A simulation study of maximum likelihood estimation in logistic regression with cured individuals

Aba Diop (1, 2) , Aliou Diop (2) , Jean-François Dupuy (3)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
3 IRMAR - Institut de Recherche Mathématique de Rennes

The logistic regression model is widely used to investigate the relationship between a binary outcome Y and a set of potential predictors X. Diop et al. (2011) present some conditions under which the maximum likelihood estimator is consistent and asymptotically normal in the logistic regression model with a cure fraction. So far, however, only limited simulation results are available to judge the quality of this estimator in finite samples. Therefore in this paper, we conduct a detailed simulation study of its numerical properties. We evaluate its accuracy and the quality of the normal approximation of its asymptotic distribution. We also study the quality of the approximation for constructing asymptotic Wald-type tests of hypothesis. Finally, we consider the problem of estimating the conditional probability of the outcome. Our results indicate that when the proportion of cured individuals is moderate to moderately large, and the sample size is large enough, reliable statistical inferences can be obtained for the regression effects and the probability of the outcome. Our results also indicate that the approximations can be problematic when the cure fraction is very large.

Mots clés: Zero-inflation; mixture model; maximum likelihood estimation

Domaines: Méthodologie [stat.ME]; Calcul [stat.CO]

Aba Diop, Aliou Diop, Jean-François Dupuy. A simulation study of maximum likelihood estimation in logistic regression with cured individuals. 2011. ⟨hal-00636486⟩