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Augmenting Markov Cohort Analysis to Compute (Co)Variances: Implications for Strength of Cost-Effectiveness

Markov cohort analysis is a popular deterministic method in medical decision making for calculating mean outcomes in a Markov model by following a cohort of individuals through time. At present, obtaining outcome variances requires either forsaking cohort analysis in favor of a Markov decision process model or using Monte Carlo simulation (microsimulation), a more computationally demanding procedure that provides only statistical estimates. Here we derive an augmented version of cohort analysis that allows exact computation (not merely estimation) of (co)variances. In second-order models that incorporate parameter uncertainty, augmented cohort analysis can replace the “inner loop” required in Monte Carlo simulation, resulting in quicker and more accurate estimates. One reason for computing variances is to calculate a measure of the strength of an affirmative cost-effectiveness conclusion. In Markov cost-effectiveness analysis, an equivalent measure of cost-effectiveness is positivity of the expected incremental net monetary benefit. Augmented cohort analysis allows calculation of the number of standard deviations that this quantity falls above zero. As a measure of strength of cost-effectiveness, this quantity increases with cohort size. This means that the common practice of taking cohort size to be one can substantially underestimate the strength of a resulting cost-effectiveness conclusion under realistically large cohorts. Moreover, if realistic cohort size is large, then modelers can avoid microsimulation by using augmented cohort analysis and Chebyshev bounds to guarantee the probability of cost effectiveness is close to one.