A modification of the Andersen-Gill gamma shared frailty model is presented. The variance of the frailty is directly modeled by means of a generalized linear model, the EM algorithm is modified in order to simultaneously estimate a semiparametric model for the failure times and a model for the variance of the frailty. A simulation study is conducted to evaluate the performance of the proposed algorithm (EMB algorithm) and compared with other methods, a marginal model, and a conditional model. Multivariate data from a nosocomial infection study is used to illustrate the methods. The EMB fit turned out to be better than the fit obtained from a marginal model or from a conditional model. The EMB provided the best fit (being the least over-dispersed and having the highest AIC and the highest pseudo-R square) and estimated the parameters most efficiently. The proposed method is able to capture and to take into account unobservable random effects in semiparametric models.
Barceló, Maria Antònia and Saez, Marc
"A Modification Of The EM Algorithm To Estimate An Andersen-Gill Gamma Frailty Model For Multivariate Failure Time Data,"
Journal of Modern Applied Statistical Methods: Vol. 3
, Article 21.
Available at: http://digitalcommons.wayne.edu/jmasm/vol3/iss2/21