On some inferential issues for the destructive COM-Poisson-generalized gamma regression cure rate model

Abstract

In this paper, we assume the initial number of malignant cells to undergo a destructive process and hence what we record is only from the undamaged portion of the original number of malignant cells. This gives a realistic and practical interpretation of the biological mechanism of the occurrence of a cancerous tumor. We propose to model the initial number of malignant cells by the flexible Conway-Maxwell (COM) Poisson distribution, which includes some of the commonly used discrete distributions as its particular cases. Furthermore, we propose to model the time taken by each active malignant cell after an initial treatment by the wider class of generalized gamma distribution, which includes some of the commonly used lifetime distributions as its particular cases. The main contribution is in developing the likelihood inference based on the expectation maximization algorithm for such a flexible and general destructive cure rate model. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method. The flexibilities of the COM-Poisson distribution and the generalized gamma distribution are also utilized to carry out a two-way model discrimination using some likelihood-based methods. Finally, a melanoma dataset is analyzed for illustrative purposes.