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Constructing Inverse Probability Weights for Continuous Exposures: A Comparison of Methods

Naimi, Ashley I.a; Moodie, Erica E.M.a; Auger, Nathalieb; Kaufman, Jay S.a

doi: 10.1097/EDE.0000000000000053

Abstract: Inverse probability–weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

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From the aDepartment of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, QC, Canada; and bInstitut national de santé publique du Québec, and Research Centre of the University of Montreal Hospital Centre, Montreal, QC, Canada.

The authors report no conflicts of interest.

Supported by Post-Doctoral Research Award from the Fonds de recherche du Québec-Santé (A.I.N.), Natural Sciences and Engineering Research Council University Faculty Award (E.E.M.M.), Career Award from the Fonds de recherche du Québec-Santé (N.A.), and supported by the Canada Research Chairs Program (J.S.K.).

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article ( This content is not peer-reviewed or copy-edited; it is the sole responsibility of the author.

Correspondence: Ashley I. Naimi, Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Purvis Hall, 1020 Pine Ave West, Montreal, QC, Canada H3A 1A2. E-mail:

© 2014 by Lippincott Williams & Wilkins, Inc