Doubly weighted estimating equations and weighted multiple imputation for causal inference with an incomplete subgroup variable

Abstract

Health research often aims to investigate whether the effect of an exposure variable is common across different subgroups of individuals, but sometimes the variable defining subgroups is not recorded in all individuals. We propose and evaluate two methods for estimation of the marginal causal effect of an exposure variable within subgroups in the observational setting where the subgroup variable is incompletely observed. The first approach involves doubly weighted estimating functions with one weight based on a propensity score for exposure and a second weight addressing the selection bias when analyses are restricted to individuals with complete data. The second approach uses the inverse probability of exposure weights in conjunction with multiple imputation for the incomplete subgroup variable. The resulting estimators are consistent when the auxiliary models are correctly specified; we assess the finite sample performance via simulation. An illustrative analysis is provided involving patients with psoriatic arthritis treated with biologic therapy where interest lies in the effect of therapy according to the presence or absence of the human leukocyte antigen marker HLA-B27 which is incompletely observed.

Keywords:

• Causal inference
• effect modification
• inverse probability weight
• incomplete data
• multiple imputation

Acknowledgments

The authors thank Drs. Dafna Gladman, Vinod Chandran and Lihi Eder for stimulating discussion regarding the University of Toronto Psoriatic Arthritis Registry.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada [RGPIN 1280961 for LD, RGPIN 402474-2011 and 2019-04174 for CAC and RGPIN 155849 and RGPIN 04207 for RJC]; and Canadian Institutes of Health Research [FRN 13887 for RJC].

Notes on contributors

M. S. Cuerden

Meaghan Cuerden is a Biostatistician with the Kidney Clinical Research Unit at London Health Sciences Centre in London, Ontario, Canada.

L. Diao

Liqun Diao is a Research Assistant Professor in the Department of Statistics and Actuarial Science at the University of Waterloo in Waterloo, Ontario, Canada.

C. A. Cotton

Cecilia A. Cotton is an Associate Professor in the Department of Statistics and Actuarial Science at the University of Waterloo in Waterloo, Ontario, Canada.

R. J. Cook

Richard J. Cook is a Professor in the Department of Statistics and Actuarial Science and Faculty of Mathematics Research Chair at the University of Waterloo in Waterloo, Ontario, Canada.