A threshold causal model for clinical trials with departures from intended treatment

Abstract

Randomized clinical trials often are planned to study a specific intervention. However, the collection of data on treatment actually received often reveals variable levels of treatment exposure (or 'dose') across subjects, due to non-compliance or other reasons. This paper presents a new method, using such 'dose' data as well as control group responses, to assess a causal dose-response relationship. The specific model utilizes a threshold function and incorporates a random effect term to allow for heterogeneous treatment responses among subjects. Further modelling of the random effects allows for reduction of error variance and control for potential confounders. The threshold dose is estimated using a residual variance criterion based on a transformed model. Estimates of standard errors and confidence intervals are obtained using a bootstrap procedure. The method is applied to data from an AIDS clinical trial. A simulation study demonstrates the adequacy of the threshold estimates for particular sample sizes and error variances. The limitations of this essentially exploratory method, as well as some possible extensions, are discussed.