An EM algorithm for the destructive COM-Poisson regression cure rate model

• Published in: Metrika Vol. 81; no. 2; pp. 143 - 171
• Main Authors: Pal, Suvra, Majakwara, Jacob, Balakrishnan, N.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018; Springer Nature B.V
• Subjects: Computer simulation; Dispersion; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Poisson density functions; Probability Theory and Stochastic Processes; Regression analysis; Regression models; Statistical analysis; Statistics; Weibull distribution; Maximum likelihood estimates (MLEs); Profile likelihood; Long-term survivors; Competing cause scenario; COM-Poisson distribution
• ISSN: 0026-1335; 1435-926X
• DOI: 10.1007/s00184-017-0638-8

In this paper, we consider a competitive scenario and assume the initial number of competing causes to undergo a destruction after an initial treatment. This brings in a more realistic and practical interpretation of the biological mechanism of the occurrence of tumor since what is recorded is only from the undamaged portion of the original number of competing causes. Instead of assuming any particular distribution for the competing cause, we assume the competing cause to follow a Conway–Maxwell Poisson distribution which brings in flexibility as it can handle both over-dispersion and under-dispersion that we usually encounter in count data. Under this setup and assuming a Weibull distribution to model the time-to-event, we develop the expectation maximization algorithm for such a flexible destructive cure rate model. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method. Finally, a melanoma data is analyzed for illustrative purpose.