Regression modeling with missing outcomes : competing risks and longitudinal data

Missing data are a common occurrence in medical studies. In regression modeling, missing outcomes limit our capability to draw inferences about the covariate effects of medical interest, which are those describing the distribution of the entire set of planned outcomes. In addition to losing precision, the validity of any method used to draw inferences from the observed data will require that some assumption about the mechanism leading to missing outcomes holds. Rubin (1976, Biometrika, 63:581-592) called the missingness mechanism MAR (for “missing at random”) if the probability of an outcome being missing does not depend on missing outcomes when conditioning on the observed data, and MNAR (for “missing not at random”) otherwise. This distinction has important implications regarding the modeling requirements to draw valid inferences from the available data, but generally it is not possible to assess from these data whether the missingness mechanism is MAR or MNAR. Hence, sensitivity analyses should be routinely performed to assess the robustness of inferences to assumptions about the missingness mechanism. In the field of incomplete multivariate data, in which the outcomes are gathered in a vector for which some components may be missing, MAR methods are widely available and increasingly used, and several MNAR modeling strategies have also been proposed. On the other hand, although some sensitivity analysis methodology has been developed, this is still an active area of research. The first aim of this dissertation was to develop a sensitivity analysis approach for continuous longitudinal data with drop-outs, that is, continuous outcomes that are ordered in time and completely observed for each individual up to a certain time-point, at which the individual drops-out so that all the subsequent outcomes are missing. The proposed approach consists in assessing the inferences obtained across a family of MNAR pattern-mixture models indexed by a so-called sensitivity parameter that quantifies the departure from MAR. The approach was prompted by a randomized clinical trial investigating the benefits of a treatment for sleep-maintenance insomnia, from which 22% of the individuals had dropped-out before the study end. The second aim was to build on the existing theory for incomplete multivariate data to develop methods for competing risks data with missing causes of failure. The competing risks model is an extension of the standard survival analysis model in which failures from different causes are distinguished. Strategies for modeling competing risks functionals, such as the cause-specific hazards (CSH) and the cumulative incidence function (CIF), generally assume that the cause of failure is known for all patients, but this is not always the case. Some methods for regression with missing causes under the MAR assumption have already been proposed, especially for semi-parametric modeling of the CSH. But other useful models have received little attention, and MNAR modeling and sensitivity analysis approaches have never been considered in this setting. We propose a general framework for semi-parametric regression modeling of the CIF under MAR using inverse probability weighting and multiple imputation ideas. Also under MAR, we propose a direct likelihood approach for parametric regression modeling of the CSH and the CIF. Furthermore, we consider MNAR pattern-mixture models in the context of sensitivity analyses. In the competing risks literature, a starting point for methodological developments for handling missing causes was a stage II breast cancer randomized clinical trial in which 23% of the deceased women had missing cause of death. We use these data to illustrate the practical value of the proposed approaches.