### The context of the case study is as follows

The cost-effectiveness model has been described elsewhere (Fig. 1) [9]. Briefly, a Markov cohort model was built in Microsoft Excel with eight health states for schizophrenia (hereinafter referred to as the Mohr-Lenert health states) defined by Mohr et al. in 2004 and a death state [10]. The definition of the health states can also be found in a concise format in Table 2 of the paper presenting the cost-effectiveness model [9]. As the pivotal clinical trial in which the model was based on provided no data on mortality, as there were not any participants who died during the study period, the age- and sex-specific mortality rates of the general population were used in the model, and no difference in the mortality between the two treatment groups was assumed [11]. Considering the pharmacokinetic properties of cariprazine [12], the modelled time period was split into two periods: an initial 6-week time period with weekly cycles and 12-week long cycles occurring thereafter. Because the full clinical effects of cariprazine are expected to occur after the first 6 weeks, different transition probabilities were necessary for the first 6 weeks and for the subsequent model time period. Because the aim of this paper is to present a method of estimating the transition probability matrix for Markov models based on both expert opinion and clinical trial data, we used only the first 6-week period as an illustration of the method. The same method was applied for the subsequent period but with different observed data and prior probabilities.

Data to estimate the weekly transition probabilities for the first 6 weeks of the modelled time period for both the cariprazine and the risperidone arms were available from the first 4-week period of the Németh et al. clinical trial [11]. In the original publication, the model was used to estimate the utility of the cariprazine treatment compared to the risperidone treatment.

### Prior elicitation

The prior probabilities in the transition matrix were elicited with the involvement of three leading clinical experts from Hungary who are actively involved in treating patients with schizophrenia and have deep insight into the typical courses of the disease (IB, BM, JR), and who were involved in the project. An additional criterion at the selection was to have considerable research experience. The prior probabilities were elicited using Prior Elicitation Graphical Software (PEGS) [8]. The feasibility of using the application, and the process of the elicitation was pilot tested without the involvement of the experts. The definitions of the Mohr-Lenert health states were explained to the experts. Besides this information given verbally, and the technical description of the exercise there were not any additional information given to the experts regarding the transitional probabilities between the studied health states. Then, the experts were asked individually face-to face to give their opinion about the probabilities of patients with predominantly negative symptoms of schizophrenia moving from a given Mohr-Lenert health state to another state conditional on the comparator treatment (i.e., risperidone). The experts were aware of main results of the clinical trial regarding the efficacy of cariprazine, but they were unaware of the trial results about the transition probabilities between different Mohr-Lenert health states. At each step we verified whether the experts understood what they had to assess (i.e., the descriptions of the patients in a certain state, which was used as the current state, and that they had to estimate the proportion of patients moving from this state to another state). In the assessment process, all experts were asked to assess the marginal medians and quartiles of the probability of each transition. Because directly estimating these statistics is difficult for clinical experts, we elicited this information by asking the following questions. For the median, the question was phrased as follows: “Considering patients in state A, what is the most likely proportion of patients moving to state B within one week during the first six weeks of treatment? Consider it equally likely that the true proportion is above this value or below this value. For example, suppose you assess this value as 0.4, you should think it is equally likely that the true proportion will be above 0.4 as it will be below 0.4.” For the lower quartiles, the question was phrased as follows: “If you were told that the true proportion was smaller, what is the value that you think is still reasonable? Estimate a proportion for which it holds that the probability that the true proportion is below equals the probability that the true proportion is between it and 0.4 (the median)”. Similar questions were asked to assess the upper quartiles.

In the next step, the experts were told that “the probabilities of the different patient movements from a given health state must add to one, and the assessments must also meet certain other requirements to be internally consistent. The application gives you three options for reconciling your assessments to meet these requirements. Select the one which best represents your opinion.” Once a clinical expert made a choice about these options, he or she was confronted with the result. Then, he or she still had an opportunity to change any quartiles. After the modifications, the application again calculated the coherent marginal quartiles for the Dirichlet distribution and presented them together with the expert’s revised values. Finally, when the expert thought that the proposition was in line with his or her view, the application presented the estimated transition probabilities with their variance and the hyperparameters of the Dirichlet distribution.

As the same prior was later used for modelling patients’ paths in the cariprazine arm, the difference in treatment efficacy originated only from the trial data. The estimated transition probabilities by the three experts were averaged and scaled to one person in each source state, ensuring high uncertainty of the prior probabilities and thereby allowing a large influence of the clinical trial data.

### Estimation of the transition probability matrix

The transition probability matrix was finally estimated by WinBUGS based on the priors and the clinical evidence from the trial with 1000 burn-in samples and 50,000 estimation samples; see the code in (Additional file 1). Two chains were run, and convergence was assessed by visual inspection of the trace plots and by tracking the Brooks-Gelman-Rubin diagnostics.

We generated the treatment-specific transition probability matrices for the Markov model in three different ways: (1) based only on the observed clinical trial data (transition probabilities not observed within the trial were set to 0); (2) based on Bayesian estimation where prior transition probabilities came from experts’ opinions (as described previously); and (3) based on Bayesian estimation with vague prior transition probabilities (flat Dirichlet prior distributions). Furthermore, we compared the transition probability matrices and the incremental quality-adjusted life years (QALYs) across the three approaches.