Parametric versus Nonparametric Treatment of Unobserved Heterogeneity in Multivariate Failure Times

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.