Health economics · Reporting

State-Transition (Markov) Diagram & Cohort Trace

The structure of a Markov cost-effectiveness model (states and transition probabilities) alongside its cohort trace — the share of the cohort in each state over model cycles.

Download SVG Open code and full worked example

When to use it

To document and sanity-check a state-transition economic model. The diagram communicates structure; the trace verifies the model behaves sensibly (membership sums to 1 each cycle, the absorbing state fills monotonically) before costs/QALYs are attached.

How to read it

Diagram arrows are per-cycle transition probabilities (rows of the transition matrix sum to 1). In the trace, each band is a state's share over time; a well-formed model drains transient states into the absorbing (Dead) state.

Worked example

A 3-state model (Stable → Progressed → Dead) with a transition matrix is run for 40 monthly cycles starting from everyone Stable. Each cycle the state vector is multiplied by the transition matrix to produce the next cycle's membership.

Transition matrix rows: Stable [0.80, 0.15, 0.05]; Progressed [0, 0.80, 0.20]; Dead [0, 0, 1]. Start state = [1, 0, 0].

Result: After one cycle the cohort is [0.80, 0.15, 0.05] (1×0.80, 1×0.15, 1×0.05); after two cycles Stable = 0.80×0.80 = 0.64. Over 40 cycles the trace drains into Dead, with Progressed peaking mid-horizon — the expected, well-behaved shape.

Produced by

Markov transition probabilities Partitioned survival models

Reference: Gatto NM, Wang SV, Murk W, et al. Visualizations throughout pharmacoepidemiology study planning, implementation, and reporting. Pharmacoepidemiol Drug Saf. 2022;31(11):1140-1152.