Hornsteiner, U.; Hamerle, Alfred; Michels, P.
Parametric versus Nonparametric Treatment of Unobserved Heterogeneity in Multivariate Failure Times.
Collaborative Research Center 386, Discussion Paper 80
Two contrary methods for the estimation of a frailty model of multivariate failure times are presented. The assumed Accelerated Failure Time Model includes censored data, observed covariates and unobserved heterogeneity. The parametric estimator maximizes the marginal likelihood whereas the method which does not require distributional assumptions combines the GEE approach (Liang and Zeger, 1986) with the Buckley-James (1979) estimator for censored data. Monte Carlo experiments are conducted to compare the methods under various conditions with regard to bias and efficiency. The ML estimator is found to be rather robust against some misspecifications and both methods seem to be interesting alternatives in uncertain circumstances which lack exact solutions. The methods are applied to data of recurrent purchase acts of yogurt brands.