Supplementing the Intent-to-Treat Analysis: Accounting for Covariates Observed Postrandomization in Clinical Trials

Abstract

A problem that arises frequently in the analysis of clinical trials is accounting for covariates observed postrandomization. Two examples are patient compliance measured through pill counts and the dose of a concomitant medication. Typically these are measured concurrently with the primary endpoint at the regularly scheduled follow-ups during the course of the study. To account for these effects, the confounders are sometimes introduced as time-dependent covariates into the statistical model. But there are conceptual and statistical difficulties with this approach. In this article we adopt the view that because the confounder is observed postrandomization, it must be considered as an endpoint in its own right. A seemingly unrelated regression (SUR) model is proposed to relate the two sets of repeated measures to important explanatory variables, and a vector autoregressive moving average (ARMA) time series model is used to characterize the disturbance terms within and across the two series. This accommodates the evolving relationship between the two variables and results in a parsimonious structure in the joint covariance matrix. Maximum likelihood estimation is applied using a Fisher scoring algorithm. Inference in this model is then performed by considering hypotheses on the primary endpoint conditionally on some behavior for the confounder. For example, if the two treatment groups had received an equivalent amount of concomitant medication, is there a significant difference in the primary endpoint? The methodology is illustrated with an example.

Key Words:

• Conditional inference
• Confounding
• Longitudinal data
• Maximum likelihood
• Vector ARMA model