A copula-based mixed Poisson model for bivariate recurrent events under event-dependent censoring.
In many chronic disease processes subjects are at risk of two or more types of events. We describe a bivariate mixed Poisson model in which a copula function is used to model the association between two gamma distributed random effects. The resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process. Methods for parameter estimation are described for parametric and semiparametric models based on an EM algorithm. We also consider the issue of event-dependent censoring based on one type of event, which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study. The asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed, as well as associated treatment effects. Because the joint model is fit based on a likelihood, consistent estimates are obtained. Simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event-dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach.
Cook
Richard J
RJ
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L 3G1. rjcook@uwaterloo.ca
Lawless
Jerald F
JF
Lee
Ker-Ai
KA
D001842:Bone and Bones / Q000503:physiopathology; D001943:Breast Neoplasms; D002908:Chronic Disease; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D005260:Female; D006801:Humans; D009362:Neoplasm Metastasis; D016012:Poisson Distribution; D029424:Pulmonary Disease, Chronic Obstructive; D028761:Withholding Treatment / Q000706:statistics & numerical data*