Semiparametric proportional means model for marker data contingent on recurrent event

In many biomedical studies with recurrent events, some markers can only be measured when events happen. For example, medical cost attributed to hospitalization can only incur when patients are hospitalized. Such marker data are contingent on recurrent events. In this paper, we present a proportional means model for modelling the markers using the observed covariates contingent on the recurrent event. We also model the recurrent event via a marginal rate model. Estimating equations are constructed to derive the point estimators for the parameters in the proposed models. The estimators are shown to be asymptotically normal. Simulation studies are conducted to examine the finite-sample properties of the proposed estimators and the proposed method is applied to a data set from the Vitamin A Community Trial.

[1]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[2]  Zhiliang Ying,et al.  Semiparametric Transformation Models for Point Processes , 2001 .

[3]  M. Barreto,et al.  Effect of vitamin A supplementation on diarrhoea and acute lower-respiratory-tract infections in young children in Brazil , 1994, The Lancet.

[4]  S. Ratcliffe,et al.  Joint Modeling of Longitudinal and Survival Data via a Common Frailty , 2004, Biometrics.

[5]  Yijian Huang,et al.  Semiparametric estimation of marginal mark distribution , 2006 .

[6]  Zhiliang Ying,et al.  Semiparametric regression for the mean and rate functions of recurrent events , 2000 .

[7]  Zhiliang Ying,et al.  Semiparametric and Nonparametric Regression Analysis of Longitudinal Data , 2001 .

[8]  Lee-Jen Wei,et al.  Regression Parameter Estimation from Panel Counts , 2003 .

[9]  Juan Yang,et al.  Bayesian Modeling of Multiple Episode Occurrence and Severity with a Terminating Event , 2007, Biometrics.

[10]  Raymond J. Carroll,et al.  Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process , 1988 .

[11]  T. Martinussen,et al.  A nonparametric dynamic additive regression model for longitudinal data , 2000 .

[12]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[13]  K. Deimling.  Nonlinear functional analysis , 1985 .

[14]  S. Zeger,et al.  Joint analysis of longitudinal data comprising repeated measures and times to events , 2001 .

[15]  M. Wulfsohn,et al.  Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS , 1995 .

[16]  Hulin Wu,et al.  Semiparametric Time‐Varying Coefficients Regression Model for Longitudinal Data , 2005 .

[17]  Torben Martinussen,et al.  Sampling Adjusted Analysis of Dynamic Additive Regression Models for Longitudinal Data , 2001 .