Sieve estimation of the accelerated mean model based on panel count data

Abstract

Panel count data are gathered when subjects are examined at discrete times during a study, and only the number of recurrent events occurring before each examination time is recorded. We consider a semiparametric accelerated mean model for panel count data in which the effect of the covariates is to transform the time scale of the baseline mean function. Semiparametric inference for the model is inherently challenging because the finite-dimensional regression parameters appear in the argument of the (infinite-dimensional) functional parameter, i.e., the baseline mean function, leading to the phenomenon of bundled parameters. We propose sieve pseudolikelihood and likelihood methods to construct the random criterion function for estimating the model parameters. An inexact block coordinate ascent algorithm is used to obtain these estimators. We establish the consistency and rate of convergence of the proposed estimators, as well as the asymptotic normality of the estimators of the regression parameters. Novel consistent estimators of the asymptotic covariances of the estimated regression parameters are derived by leveraging the counting process associated with the examination times. Comprehensive simulation studies demonstrate that the optimization algorithm is much less sensitive to the initial values than the Newton–Raphson method. The proposed estimators perform well for practical sample sizes, and are more efficient than existing methods. An example based on real data shows that due to this efficiency gain, the proposed method is better able to detect the significance of practically meaningful covariates than an existing method.