Development, calibration, and external validation of a semi-Markov model for hypertension in older adults with Medicare coverage in the United States

Objective: To develop a semi-Markov model of hypertension specifically using estimates from primary analysis of Medicare data, and calibrate and validate using external trial and observational data. Methods: A semi-Markov model of hypertension with ten disease states was developed using clinical expertise and literature review: hypertension, myocardial infarction (MI), congestive heart failure (CHF), stroke, transient ischemic attack (TIA), other cardiovascular disease (CVD), chronic CVD, early-stage chronic kidney disease (ES CKD), late-stage CKD (LS CKD), and death. Most transition probabilities and hazard ratios for excess mortality were obtained from analysis of Medicare data (2018-2021). Transition probabilities and hazard ratios were calibrated against findings from the Systolic Hypertension in the Elderly Program (SHEP) trial and post-trial follow-up studies. Iterative grid search using Latin Hypercube Sampling was used for calibration, followed by a recalibration using Nelder-Mead simplex method with common random numbers. External validation was performed using mortality data after MI and stroke. Results: Final monthly transition probabilities from hypertension to other states were: other CVD (0.026), ES CKD (0.010), CHF (0.004), stroke (0.004), TIA (0.002), and MI (0.002). Final hazard ratios were: MI (3.29), CHF (3.99), stroke (3.79), TIA (1.39), other CVD (3.84), chronic CVD (1.39), ES CKD (1.24), and LS CKD (4.16). In the external validation, mortality rates per 100 person-years among stroke survivors were 7.8 (modeled) and 8.2 (observed). Conclusion: Our model was reasonably calibrated except for CHF incidence and stroke-related mortality. External validation showed the model performed well over longer timeframe, but discrepancies were observed for shorter periods.