Contrast-specific propensity scores

Abstract

Basic propensity score methodology is designed to balance the distributions of multivariate pre-treatment covariates when comparing one active treatment with one control treatment. However, practical settings often involve comparing more than two treatments, where more complicated contrasts than the basic treatment-control one, $(1,-1)$, are relevant. Here, we propose the use of contrast-specific propensity scores (CSPS), which allows the creation of treatment groups of units that are balanced with respect to bifurcations of the specified contrasts and the multivariate space spanned by these bifurcations.

Keywords:

• Causal inference
• covariate balance
• multiple treatments

Acknowledgments

We thank the referees for helpful comments and Rui Dong and Ke Zhu for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Shasha Han

Shasha Han is currently a postdoctoral researcher in Beijing International Center for Mathematical Research, Peking University; and Department of Health Care Policy, Harvard Medical School. Her research focuses on forge a scientific basis of health interventions through tackling problems arising in evidence-based decisions in the presence of complexity and uncertainty, from perspectives on health policy, managerial decision-making and individual medication. She completed her PhD from National University of Singapore, with the pleasure being advised by Joel Goh, Melvyn Sim, Donald Rubin. She has expertise in develops and applies causal inference and optimization methods with the large real-world data of health system. Her research has appeared in Annals of Internal Medicine.

Donald. B. Rubin

Donald B. Rubin is currently Professor in the Yau Center for Mathematical Sciences, Tsinghua University; Murray Schusterman Senior Research Fellow, Fox Business School, Temple University; and Professor of Statistics Emeritus, Harvard University. He has been elected to be a Fellow/Member/Honorary Member of: the Woodrow Wilson Society, Guggenheim Memorial Foundation, Alexander von Humboldt Foundation, American Statistical Association, Institute of Mathematical Statistics, International Statistical Institute, American Association for the Advancement of Science, American Academy of Arts and Sciences, European Association of Methodology, the British Academy, and the U.S. National Academy of Sciences. As of 2021, he has authored/coauthored nearly 500 publications (including ten books), has four joint patents, and for many years has been one of the most highly cited authors in the world, with currently over 340,000 citations, and over 2,5000 per year in recent years (Google Scholar). Of his many publications with over 1,000 citations each, over ten of them are solely authored by Rubin. He has received honorary doctorate degrees from Otto Friedrich University, Bamberg, Germany; the University of Ljubljana, Slovenia; Universidad Santo Tomás, Bogotá, Colombia; Uppsala University, Sweden; and Northwestern University, Evanston, Illinois. He has also received honorary professorships from the University of Utrecht, The Netherlands; Shanghai Finance University, China; Nanjing University of Science & Technology, China; Xi’an University of Technology, China; and University of the Free State, Republic of South Africa. He is a widely sought international lecturer and consultant on a variety of statistical topics.