Open Access
2011 Maximum likelihood estimation in the logistic regression model with a cure fraction
Aba Diop, Aliou Diop, Jean-François Dupuy
Electron. J. Statist. 5: 460-483 (2011). DOI: 10.1214/11-EJS616


Logistic regression is widely used in medical studies to investigate the relationship between a binary response variable Y and a set of potential predictors X. The binary response may represent, for example, the occurrence of some outcome of interest (Y=1 if the outcome occurred and Y=0 otherwise). In this paper, we consider the problem of estimating the logistic regression model with a cure fraction. A sample of observations is said to contain a cure fraction when a proportion of the study subjects (the so-called cured individuals, as opposed to the susceptibles) cannot experience the outcome of interest. One problem arising then is that it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In this setting, a logistic regression analysis of the relationship between X and Y among the susceptibles is no more straightforward. We develop a maximum likelihood estimation procedure for this problem, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model. Then, we establish the consistency and asymptotic normality of the proposed estimator, and we conduct a simulation study to investigate its finite-sample behavior.


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Aba Diop. Aliou Diop. Jean-François Dupuy. "Maximum likelihood estimation in the logistic regression model with a cure fraction." Electron. J. Statist. 5 460 - 483, 2011.


Published: 2011
First available in Project Euclid: 23 May 2011

zbMATH: 1274.62480
MathSciNet: MR2802052
Digital Object Identifier: 10.1214/11-EJS616

Primary: 62J12
Secondary: 62F12

Keywords: asymptotic normality , consistency , maximum likelihood estimation , simulations , zero-inflation

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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