Proposing a Weight-Based Expectation-Maximization Algorithm for Estimating Discrete-Time Markov Transition Probability Matrices with a Proof-of-Concept Example in Health Technology Assessment

Discrete-time Markov cohort-state transition models are now well-established as the preferred choice of analysts across application areas including health technology assessment. This preference arises out of its relative intuition and its capability to strike a fine balance between complex disease pathways, statistical precision, and parsimony although being criticized by a wide variety of stakeholders. Transition probability matrices (TPMs) are the “heart and soul” of such models responsible for estimating patient dispositions. However, estimating such TPMs comes with its own set of challenges. In some situations, the transition data may be censored such that the health state of a patient is unknown for multiple time steps before the next observation or data immaturity especially in rare diseases. Craig and Sendi proposed the expectation-maximization (EM) algorithm using uniform weights as a solution for unequal estimation intervals for partially observed data. However, this typically comes at the cost of increased within-state output variations with no optimization technique available in the literature.

The objective of this paper is to explore an optimized weighted version of the original EM algorithm, that aims to estimate the set of weights which minimizes the uncertainty of the estimated TPM against a target objective function. The weighting reduces the uncertainty of the estimate by considering the difference in temporal sparsity of the data when there are missing time steps. Further, we demonstrate the applicability of this weighting method using a fictitious cost-effectiveness model with our approach, showing a fine but definitive change over the original approach.