Analysis and Sensitivity Analysis for Incomplete Data from Clinical Studies

Geert Molenberghs, Professor of Biostatistics, Center for Statistics, Limburgs Universitair Centru, Belgium

Over the last couple of decades a variety of models to analyze incomplete multivariate and longitudinal data have been proposed, many of which allowing for the missingness to be not at random (MNAR), in the sense that the unobserved measurements influence the process governing missingness, in addition to influences coming from observed measurements and/or covariates. The fundamental problems implied by such models, to which we refer as sensitivity to unverifiable modeling assumptions, has, in turn, sparked off various strands of research in what is now termed sensitivity analysis. The nature of sensitivity originates from the fact that an MNAR model is not fully verifiable from the data, rendering the empirical distinction between MNAR and random missingness (MAR), where only covariates and observed outcomes influence missingness, hard or even impossible, unless one is prepared to accept the posited MNAR model in an unquestioning way. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Of course, such a pair of models will produce different predictions of the unobserved outcomes, given the observed ones. Theoretical considerations are supplemented with practical illustrations.

References

Creemers, A., Hens, N., Aerts, M., Molenberghs, G., Verbeke, G., and Kenward, M.G. (2011). Generalized shared-parameter models and missingness at random. Statistical Modeling 11, 279-311.

Jansen, I., Hens, N., Molenberghs, G., Aerts, M., Verbeke, G., and Kenward, M.G. (2006). The nature of sensitivity in missing not at random models. Computational Statistics and Data Analysis 50, 830-858.

Molenberghs, G., Beunckens, C., Sotto, C., and Kenward, M.G. (2008) Every missing not at random model has got a missing at random counterpart with equal fit. Journal of the Royal Statistical Society, Series B 70, 371-388.

Verbeke, G. and Molenberghs, G. (2011). Arbitrariness of models for augmented and coarse data, with emphasis on incomplete-data and random-effects models. Statistical Modelling 11, 391-419.