Modeling chronic HBV infections with survival probability metrics

Abstract

Progressions of chronic diseases can be modeled as Markov processes. Frequently, the model parameters are concluded based on distinct short-term clinical studies because of the difficulty of observing the entire progression process in one clinical study. Though this piece-by-piece approach provides a global picture to the disease progression process, it could lead to unrealistic results under in-depth analysis. For instance, without careful calibration, patients’ life expectancy computed from the model might be longer than that of the general population. Such results usually arise from that the effect of population mortality is not sensible or not well included in these short-term clinical studies. For chronic diseases with which patients may experience a long chain of successive states, this inaccuracy is more obvious. Beck and Pauker propose that the population mortality may be integrated into a disease progression model in their work. Their method provides a solution to the aforementioned difficulty. However, their approach to integrate the population mortality into the model implicitly assumes that the population mortality solely affects the transition probabilities for transitions to the death state and for self-transitions remaining in the initial states. They do not explain why only these two types of transitions are affected by the imposed population mortality. From realistic situations, no matter what state transitions patients experience, they are all under the risk of death caused by population mortality. Based on this observation, a new modeling approach is proposed in this study. The proposed approach assumes that population mortality independently affects all state transitions of a Markov model. This extends Beck and Pauker’s idea and makes their method more reasonable.The proposed approach is applied to disease progression analysis of chronic hepatitis B virus (HBV) infection and considered for further applications. Specifically, with the natural history of chronic HBV infection originally described by a coarse Markov model a new model is developed by calibrating the coarse model with the proposed method. Numerical results show that the new model can obtain realistic estimates to patients’ life expectancy and survival probabilities. Meanwhile, the concept of first hitting time can find its interesting application in deriving the probabilities for patients’ first experiencing critical medical status during a specified duration. This delivers valuable information to chronic HBV patients. The model’s possible extensions such as its application to different countries and taking patients’ risk factors into account are also discussed for future study.