Abstract
Panel count data frequently occurs in follow-up studies, such as medical research, social sciences, reliability studies, and tumorigenicity experiences. This type data has been extensively studied by various statistical models with time-invariant regression coefficients. However, the assumption of invariant coefficients may be violated in some reality, and the temporal covariate effects would be of great interest in research studies. This motivates us to consider a more flexible time-varying coefficient model. For statistical inference of the unknown functions, the quantile regression approach based on the B-spline approximation is developed. Asymptotic results on the convergence of the estimators are provided. Some simulation studies are presented to assess the finite-sample performance of the estimators. Finally, two applications of bladder cancer data and US flight delay data are analyzed by the proposed method.
Highlights
In longitudinal follow-up studies, panel count data is frequently encountered in many fields such as medical research, social sciences, reliability studies, and tumorigenicity experiences, which has been widely analyzed by many authors
We proposed a spline-based quantile regression estimation method in the timevarying coefficient panel count data model
This model discussed in our paper is more general than [15], with no Poisson restriction on the recurrent event process
Summary
In longitudinal follow-up studies, panel count data is frequently encountered in many fields such as medical research, social sciences, reliability studies, and tumorigenicity experiences, which has been widely analyzed by many authors This type data is usually collected from the discrete observations in recurrent event process, as the continuous observations might be too expensive to be carried out. [15] proposed a nonparametric proportional mean model of the panel count data with time-varying coefficients. The main contribution of the paper is that we propose a new spline-based quantile estimation procedure for the time-varying coefficient panel count data model, which has not been discussed in the literature. For the model defined above, [15] developed the likelihood and pseudo-likelihood methods to get the estimation of the baseline intensity function λ0(u) and the varying coefficient functions β(u) based on the Poisson distribution assumption on Ni(t). Quantile regression is developed for the inference in the last step
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