EM Algorithm-Based Likelihood Estimation for Some Cure Rate Models

• Published in: Journal of statistical theory and practice Vol. 6; no. 4; pp. 698 - 724
• Main Authors: Balakrishnan, N., Pal, S.
• Format: Journal Article
• Language: English
• Published: Cham Taylor & Francis Group 01.12.2012; Springer International Publishing
• Subjects: Asymptotic variances; Conway-Maxwell Poisson (COM-Poisson) distribution; Cure rate models; EM algorithm; Exponential distribution; Lifetime data; Mathematics and Statistics; Maximum likelihood estimators; Probability Theory and Stochastic Processes; Profile likelihood; Statistical Theory and Methods; Statistics; Profile likelihood; 62P10; Conway-Maxwell Poisson (COM-Poisson) distribution; Exponential distribution; 62N02; Maximum likelihood estimators; Cure rate models; Lifetime data; EM algorithm; Asymptotic variances
• DOI: 10.1080/15598608.2012.719803
• ISSN: 1559-8608

In the recent work of Rodrigues et al. (2009) , a flexible cure rate survival model was developed by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. As the data obtained from cancer clinical trials are often subject to right censoring, the expectation maximization (EM) algorithm can be used as a powerful and efficient tool for the estimation of the model parameters based on right censored data. In this paper, the cure rate model developed by Rodrigues et al. (2009) is considered and assuming the time-to-event to follow the exponential distribution, exact likelihood inference is developed based on the EM algorithm. The inverse of the observed information matrix is used to compute the standard errors of the maximum likelihood estimates (MLEs). An extensive Monte Carlo simulation study is performed to illustrate the method of inference developed here. Finally, the proposed methodology is illustrated with real data on cutaneous melanoma.