Statistical Methods for Classification of Disease Recurrence with Transition of Markers

When an infectious disease recurs, it may be due to treatment failure or a new infection. Distinguishing and classifying 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 dissertation aims to demonstrate that the transition likelihoods of covariates can distinguish one cause from another with high accuracy in infectious diseases. A more general model for disease progression can be constructed to allow for additional information. We start from a multinomial logit model to estimate the disease recurrence probabilities and then utilize covariate’s transition information to provide a more accurate classification result. We apply the Expectation-Maximization (EM) algorithm to estimate unknown parameters. A simulation study comparing our classifier to the existing two-stage method shows that our classifier has better accuracy. The proposed method determines relapse vs. reinfection outcomes in P. vivax treatment studies from Cambodia to demonstrate its practical use. In the next project, we extend the idea of using transitional likelihoods to competing risk data when the cause of failure is unknown. This project presents a novel method for classifying the latent cause of failure under a semiparametric density ratio model in competing risks. In addition, transition likelihoods between covariates are used to provide a better classification result. The simulation results show that the proposed classifier performs well under all settings. We also apply the proposed method to the P. vivax malaria data. In our third project, we extend our previous inference methods to recurrent event data with multiple event types where event types may be partially missing. We estimate the regression coefficients in a renewal model where type-specific intensity functions are related to transient mark variables through a proportional hazards relationship and the baseline intensity is dependent of the gap time from immediately preceding event. We show that including transition likelihoods provides a more efficient estimator. Results are also illustrated with data from patients with Cystic Fibrosis (CF) who suffer from recurrent Pseudomonas Aeruginosa (PA) infections.