title: Laplace's approximation for relative risk frailty models.
abstract: Relative risk frailty models are used extensively in analyzing clustered and/or recurrent time-to-event data. In this paper, Laplace's approximation for integrals is applied to marginal distributions of data arising from parametric relative risk frailty models. Under regularity conditions, the approximate maximum likelihood estimators (MLE) are consistent with a rate of convergence that depends on both the number of subjects and number of members per subject. We compare the approximate MLE against alternative estimators using limited simulation and demonstrate the utility of Laplace's approximation approach by analyzing U.S. patient waiting time to deceased kidney transplant data.
authors.affiliation: Genentech, Inc., South San Francisco, CA 94080, USA. shibaof@gene.com
authors.forename: Shibao
authors.initials: S
authors.lastname: Feng
authors.forename: Lei
authors.initials: L
authors.lastname: Nie
authors.forename: Robert A
authors.initials: RA
authors.lastname: Wolfe
mesh_terms: D000465:Algorithms; D006801:Humans; D007676:Kidney Failure, Chronic / Q000601:surgery; D016030:Kidney Transplantation / Q000706:statistics & numerical data; D016013:Likelihood Functions; D015233:Models, Statistical; D015999:Multivariate Analysis; D016012:Poisson Distribution; D016016:Proportional Hazards Models; D012306:Risk; D018709:Statistics, Nonparametric; D013997:Time Factors; D009927:Tissue and Organ Procurement / Q000706:statistics & numerical data; D014481:United States; D014850:Waiting Lists