Classification of disease recurrence using transition likelihoods with expectation-maximization algorithm

When an infectious disease recurs, it may be due to treatment failure or a new infection. Being able to distinguish and classify these two different outcomes is critical in effective disease control. A multi-state model based on Markov processes is a typical approach to estimating the transition probability between the disease states. However, it can perform poorly when the disease state is unknown. This article aims to demonstrate that the transition likelihoods of baseline covariates can distinguish one cause from another with high accuracy in infectious diseases such as malaria. A more general model for disease progression can be constructed to allow for additional disease outcomes. We start from a multinomial logit model to estimate the disease transition probabilities and then utilize the baseline covariate's transition information to provide a more accurate classification result. We apply the expectation-maximization (EM) algorithm to estimate unknown parameters, including the marginal probabilities of disease outcomes. A simulation study comparing our classifier to the existing two-stage method shows that our classifier has better accuracy, especially when the sample size is small. The proposed method is applied to determining relapse vs reinfection outcomes in two Plasmodium vivax treatment studies from Cambodia that used different genotyping approaches to demonstrate its practical use.