×

Statistical inference in quantile regression for zero-inflated outcomes. (English) Zbl 1524.62183

Summary: An extension of quantile regression is proposed to model zero-inflated outcomes, which have become increasingly common in biomedical studies. The method is flexible enough to depict complex and nonlinear associations between the covariates and the quantiles of the outcome. We establish the theoretical properties of the estimated quantiles, and develop inference tools to assess the quantile effects. Extensive simulation studies indicate that the novel method generally outperforms existing zero-inflated approaches and the direct quantile regression in terms of the estimation and inference of the heterogeneous effect of the covariates. The approach is applied to data from the Northern Manhattan Study to identify risk factors for carotid atherosclerosis, measured by the ultrasound carotid plaque burden.

MSC:

62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chernozhukov, V., Fernández-Val, I. and Galichon, A. (2010). Quantile and probability curves without crossing. Econometrica 78, 1093-1125. · Zbl 1192.62255
[2] Cheung, Y. K., Moon, Y. P., Kulick, E. R., Sacco, R. L., Elkind, M. S. and Willey, J. Z. (2017). Leisure-time physical activity and cardiovascular mortality in an elderly popu-lation in northern Manhattan: A prospective cohort study. Journal of General Internal Medicine 32, 168-174.
[3] Duan, N., Manning, W. G., Morris, C. N. and Newhouse, J. P. (1983). A comparison of alter-native models for the demand for medical care. Journal of Business & Economic Statis-tics 1, 115-126.
[4] He, X. and Ng, P. (1999). Cobs: Qualitatively constrained smoothing via linear programming. Computational Statistics 14, 315-337. · Zbl 0941.62037
[5] Heras, A., Moreno, I. and Vilar-Zanón, J. L. (2018). An application of two-stage quantile re-gression to insurance ratemaking. Scandinavian Actuarial Journal 2018, 753-769. · Zbl 1418.91242
[6] Heyman, D. P., Tabatabai, A. and Lakshman, T. (1992). Statistical analysis and simulation study of video teleconference traffic in ATM networks. In IEEE Transactions on Circuits and Systems for Video Technology 2, 49-59.
[7] Jorgensen, B. (1987). Exponential dispersion models. Journal of the Royal Statistical Society. Series B (Methodological) 49, 127-162. · Zbl 0662.62078
[8] Koenker, R. (2005). Quantile regression. Cambridge University Press, Cambridge. · Zbl 1111.62037
[9] Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica 46, 33-50. · Zbl 0373.62038
[10] Lambert, D. (1992). Zero-inflated poisson regression, with an application to defects in manufac-turing. Technometrics 34, 1-14. · Zbl 0850.62756
[11] Lee, S., Wu, M. C. and Lin, X. (2012). Optimal tests for rare variant effects in sequencing association studies. Biostatistics 13, 762-775.
[12] Lim, H. K., Li, W. K. and Philip, L. (2014). Zero-inflated poisson regression mixture model. Computational Statistics & Data Analysis 71, 151-158. · Zbl 1471.62116
[13] Mullahy, J. (1986). Specification and testing of some modified count data models. Journal of Econometrics 33, 341-365.
[14] Shorack, G. and Wellner, J. (1986). Empirical processes with applications to statistics. John Wiley & Sons, New York. · Zbl 1170.62365
[15] Wei, Y. and Carroll, R. J. (2009). Quantile regression with measurement error. Journal of the American Statistical Association 104, 1129-1143. · Zbl 1388.62210
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.