An information criterion for marginal structural models

Abstract

Marginal structural models were developed as a semiparametric alternative to the G-computation formula to estimate causal effects of exposures. In practice, these models are often specified using parametric regression models. As such, the usual conventions regarding regression model specification apply. This paper outlines strategies for marginal structural model specification and considerations for the functional form of the exposure metric in the final structural model. We propose a quasi-likelihood information criterion adapted from use in generalized estimating equations. We evaluate the properties of our proposed information criterion using a limited simulation study. We illustrate our approach using two empirical examples. In the first example, we use data from a randomized breastfeeding promotion trial to estimate the effect of breastfeeding duration on infant weight at 1 year. In the second example, we use data from two prospective cohorts studies to estimate the effect of highly active antiretroviral therapy on CD4 count in an observational cohort of HIV-infected men and women. The marginal structural model specified should reflect the scientific question being addressed but can also assist in exploration of other plausible and closely related questions. In marginal structural models, as in any regression setting, correct inference depends on correct model specification. Our proposed information criterion provides a formal method for comparing model fit for different specifications.

Figure B1

Residuals for the four candidate models for Example 1, plotted against observation number.

Figure B2

Residuals for the six candidate models for Example 2, plotted against years on study.

Figure 1

Fitted mean weight at 12 months (kg) as a function of months breastfed, for exposure saturated model with 95 percent point-wise confidence bands in grey-shade for 17,044 infants in a randomized breastfeeding promotion trial conducted in Belarus.

Figure 2

Difference in CD4 count (cells/mm³) for 5519 antiretroviral therapy exposed and 6516 unexposed visits between April 1996 and April 2002 for 1,763 HIV-positive participants from two US cohort studies, by years of follow up using under-stabilized inverse probability-of-treatment-and-censoring weights as described in text and point-wise 95 percent confidence band in grey-shade.