A new cure rate model with discrete and multiple exposures

Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2008, Tournoud and Ecochard first proposed a mechanistic formulation of cure rate model in the context of infectious diseases with multiple exposures to infection. However, they assumed a simple Poisson distribution to capture the unobserved pathogens at each exposure time. In this paper, we propose a new cure rate model to study infectious diseases with discrete multiple exposures to infection. Our formulation captures both over-dispersion and under-dispersion with respect to the count on pathogens at each time of exposure. We also propose a new estimation method based on the expectation maximization algorithm to calculate the maximum likelihood estimates of the model parameters. We carry out a detailed Monte Carlo simulation study to demonstrate the performance of the proposed model and estimation algorithm. The flexibility of our proposed model also allows us to carry out a model discrimination. For this purpose, we use both likelihood ratio test and information-based criteria. Finally, we illustrate our proposed model using a recently collected data on COVID-19.