Analysis and Sensitivity Analysis for Incomplete Longitudinal Data

Abstract

After the key paper of Rubin (1976) who established incomplete data as a field of study within the domain of statistics, a large amount of research output has been devoted to the problem of missing data. Within the methodological development we can distinguish between the parametric school, based on the likelihood and Bayesian frameworks, and a semi-parametric school, including estimating equations ideas. Even though there is a noticeable divergence between these various lines of thinking, researchers agree that no single modeling approach can overcome the limitation of not having access to the missing data. All parties, that is, academia, industry, and regulatory authorities, emphasize the need for sensitivity analysis, whereas there is less agreement on the kind of sensitivity analysis. An important condition to put forward a particular method as a feasible method within a sensitivity analysis, is the availability of trustworthy and easy-to-use software. In this thesis, we have shown it is unfortunate that there has been so much emphasis on simple methods, such as complete case analysis or last observation carried forward, which at least require the missingness mechanism to be MCAR. These simple methods have been compared to direct-likelihood analysis, which uses all available information without the need of additional data manipulation and are valid under the less restrictive and more realistic assumption of MAR missingness. Moreover, in case inferences are obtained within the likelihood or Bayesian framework, there is no need to model the missingness process. Consequently, linear mixed models (Verbeke and Molenberghs, 2000) or generalized linear mixed models (Molenberghs and Verbeke, 2005), within the random-effects model family, can be used for respectively Gaussian and non-Gaussian incomplete longitudinal outcomes. These methods are as simple to conduct as it would be in contexts where data are complete. Up to here, it has been made clear that the simple ad hoc methods, which have been in common use for a long time, actually belong in the museum of statistics, and the primary analysis should consist of methods which assume the missing data to be MAR. On the other hand though, one can hardly ever rule out the possibility of missing data to be MNAR, which implies that the need may exist to consider MNAR models. Therefore, we have provided an overview of existing MNAR models, with the main focus on the models proposed by Diggle and Kenward (1994) for Gaussian outcomes and by Baker, Rosenberger and DerSimonian (BRD, 1992) for binary outcomes. An important feature of statistical modelling in the incomplete data setting is that the quality of the fit to the observed data does not render the appropriateness of the implied structure governing the unobserved data. This point is independent of the MNAR route taken, whether a parametric model or a semi-parametric approach is chosen. MNAR models are based on assumptions regarding the unobserved outcomes which are not verifiable from the available, observed data. Moreover, in this thesis we have proven that the empirical distinction between MNAR and MAR is not possible, in the sense that the fit of each MNAR model to a set of observed data can be reproduced exactly by an MAR counterpart. …. A further route for sensitivity analysis is to consider pattern-mixture models as a complement to selection models or as shown in this thesis, use so-called latent-class mixture models…..