Kernel Estimation of Bivariate Time-Varying Coefficient Model for Longitudinal Data with Terminal Event

• Published in: Journal of the American Statistical Association Vol. 119; no. 546; pp. 1102 - 1111
• Main Authors: Wang, Yue, Nan, Bin, Kalbfleisch, John D.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 02.04.2024; Taylor & Francis Ltd
• Subjects: Bivariate analysis; Complete case analysis; Conditional model; Cost analysis; Covariance matrix; End-stage renal disease; Estimation; Followup; Kidney diseases; Nonparametric regression; Normal distribution; Pointwise confidence interval; Regression coefficients; Regression models; Statistical analysis; Statistics; variance covariance matrix; End-stage renal disease; Pointwise confidence interval; Complete case analysis; Conditional model; Nonparametric regression
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2023.2169702

We propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal trajectories of covariate effects along with both the followup time and the residual lifetime. The proposed model extends the parametric conditional approach given terminal event time in recent literature, and thus avoids potential model misspecification. We consider a kernel smoothing method for estimating regression coefficients in our model and use cross-validation for bandwidth selection, applying undersmoothing in the final analysis to eliminate the asymptotic bias of the kernel estimator. We show that the kernel estimates follow a finite-dimensional normal distribution asymptotically under mild regularity conditions, and provide an easily computed sandwich covariance matrix estimator. We conduct extensive simulations that show desirable performance of the proposed approach, and apply the method to analyzing the medical cost data for patients with end-stage renal disease. Supplementary materials for this article are available online.