Informative priors and sensitivity analysis for longitudinal clinical trials with dropout
*Joseph W. Hogan, Brown University 

Keywords: Missing data, repeated measures, Bayesian analysis, Model robustness

Missing data due to dropout continues to be a pervasive problem in the conduct and analysis of longitudinal studies. There exist a wide variety of model-based and ad-hoc methods for handling missing data, but many of these rely on one or more untestable assumptions, and deliver only a point estimate and confidence interval corresponding to the assumptions.

A more principled approach is to conduct a sensitivity analysis that allows consumers of the final inferences to understand the effect of assumptions on substantive conclusions of a study. In fact, this is a major recommendation of a recent report issued by the National Academies of Science, entitled 'Prevention and Treatment of Missing Data in Clinical Trials.'

We describe a sensitivity analysis framework in which untestable assumptions are encoded by one or more parameters, and both point estimates and confidence intervals are depicted as functions of these parameters. An important feature of our approach is that the 'sensitivity parameters' correspond strictly to untestable assumptions about the missing data mechanism, and therefore cannot be estimated from the data.

An added feature of our approach is that (informative) prior distributions can be placed on the sensitivity parameters to reflect strength of belief in assumptions like missing at random. We use this feature to demonstrate that all analyses involving incomplete data are inherently Bayesian in nature, in that they rely on purely subjective assumptions about the distribution of missing responses.

These ideas are illustrated with two detailed examples. The first is an analysis of a randomized trial of growth hormone for increasing muscle strength in the elderly; the second is a behavioral intervention trial to reduce smoking rates among substance abusers. Extensions to observational studies will be briefly discussed.

The examples in this presentation are taken from the book Missing Data in Longitudinal Studies, by Michael J Daniels and Joseph W Hogan (Chapman & Hall/CRC Press, 2008).