Extending Marginal Structural Models through Local, Penalized, and Additive Learning

Daniel Rubin, Division of Biostatistics, School of Public Health, University of California, Berkeley
Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

Marginal structural models (MSMs) allow one to form causal inferences from data, by specifying a relationship between a treatment and the marginal distribution of a corresponding counterfactual outcome. Following their introduction in Robins (1997), MSMs have typically been fit after assuming a semiparametric model, and then estimating a finite dimensional parameter. van der Laan and Dudoit (2003) proposed to instead view MSM fitting not as a task of semiparametric parameter estimation, but of nonparametric function approximation. They introduced a class of causal effect estimators based on mapping loss functions suitable for the unavailable counterfactual data to those suitable for the data actually observed, and then applying what has been known in nonparametric statistics as empirical risk minimization, or global learning.

However, it has long been recognized in the statistical learning community that global learning is only one of several paradigms for estimator construction. Building upon van der Laan and Dudoit's work, we show how marginal structural models for causal effects can be extended through the alternative techniques of local, penalized, and additive learning. We discuss how these new methods can often be implemented by simply adding observation weights to existing algorithms, demonstrate the gains made possible by these extended MSMs through simulation results, and conclude that nonparametric function estimation methods can be fruitfully applied for making causal inferences.