#### Title

#### Abstract

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is mediated by a given intermediate variable (the indirect effect of the treatment), and the component that is not mediated by that intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Under the assumption of no-unmeasured confounders for treatment and the intermediate variable, Robins & Greenland (1992) define an individual direct effect as the counterfactual effect of a treatment on an outcome when the intermediate variable is set at the value it would have had if the individual had not been treated, and the population direct effect as the mean of these individual counterfactual direct effects. In this article we first generalize this definition of a direct effect. Given a user-supplied model for the population direct effect of treatment actions, possibly conditional on a user-supplied subset of the baseline co-variables, we propose inverse probability of treatment weighted estimators, likelihood-based estimators, and double robust inverse probability of treatment weighted estimators of the unknown parameters of this model. The inverse probability of treatment weighted estimator corresponds with a weighted regression and can thus be implemented with standard software.

#### Disciplines

Biostatistics | Epidemiology | Longitudinal Data Analysis and Time Series | Statistical Methodology | Statistical Models | Statistical Theory

#### Suggested Citation

van der Laan, Mark J. and Petersen, Maya L., "Direct Effect Models" (August 2005). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 187.

https://biostats.bepress.com/ucbbiostat/paper187

#### Included in

Biostatistics Commons, Epidemiology Commons, Longitudinal Data Analysis and Time Series Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons