Assessing the effects of interventions using longitudinal data with samples subject to selection

Consider an uncontrolled study in which subjects are selected to start a new intervention because one or more previous measurements of a variable are within a particular range. Our aim is to use the repeated values obtained prior and subsequent to the start of the intervention to assess the effects of its introduction. However, because selection is based on the same variable as is being used to assess efficacy, regression to the mean will confound the interpretation of the results. In this paper, we present a likelihood-based method for evaluating the effects of the intervention using the repeated measurements while adjusting for the effects of the selection. The method uses a linear model to describe each subject's pattern of responses before and after the start of the new intervention. Additionally, it assumes that the effect of starting the new intervention on an individual's intercept and slope is the same for all subjects. However, no distributional assumption is made about the pattern of the linear model across subjects, thus making it particularly appropriate for phase I/II studies when patient histories on those not selected for the study are not available.