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Semiparametric additive time‐varying coefficients model for longitudinal data with censored time origin

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  • Yanqing Sun
  • Qiong Shou
  • Peter B. Gilbert
  • Fei Heng
  • Xiyuan Qian

Abstract

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time‐varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan–Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two‐stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two‐stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccine study.

Suggested Citation

  • Yanqing Sun & Qiong Shou & Peter B. Gilbert & Fei Heng & Xiyuan Qian, 2023. "Semiparametric additive time‐varying coefficients model for longitudinal data with censored time origin," Biometrics, The International Biometric Society, vol. 79(2), pages 695-710, June.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:695-710
    DOI: 10.1111/biom.13610
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    References listed on IDEAS

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    1. Yanqing Sun & Peter B. Gilbert, 2012. "Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 34-52, March.
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    5. Guangren Yang & Yanqing Sun & Li Qi & Peter B. Gilbert, 2017. "Estimation of Stratified Mark-Specific Proportional Hazards Models Under Two-Phase Sampling with Application to HIV Vaccine Efficacy Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 259-283, June.
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