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.
Panel count data arise when the number of recurrent events experienced by each subject is observed intermittently at discrete examination times. The examination time process can be informative about the underlying recurrent event process even after conditioning on covariates. We consider a semiparametric accelerated mean model for the recurrent event process and allow the two processes to be correlated through a shared frailty. The regression parameters have a simple marginal interpretation of modifying the time scale of the cumulative mean function of the event process. A novel estimation procedure for the regression parameters and the baseline rate function is proposed based on a conditioning technique. In contrast to existing methods, the proposed method is robust in the sense that it requires neither the strong Poisson-type assumption for the underlying recurrent event process nor a parametric assumption on the distribution of the unobserved frailty. Moreover, the distribution of the examination time process is left unspecified, allowing for arbitrary dependence between the two processes. Asymptotic consistency of the estimator is established, and the variance of the estimator is estimated by a model-based smoothed bootstrap procedure. Numerical studies demonstrated that the proposed point estimator and variance estimator perform well with practical sample sizes. The methods are applied to data from a skin cancer chemoprevention trial.
more » « less- Award ID(s):
- 1659328
- NSF-PAR ID:
- 10485820
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 74
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 944-953
- Size(s):
- ["p. 944-953"]
- Sponsoring Org:
- National Science Foundation
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