Post-thrombotic syndrome (PTS) is a chronic venous disease that can occur after deep-vein thrombosis and substantially impacts on quality of life. This paper develops and extends Markov Chain Monte Carlo (MCMC) methods (Welton 2005) to estimate the rates of transition between PTS health states using published summary data. A clinical study reported aggregate baseline and follow-up outcomes for 97 PTS patients, of whom 46(47%) were severe and 39(40%) moderate PTS (Black 2018). After 2 years, 7 were severe, 6 moderate, 22 mild and 18 had no PTS, with 44 missing data. A MCMC model was constructed in Winbugs to estimate the underlying rates of transition between severe PTS to moderate (r1), moderate to mild (r2) and mild to no PTS (r3), taking account that transitions are unobserved and assuming missing data were missing completely at random. The set of Kolmogorov forward equations required to map between transition rates and probabilities were calculated algebraically using matrix decomposition (Jones 2017). The MCMC model estimated mean (standard error) rates of r1=0.52(0.23), r2=2.16(0.50), and r3=0.83(0.21). These rates make predictions that fit reasonably well with the observed data at 2 years, predicting with the same baseline patients, 7 severe, 5 moderate, 23 mild and 18 no PTS at 2 years. The MCMC model made estimates that fit well with observed data to be used as baseline rates in a state-transition decision model. The advantage of estimating rates using MCMC rather than other methods for obtaining transition probabilities (e.g. assuming a multivariate Dirichlet distribution) is that rates can be directly multiplied by relative treatment effects obtained from literature review of randomized controlled trials, and permit more straightforward extrapolation beyond the time horizon of the original study.