Adjusting for treatment effects in studies of quantitative traits: antihypertensive therapy and systolic blood pressure

A population-based study of a quantitative trait may be seriously compromised when the trait is subject to the effects of a treatment. For example, in a typical study of quantitative blood pressure (BP) 15 per cent or more of middle-aged subjects may take antihypertensive treatment. Without appropriate correction, this can lead to substantial shrinkage in the estimated effect of aetiological determinants of scientific interest and a marked reduction in statistical power. Correction relies upon imputation, in treated subjects, of the underlying BP from the observed BP having invoked one or more assumptions about the bioclinical setting. There is a range of different assumptions that may be made, and a number of different analytical models that may be used. In this paper, we motivate an approach based on a censored normal regression model and compare it with a range of other methods that are currently used or advocated. We compare these methods in simulated data sets and assess the estimation bias and the loss of power that ensue when treatment effects are not appropriately addressed. We also apply the same methods to real data and demonstrate a pattern of behaviour that is consistent with that in the simulation studies. Although all approaches to analysis are necessarily approximations, we conclude that two of the adjustment methods appear to perform well across a range of realistic settings. These are: (1) the addition of a sensible constant to the observed BP in treated subjects; and (2) the censored normal regression model. A third, non-parametric, method based on averaging ordered residuals may also be advocated in some settings. On the other hand, three approaches that are used relatively commonly are fundamentally flawed and should not be used at all. These are: (i) ignoring the problem altogether and analysing observed BP in treated subjects as if it was underlying BP; (ii) fitting a conventional regression model with treatment as a binary covariate; and (iii) excluding treated subjects from the analysis. Given that the more effective methods are straightforward to implement, there is no argument for undertaking a flawed analysis that wastes power and results in excessive bias.