Methods for a longitudinal quantitative outcome with a multivariate Gaussian distribution multi-dimensionally censored by therapeutic intervention.

In longitudinal studies, a quantitative outcome (such as blood pressure) may be altered during follow-up by the administration of a non-randomized, non-trial intervention (such as anti-hypertensive medication) that may seriously bias the study results. Current methods mainly address this issue for cross-sectional studies. For longitudinal data, the current methods are either restricted to a specific longitudinal data structure or are valid only under special circumstances. We propose two new methods for estimation of covariate effects on the underlying (untreated) general longitudinal outcomes: a single imputation method employing a modified expectation-maximization (EM)-type algorithm and a multiple imputation (MI) method utilizing a modified Monte Carlo EM-MI algorithm. Each method can be implemented as one-step, two-step, and full-iteration algorithms. They combine the advantages of the current statistical methods while reducing their restrictive assumptions and generalizing them to realistic scenarios. The proposed methods replace intractable numerical integration of a multi-dimensionally censored MVN posterior distribution with a simplified, sufficiently accurate approximation. It is particularly attractive when outcomes reach a plateau after intervention due to various reasons. Methods are studied via simulation and applied to data from the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications study of treatment for type 1 diabetes. Methods proved to be robust to high dimensions, large amounts of censored data, low within-subject correlation, and when subjects receive non-trial intervention to treat the underlying condition only (with high Y), or for treatment in the majority of subjects (with high Y) in combination with prevention for a small fraction of subjects (with normal Y).