Inverse Probability Weighted Estimation of Risk Under Representative Interventions in Observational Studies

ABSTRACT

Researchers are often interested in using observational data to estimate the effect on a health outcome of maintaining a continuous treatment within a prespecified range over time, for example, “always exercise at least 30 minutes per day.” There may be many precise interventions that could achieve this range. In this article, we consider representative interventions. These are special cases of random dynamic interventions: interventions under which treatment at each time is assigned according to a random draw from a distribution that may depend on a subject’s measured past. Estimators of risk under representative interventions on a time-varying treatment have previously been described based on g-estimation of structural nested cumulative failure time models. In this article, we consider an alternative approach based on inverse probability weighting (IPW) of marginal structural models. In particular, we show that the risk under a representative intervention on a time-varying continuous treatment can be consistently estimated via computationally simple IPW methods traditionally used for deterministic static (i.e., “nonrandom” and “nondynamic”) interventions for binary treatments. We present an application of IPW in this setting to estimate the 28-year risk of coronary heart disease under various representative interventions on lifestyle behaviors in the Nurses' Health Study. Supplementary materials for this article are available online.

KEYWORDS:

• Causal inference
• g-formula
• Longitudinal data
• Marginal structural models
• Survival analysis

Supplementary Materials

The supplementary materials contain Appendices A-G referenced in the main text. Appendix A contains proof of equivalence of expressions (7) and (8). Appendix B reviews alternative semi-parametric estimators of risk under a representative intervention. Appendices C and D describe extensions of the IPW algorithm in Section 5.2 to allow for observed data structures with incomplete/loss to follow-up and competing risks, respectively. Appendix E describes an IPW estimator for risk under the “natural course“. Appendix F reviews alternative interventions that maintain a continuous treatment within a pre-specified range along with the parametric g-formula algorithm. Appendix G details the functional form of weight models used in the data analysis described in Section 6.

Acknowledgments

The authors thank the Channing Division of Network Medicine, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School. The authors are also grateful to Sarah Taubman and Murray Mittleman for their contributions and comments to early drafts of this manuscript.

Additional information

Funding

This study was supported by grants R01 HL080644, UM1 CA186107, HL034594, R01 HL088521, DP1 ES025459, R01 AI112339, and R01 AI27271 from the National Institutes of Health (Bethesda, MD).