Quantile adaptive lasso: variable selection for quantile treatment effect estimation

Quantile treatment effects (QTEs) characterize different causal effects of treatment on outcome distribution. Propensity score (PS) methods are commonly employed for estimating QTEs in non-randomized studies. Previous studies have shown that insufficient and unnecessary adjustment for covariates in PS models leads to bias and efficiency loss of treatment effects. Confounders may vary across different quantiles of outcome distribution. To allow for the selection of covariates related to outcome at interesting quantiles corresponding to QTE, we proposed quantile adaptive lasso (QAL) to select covariates that can provide unbiased and efficient QTE estimation. QAL utilized linear quantile regression models to construct penalty weights. Theoretical analyses showed that QAL enjoys several asymptotic properties. Simulations showed the superiority of QAL over existing methods in variable selection and QTE estimation. We applied QAL to datasets from the China Health and Retirement Longitudinal Study to explore the impact of smoking on the severity of depression.