Maximum penalized likelihood estimation in a gamma-frailty model.
The shared frailty models allow for unobserved heterogeneity or for statistical dependence between observed survival data. The most commonly used estimation procedure in frailty models is the EM algorithm, but this approach yields a discrete estimator of the distribution and consequently does not allow direct estimation of the hazard function. We show how maximum penalized likelihood estimation can be applied to nonparametric estimation of a continuous hazard function in a shared gamma-frailty model withright-censored and left-truncated data. We examine the problem of obtaining variance estimators for regression coefficients, the frailty parameter and baseline hazard functions. Some simulations for the proposed estimation procedure are presented. A prospective cohort (Paquid) with grouped survival data serves to illustrate the method which was used to analyze the relationship between environmental factors and the risk of dementia.
Equipe Mixte INSERM E0338 (Biostatistique), Université Victor Segalen Bordeaux 2, 146 rue Léo Saignat, 33076 Bordeaux Cedex, France. Virginie.Rondeau@isped.u-bordeaux2.fr
Virginie
V
Rondeau
Daniel
D
Commenges
Pierre
P
Joly
D000465:Algorithms; D000535:Aluminum / Q000009:adverse effects; D000544:Alzheimer Disease / Q000139:chemically induced / Q000453:epidemiology; D015331:Cohort Studies; D004781:Environmental Exposure / Q000009:adverse effects; D005602:France; D006801:Humans; D016013:Likelihood Functions; D016016:Proportional Hazards Models; D016019:Survival Analysis
D000535:Aluminum