared to placebo. The study suffered from a moderate degree of missing data in each treatment arm. The thesis proceeds with a critique on the per-protocol and intention-to-treat estimands, and revisits their meaning when missing data occur. Two new estimands are introduced, which are particularly amenable to studies with missing data. They are termed de-jure and de-facto. Following that, the main methods for dealing with missing data are introduced, with a particular emphasis on multiple imputation, and how it can easily incorporate missing not at random (MNAR) analyses. A thorough presentation of the new methodology is given. This is built around a set of assumptions, that reflect possible distributional behaviours of the subjects after protocol deviation. The assumptions are Randomised-treatment Missing at Random (MAR), Jump to Reference, Last Mean Carried Forward, Copy Increments in Reference, and Copy Reference. Estimation and inference is achieved via multiple imputation, and it is shown how the predictive distribution of the imputation model can be constructed from parameters borrowed from an MAR model and manipulated in a pattern-mixture model approach, to obtain the five assumptions for the 4 unobserved component of groups of individuals. A number of simulations whose aim is to explore the statistical properties of the new method, are carried out. The simulated datasets, which are based on the parameters from the Alzheimer’s study, focus on the estimator bias, the size and power of the methods, the bias of the variance estimator, and coverage. The results obtained from the simulations show the method has sensible properties; no bias for the estimator was detectable and the sizes and power of the methods agreed closely with their theoretical equivalents. The main result however, pertains to Rubin’s variance estimator, which proves to appropriately reflect the loss of information from missing data. It is therefore argued, it is the right estimator to use in this setting. The results from the application of the proposed method on the Alzheimer’s dataset are presented in tables. Inferences from the sensitivity analysis assumptions were consistent with those from the original MAR analyses. The comparison between high dose rosiglitazone and placebo did not show any evidence in favour of the treatment under any sensitivity assumption. Some evidence of treatment difference existed when the low dose treatment was compared to placebo. This finding though, should be interpreted with caution, as the differences were obtained from analyses not subjected to the rigorous inferential process that was used in the Harringtons study. It was further argued, this finding might have been due to chance, and it was not replicated in a different study.