Probabilistic Cost-effectiveness Analysis with Bayesian Statistical Viewpoint

Background The recently proposed indicator of the probability being cost-effective for a specific intervention on treatment versus the comparator in acceptability curve used in probabilistic economic evaluation has been misinterpreted with frequentist viewpoint and had better be expounded by Bayesian framework that easily accommodate the uncertainty of acceptability curve since the estimate in the probability of being cost-effective in acceptability may vary with the ceiling ratio of willingness-to-pay (WTP). It is also interesting to examine how sub-group or individual-specific WTP measured by an empirical survey on WTP can answer the affordability given the WTP obtained from acceptability curve. Aim The thesis aimed to demonstrate how to derive 95% credible interval or relevant ranges of acceptability given frequentist viewpoint and Bayesian perspective by using sensitivity analysis of changing the ranges of parameter and developing Bayesian directed acyclic graphic (DAG) model, respectively. Bayesian cost-effectiveness acceptability curve was further used to measure sub-group or individual WTP for the treatment of interest. Material and method 1.Data sources: Data used for demonstration include (1) Anastrozole versus Tamoxifen for treatment of breast cancer abstracted from literature review on cost and effectiveness; (2) Acupressure versus Physical therapy for treating low back pain (LBP) on cost and effectiveness; (3) WTP for measuring Acupressure with covariates by using different methods (such as bidding method and binary method). 2.Methods (1)Analytic Markov decision model The framework of analytical Markov decision model was proposed in the light of both datasets. (2)Estimation Moment methods with beta-binomial and gamma distribution are used to derive both distributions given each study and the sensitivity of analysis by changing the range of parameter to derive the lower and upper limit of acceptability curve; (3)Bayesian DAG model was built to estimate the posterior joint distribution of both incremental cost and incremental effectiveness with inverse Wishart prior distribution and bivariate normal distribution. Results By using Markov decision model, Anastrozole used gained an additional 0.08 QALYs compared with Tamoxifen use. The incremental cost-utility ratio (ICUR) for Anastrozole use versus Tamoxifen use was $US-7,178 in deterministic approach. The variation of cost-effectiveness acceptability curve (CEAC) varied with the changing of assigned parameters. After applying Bayesian DAG model, the ICUR was $US-6,133 (95% CI: -182,200-148,400) for Anastrozole use versus Tamoxifen use. The results suggest cost-saving for Anastrozole use. At the lower bound of being cost-effective under the WTP of $20,000, the probability of being cost-effective (Pa) was equal to 0.80 identical to the likelihood of being cost-effective under the $10,000 of WTP. At the upper bound of being cost-effective under the WTP of $20,000, Pa was equal to 0.85 identical to the likelihood of being cost-effective under the $30,000 of WTP. Acupressure versus physical therapy for low back pain resulted in an ICUR of NTD $12,490 (95% CI: 5,465-40,560) per life-year gained. Pa for acupressure under the WTP of $NTD12,000 was 51% (95%CI: 0.48-0.54). A total of 370 patients with prior experience of low back pain was directly interviewed with open-ended bidding-game questions for WTP for a novel therapy to relief 25% (n=81), 50% (n=112), 75% (n=78), and 100% (n=99) pain. The amount of WTP increased with degree of pain relieved from NTD 3,764 for 25% relief, NTD 10,866 for 50% relief, NTD 11,962 for 75% relief, and NTD 16,167 for 100% relief. With further adjustment with age, gender, income, and current pain score, the degree of pain relief was still a significant factor for WTP. Older age, higher income, greater suffering pain, and male were related to higher WTP. Pa was estimated given an additional cost of a new treatment per visit, denoted as unit cost. When unit price set as NTD200, NTD 500, and NTD1,000 for comparison, the corresponding Pa were 84% (95%CI=0.82-0.86), 43% (0.41-0.45), and 16% (0.15-0.18), respectively. On the other hand, the WTP should achieve NTD 122 (95% CI: -339, 588), 4,781 (95% CI: 4,485, 5,129), and 13092 (95% CI: 11,900, 14,539) given unit price of NTD 200, 500, and 1,000 in order to have more than 50% chance of being cost-effective. These figures enabled decision maker to identify those who were affordable for the therapy. The affordable score (AS) for predicting the WTP of acupressure was developed and generated by the multivariate regression model making allowance for significant covariates. The affordable score was 84.2 given WTP of NTD12,000 which is the amount of WTP while Pa is 50%. Subject with affordable score greater than 86.4 was more tolerant to accept acupressure therapy given WTP of NTD 12,500 (upper limited of 95% CI) which can be regarded as an optimist. On the other hand, subject with affordable score under 84.2 was not willing to accept acupressure therapy given WTP of NTD 11,500 (lower limited of 95% CI) which can be regarded as a pessimist compared with those who had affordable score over 84.2. Conclusions The novel Bayesian DAG model for CEA was developed to estimate the credible interval (the uncertainty) of acceptability curve varying with the ceiling ratio of WTP which could possibly be changed by individual characteristics. The individual-specific WTP estimated from this study is able to infer the affordability given the WTP obtained from Bayesian acceptability curve.