Ensemble learning of inverse probability weights for marginal structural modeling in large observational datasets

Abstract

Inverse probability weights used to fit marginal structural models are typically estimated using logistic regression. However, a data-adaptive procedure may be able to better exploit information available in measured covariates. By combining predictions from multiple algorithms, ensemble learning offers an alternative to logistic regression modeling to further reduce bias in estimated marginal structural model parameters. We describe the application of two ensemble learning approaches to estimating stabilized weights: super learning (SL), an ensemble machine learning approach that relies on V-fold cross validation, and an ensemble learner (EL) that creates a single partition of the data into training and validation sets. Longitudinal data from two multicenter cohort studies in Spain (CoRIS and CoRIS-MD) were analyzed to estimate the mortality hazard ratio for initiation versus no initiation of combined antiretroviral therapy among HIV positive subjects. Both ensemble approaches produced hazard ratio estimates further away from the null, and with tighter confidence intervals, than logistic regression modeling. Computation time for EL was less than half that of SL. We conclude that ensemble learning using a library of diverse candidate algorithms offers an alternative to parametric modeling of inverse probability weights when fitting marginal structural models. With large datasets, EL provides a rich search over the solution space in less time than SL with comparable results.

Keywords: data-adaptive; ensemble learning; inverse probability weighting; longitudinal data; marginal structural model; super learning.

Figure 1

Directed acyclic graph representation of simulated data for Scenarios I and II.

Figure 2

Distribution of log(SW) estimated using logistic regression, SL_naive, SL_rich, EL.10, EL.25, EL.50. The horizontal line is at the desired mean value.

Figure 3

Contribution of each algorithm in the library to the convex combination for the numerator (top) and denominator (bottom) of contribution to stabilized weights from treatment as determined by SL_rich and EL using different partition sizes.