Purpose: In clinical practice, treatment decisions for many diseases are based on the concept of risk stratification. In these situations, the question for decision analytic models is not whether all patients should be treated as a group, but rather how many patients should be treated when the group is stratified by risk.

Methods: We considered a general Markov chain in which patients progress from healthier (low-risk for death) to sicker (high-risk for death) states. We established conditions for the existence of a positive quasi-stationary distribution, in which the proportion of living patients in each of these risk-stratified states is positive at equilibrium even though all patients will eventually die. Any part of this distribution can be separately evaluated with standard Markov decision analysis to make broader inferences from narrow data and evaluate treatment with risk stratification. To illustrate, we chose a Markov chain previously derived from broad population data on heart failure patients receiving usual care and made inferences from recent but narrow data on high-risk patients in heart failure disease management trials.

Results: In the general chain, a unique positive quasi-stationary distribution exists over all risk-stratified states if and only if patients in the healthiest state have the lowest combined risk of progression or death. As predicted, in the heart failure model, patients in each risk-stratified state empirically settle at equilibrium proportions of all living patients. This quasi-stationary distribution allowed quantitative inference of patient risk in narrow trials and broader outcome evaluation over various patient risk groups. Comparing control hospitalization rates in disease management trials with broad population data, we inferred that trials have on average included only the riskiest quintile of patients. We further found that, although research and current guidelines focus on the riskiest heart failure patients, disease management is cost effective for all patients.

Conclusions: Quasi-stationary distributions in Markov chains can quantitatively define and evaluate treatment decisions along the whole spectrum of patient risk. Such evaluation is particularly useful in the absence of broad risk-stratified data and can yield unexpected findings for policy or further investigation.