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TRA-2-5
*TOP RANKED ABSTRACT AT THE 15TH BIENNIAL EUROPEAN MEETING* COMBINING MARKOV STATES: A COMPARISON OF ANALYTICAL AND HEURISTIC METHODS FOR DERIVING THE HAZARD RATES OF A COLLAPSED MARKOV STATE

**To capture clinically relevant health states in Markov models, modelers may need to combine k states with constant hazard rates (HR) into one (collapsed) state. We introduce and compare two methods for deriving correct HRs for the collapsed states and apply them to a progression model for chronic hepatitis C (CHC).**

**Purpose:**** Methods: **Heuristically, a constant HR for leaving the collapsed state can be derived by equating the mean dwelling time (MDT) in the collapsed state to the sum of the MDT in the k states and then inverting the sum of MDT. In method 2, we observe that the distribution of the sum of the dwelling times of a continuous-time Markov model with k states and constant HRs is mathematically equivalent to that of a 1-state model with a time-dependent HR derived from the k HRs (a generalized-Erlang distribution). We analytically derived the HR of the generalized-Erlang distribution to compute the HR of the collapsed state. We applied both methods to collapse the following states in our CHC model: mild CHC from Metavir-stages F0 and F1 and moderate CHC from stages F2 and F3. The HRs of progressing from mild to moderate CHC and from moderate CHC to cirrhosis were derived from the Metavir-stage-specific HRs. To compare the accuracy of each method, we calculated the absolute and relative differences in MDT (metric-1) and the relative differences in the distributions of health states across all cycles (metric-2) between the models with the collapsed and separated states.

** Results: **The analytical and the heuristic methods yielded absolute (relative) differences in MDT of 0.006 (0.03%) and 1.21 (6.54%) years, respectively. In terms of metric-2 which considers the timing of events, the analytical method generated a significantly lower relative error than the heuristic method, 0.04% vs. 49.75%. The heuristic method became less accurate in reproducing the correct distributions of states at all cycles since the method used a constant HR in the collapsed state.

** Conclusions: **Time-dependent HR of the generalized-Erlang should be used for collapsing states to accurately reproduce the MDT and the cycle-specific distribution of states.