Doubly robust estimation of partially linear models for longitudinal data with dropouts and measurement error in covariates

ABSTRACT

In longitudinal studies, missing responses and mismeasured covariates are commonly seen due to the data collection process. Without cautiousness in data analysis, inferences from the standard statistical approaches may lead to wrong conclusions. In order to improve the estimation for longitudinal data analysis, a doubly robust estimation method for partially linear models, which can simultaneously account for the missing responses and mismeasured covariates, is proposed. Imprecisions of covariates are corrected by taking advantage of the independence between replicate measurement errors, and missing responses are handled by the doubly robust estimation under the mechanism of missing at random. The asymptotic properties of the proposed estimators are established under regularity conditions, and simulation studies demonstrate desired properties. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study.

KEYWORDS:

• Doubly robust
• dropouts
• measurement error
• partially linear models

AMS SUBJECT CLASSIFICATION:

• 62-07

Acknowledgements

We greatly appreciate Drs Xuemei Sui and Steven N. Blair of the University of South Carolina for providing the LEAN study data and for their contributions in data interpretation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [11371100], China Medical Board Collaborating Program in Health Technology Assessment [Grant 16-251] and Shanghai Leading Academic Discipline Project, Project number: B118.