Review Articles

Quantile treatment effect estimation with dimension reduction

Ying Zhang ,

a Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA

Lei Wang ,

b School of Statistics and Data Science & LPMC, Nankai University, Tianjin, People's Republic of China

Menggang Yu ,

c Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA

Jun Shao

a Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA

Pages 202-213 | Received 23 Jul. 2021, Accepted 23 Jul. 2021, Published online: 23 Jul. 2021,
  • Abstract
  • Full Article
  • References
  • Citations


Quantile treatment effects can be important causal estimands in evaluation of biomedical treatments or interventions for health outcomes such as medical cost and utilisation. We consider their estimation in observational studies with many possible covariates under the assumption that treatment and potential outcomes are independent conditional on all covariates. To obtain valid and efficient treatment effect estimators, we replace the set of all covariates by lower dimensional sets for estimation of the quantiles of potential outcomes. These lower dimensional sets are obtained using sufficient dimension reduction tools and are outcome specific. We justify our choice from efficiency point of view. We prove the asymptotic normality of our estimators and our theory is complemented by some simulation results and an application to data from the University of Wisconsin Health Accountable Care Organization.


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