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A Propensity-score-based Fine Stratification Approach for Confounding Adjustment When Exposure Is Infrequent

Desai, Rishi J.; Rothman, Kenneth J.; Bateman, Brian .T; Hernandez-Diaz, Sonia; Huybrechts, Krista F.

doi: 10.1097/EDE.0000000000000595

Background: When exposure is infrequent, propensity-score matching results in reduced precision because it discards a large proportion of unexposed patients. To our knowledge, the relative performance of propensity-score stratification in these circumstances has not been examined.

Methods: Using an empirical example of the association of first trimester statin exposure (prevalence = 0.04%) with risk of congenital malformations and 1,000 simulated cohorts (n = 20,000) with eight combinations of exposure prevalence (0.5%, 1%, 5%, 10%) and outcome risk (3.5%, 10%), we compared four propensity-score-based approaches to confounding adjustment: (1) matching (1:1, 1:5, full), (2) stratification in 10, 50, and 100 strata by entire cohort propensity-score distribution, (3) stratification in 10, 50, and 100 strata by exposed group propensity-score distribution, (4) standardized mortality ratio (SMR) weighting. Weighted generalized linear models were used to derive effect estimates after weighting unexposed according to the distribution of the exposed in their stratum for the stratification approaches.

Results: In the empirical example, propensity-score stratification (cohort) approaches resulted in greater imbalances in covariate distributions between statin-exposed and unexposed compared with propensity-score stratification (exposed) and matching. In simulations, propensity-score stratification (exposed) resulted in smaller relative bias than the cohort approach with 10 and 50 strata, and greater precision than matching and SMR weighting at 0.5% and 1% exposure prevalence, but similar performance at 5% and 10%.

Conclusion: For exposures with prevalence under 5%, propensity-score stratification with fine strata, based on the exposed group propensity-score distribution, produced the best results. For more common exposures, all approaches were equivalent.

Supplemental Digital Content is available in the text.

From the aDivision of Pharmacoepidemiology and Pharmacoeconomics, Brigham and Women’s Hospital & Harvard Medical School, Boston, MA; bResearch Triangle Institute, Research Triangle Park, NC; cBoston University School of Public Health, Boston, MA; dDepartment of Anesthesia, Critical Care, and Pain Medicine, Massachusetts General Hospital, Harvard Medical School, Boston, MA; and eDepartment of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA.

This study was funded from internal sources of the Division of Pharamcoepidemiology and Pharmacoeconomics. Dr. Huybrechts is supported by a career development award from the National Institute of Mental Health (K01 MH099141). Dr. Bateman is supported by a career development award from the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the NIH (K08HD075831). Dr. Hernandez-Diaz is supported by the NIH Grant R01 MH100216 and has consulted for AstraZeneca (London, UK) for unrelated projects. The other authors declare no other relationships or activities that could appear to have influenced the submitted work.

Computing codes used in this study will be made available at The data are not available for replication because of IRB restrictions.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

Correspondence: Rishi J. Desai, Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School, 1620 Tremont Street, Suite 3030-R, Boston, MA 02120. E-mail:

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