Maximum Likelihood Estimation of Hidden Markov Model: Application To Markers of Infectious Disease Progression

Abstract

Hidden Markov models describe the probabilistic dependence between the latent state and the observed variable of a system. It is a stochastic model with a sequence of observable events where the underlying process that generates these events is unobserved. Hidden Markov models could be used to analyze the history of various diseases, including infectious disease progression.
These models in life experiments describe the disease evolution, estimate the transition rates, and evaluate the therapy effects on progression. In many cases, the states characterize the markers of the diseases. Parameter estimation is indispensable when using the hidden Markov model to model any dataset. In this work, the hidden Markov model is used to analyze the dataset of HIV-infected patients undergoing antiretroviral treatments at a university teaching hospital in Nigeria with different compliance levels. The model’s parameters were estimated using the maximum likelihood estimation (MLE) method. The variables are the CD4 counts and viral load results, often clinically characterized as markers of infectious diseases. The transition probabilities provide insights into the stability and dynamics of the hidden states, which is crucial for understanding the underlying processes modeled by the HMM. The results
indicate that stage 1 has a high probability of staying on that stage with ART treatment, whereas stage 2 has a higher chance of sliding to stage 3. The results also indicate a high chance of remaining in stage 3 once a patient is diagnosed with AIDS. The results show that
keeping the CD4 count up with antiretroviral treatments holds off symptoms and complications of the Human Immunodeficiency Virus (HIV) and helps patients live longer. These highlight the importance of maintaining an undetectable viral load with ART to ensure a healthy life  or HIV-infected individuals. Consequently, patient compliance in completing the treatment regimes is optimal.