RESTRICTION AS A METHOD FOR REDUCING BIAS IN THE ESTIMATION OF DIRECTEFFECTS

The direct effect of a treatment on some outcome is that part of the t reatment's effect not referred through a specified covariate intermedi ate on the pathway between treatment and outcome, Such direct effects are often of primary interest in a data analysis. Unfortunately, stand ard methods of analysis (for example, stratification or modelling) do not, in general, produce consistent estimates of direct effects whethe r or not the covariate is 'controlled', Robins and co-authors have pro posed two methods for estimation of direct effects applicable when rel iable information is available on the covariate. We propose a third ap proach for reducing bias: data restriction. By restricting the analysi s to strata of the data in which the effect of treatment on the covari ate is small, we can (under certain assumptions) reduce bias in estima ting treatment's direct effect. We discuss these points with reference to difference and ratio measures of treatment effect. The approach wi ll sometimes be applicable even with an unmeasured or poorly measured covariate, We illustrate these points with data from an observational study of the effect of hormone replacement therapy on breast cancer. ( C) 1998 John Wiley & Sons, Ltd.