Markov cohort state-transition model: A multinomial distribution representation

TL;DR

This paper introduces a multinomial distribution representation for Markov cohort models, enabling faster and exact variance computation and Bayesian transition probability estimation, improving efficiency over traditional methods.

Contribution

It presents a novel multinomial distribution framework for Markov models, simplifying variance calculation and Bayesian estimation, which was previously computationally intensive.

Findings

Exact variance computation is significantly faster.

Bayesian transition probability estimation is improved.

The method is verified through simulation exercises.

Abstract

Markov cohort state-transition models have been the standard approach for simulating the prognosis of patients or, more generally, the life trajectories of individuals over a time period. Current approaches for estimating the variance of a Markov model using a Monte Carlo sampling or a master equation representation are computationally expensive and analytically difficult to express and solve. We introduce an alternative representation of a Markov model in the form of a multinomial distribution. We derive this representation from principles and then verify its veracity in a simulation exercise. This representation provides an exact and fast approach to compute the variance and a way to estimate transition probabilities in a Bayesian setting.