A Bayesian framework for intent-to-treat analysis with missing data

In longitudinal clinical trials, one analysis of interest is an intention-to-treat analysis, which groups subjects according to the randomized treatment regardless of whether they stayed on that treatment or not. When in addition to going off the randomized treatment subjects may also drop out of the study and be lost to follow-up, it is unclear what an intention-to-treat analysis should be. If measurements are made after treatment drop-out on a random sample of subjects who drop the treatment, then Hogan and Laird (1996, Biometrics 52, 1002-1017) present a random effects model, well suited to this type of analysis, which fits a two-piece linear spline to the data with the knot at the time the assigned treatment is dropped. This article presents a Bayesian approach to fitting a similar two-piece linear spline model and shows how the model can be applied to data that have no off-treatment observations.