Transition probability estimation using repeated sampling from a fitted mixed model

Objectives: Markov model is one of the most used decision analytic models in health care. Transitions between health states in a Markov model is driven by transition probability matrix. When the number of patients and observed transitions are limited, transition probability estimation becomes challenging. The objective of this exercise is to demonstrate how transition probabilities can be estimated by simulating data from a statistical model fitted to patient-level data. Methods: An economic model for ranibizumab in mCNV secondary to pathological myopia (submitted to NICE in June 2013) was adapted for forthcoming Asian reimbursement submissions. BCVA (Best Corrected Visual Acuity) scores were available for limited number of East Asian patients (N= 35) from a phase III, 12-month, randomized, double-masked, multicenter, active-controlled study (RADIANCE). To populate a transition probability matrix with 8 health states based on BCVA scores, a statistical model was proposed to simulate a larger hypothetical patient cohort. A mixedeffect model was fitted on the observed BCVA scores with baseline BCVA score as covariate, patients as random effect and an autoregressive AR(1) error correlation structure amongst the repeated observations. This model was used to simulate a patient cohort of 35,000. Transition probabilities were estimated using traditional division by row sum method. Several simulations were run to confirm consistency of results. Results: From baseline to month 3, percentage of patients with BCVA ≥ 20 letters gain was 22.45% in observed data vs 22.49% in simulated data, and percentage of patients with BCVA ≥ 20 letters loss was 0.008% in observed data vs 0.009% in simulated data. BCVA change from baseline to month 3 in simulated data (mean= 13.3, SD= 8.3) was verified with that of the observed data (mean= 13.3, SD= 8.8). Conclusions: Transition probability estimation by simulation from a fitted statistical model can overcome the challenges posed by small patient cohorts and multiple state transitions.