Quantile regression in longitudinal studies with dropouts and measurement errors

ABSTRACT

Quantile regression models, as an important tool in practice, can describe effects of risk factors on the entire conditional distribution of the response variable with its estimates robust to outliers. However, there is few discussion on quantile regression for longitudinal data with both missing responses and measurement errors, which are commonly seen in practice. We develop a weighted and bias-corrected quantile loss function for the quantile regression with longitudinal data, which allows both missingness and measurement errors. Additionally, we establish the asymptotic properties of the proposed estimator. Simulation studies demonstrate the expected performance in correcting the bias resulted from missingness and measurement errors. Finally, we investigate the Lifestyle Education for Activity and Nutrition study and confirm the effective of intervention in producing weight loss after nine month at the high quantile.

KEYWORDS:

• Measurement error
• missing data
• quantile regression
• smoothing

Acknowledgments

We greatly appreciate Drs Xuemei Sui and Steven N. Blair of the University of South Carolina for providing the LEAN study data set and for their contributions in data interpretation. We sincerely thank the associate editor and a referee for their valuable comments that greatly improved presentation of our work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was partially supported by the National Nature and Science Foundation of China [11371100, 11271080], and Shanghai Leading Academic Discipline Project, Project number: B118, and the Project of Science and Technology Commission of Shanghai Municipality [13411950406].