Inverse probability weighting for categorical exposures

Inverse probability weights (IPW) are invaluably useful tools for addressing issues including censoring, missing data, selection bias, or confounding.1 In complex scenarios, such as with time-varying confounding, IPW can be used to estimate causal effects and overcome shortcomings of conventional regression-based adjustment. When used to address confounding in an observational study evaluating binary treatment, IPW functions similar to standardization, and the weights are the inverse of the observed probability of receiving treatment. In this case, the IPW weights can be determined straightforwardly using a logistic regression model of treatment as a function of measured confounders. From this model, one can obtain an estimate of the conditional probability of being treated for the treated individuals, and one minus the conditional probability of being treated for untreated individuals. These probabilities can then be used to construct weights.1 In studies considering a categorical exposure, IPW can still be used to address confounding. However, the procedure for determining IPW in the setting of an exposure with more than two levels requires a different regression modeling strategy. In this Classroom article, we demonstrate how to construct stabilized IPW for a categorical exposure using multinomial logistic regression. We begin with the publicly available National Health and Nutrition Examination Survey (NHANES) Epidemiologic Follow up Study data (NHEFS) and estimate the adjusted mean difference between exercise measured in three categories in 1972 (the treatment), and weight change between 1981 and 1972 (the outcome) using IPWs for control of confounding. We explain the data setting, explain how to construct IPWs for the three-level treatment variable and describe an approach for evaluation of potential violations of the positivity assumption. We provide code in a linked GitHub repository demonstrating how to deploy the procedures in the R programming language.