Improved kth power expectile regression with nonignorable dropouts

Abstract

The kth ($1<k\le 2$) power expectile regression (ER) can balance robustness and effectiveness between the ordinary quantile regression and ER simultaneously. Motivated by a longitudinal ACTG 193A data with nonignorable dropouts, we propose a two-stage estimation procedure and statistical inference methods based on the kth power ER and empirical likelihood to accommodate both the within-subject correlations and nonignorable dropouts. Firstly, we construct the bias-corrected generalized estimating equations by combining the kth power ER and inverse probability weighting approaches. Subsequently, the generalized method of moments is utilized to estimate the parameters in the nonignorable dropout propensity based on sufficient instrumental estimating equations. Secondly, in order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function to obtain the improved empirical likelihood procedures. The asymptotic properties of the corresponding estimators and their confidence regions are derived. The finite-sample performance of the proposed estimators is studied through simulation and an application to the ACTG 193A data is also presented.

Keywords:

• Dropout propensity
• empirical likelihood
• expectile regression
• inverse probability weighting
• missing not at random
• nonresponse instrument

Acknowledgments

We are grateful to the Editor, an associate editor and two anonymous referees for their insightful comments and suggestions, which have led to significant improvements.

Disclosure statement

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

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China [grant numbers 11871287, 11771144, 11801359], the Natural Science Foundation of Tianjin [18JCYBJC41100], Fundamental Research Funds for the Central Universities and the Key Laboratory for Medical Data Analysis and Statistical Research of Tianjin.