機率性成本效益分析貝氏統計觀點

Abstract

研究背景 經濟評估在於比較新治療方案與對照組間何者更具成本效益。透過機率性成本效益分析，可得知新治療方案在成本效益可接受曲線(acceptability curve)給定不同的願付額(willingness-to-pay)下，其具成本效益的機率。然而這個統計指標在頻率學派統計觀點下易受到錯誤的解釋。而藉由貝氏學派統計觀點，將可以更輕易描述及處理在成本效益可接受曲線中，若願付額變動時，對此統計指標之不確定性(uncertainty)所造成的影響。另外，令人感到興趣的是，在透過實證研究觀測到不同子群體或個人的願付額度後，可以透過成本效益可接受曲線得知子群體或個人的可承擔能力。 研究目的 本研究目的為透過頻率學派及貝氏學派觀點，分別以改變參數範圍之敏感度分析以及建構貝氏有向非循環圖模型(Bayesian directed acyclic graphic model)的方法去得到可接受曲線之95%可信區間或負擔能力的區間範圍。而經由貝氏統計觀點所建構的成本效益可接受曲線，可以更進一步測量有興趣的子群體或個人的願付額度。 材料與方法 1.資料來源：本研究中使用的資料包含(1)在乳癌手術後荷爾蒙輔助性治療案例中，從文獻回顧所得到的成本與效益資訊。(2)比較穴位按摩與物理治療緩解下背痛之研究的成本與效益資訊。(3)利用不同方法(如競標法(bidding method)和二項選擇法(binary method))對於穴位按摩治療所測量之願付額以及其他相關變數。 2.方法 (1)馬可夫決策分析模型 建構馬可夫決策分析模型進行乳癌及下背痛治療之決策模型。 (2)估計 使用Beta-binomial分佈及Gamma分佈之動差法推導及藉由敏感度分析變動參數來得到可接受曲線之信賴範圍之上、下界。 (3)建立貝氏有向非循環圖模型,並利用Wishart事前分布與雙元常態分配去估計成本與效益雙元變項之事後分佈. 研究結果 藉由馬可夫決策模型可知，在決定性(deterministic)成本效益分析中，使用Anastrozole作為術後荷爾蒙治療相對於Tamoxifen將額外增加0.08生活品質調整人年，成本效用比(ICUR)為-7,178美元。可接受曲線會隨模型中的參數設定變動而變動。而在透過貝氏有向非循環圖模型進行分析後，成本效用比為-6,133(95%CI:-182,200-148,400)美元。結果顯示使用Anastrozole是節約成本的。在願付額度為20,000美元下，其具成本效益的機率之下界為0.8，與在願付額度為10,000美元下具成本效益的機率相同。而在願付額度為20,000美元下，具成本效益的機率之上界為0.85，與在願付額度為30,000美元下具成本效益的機率相同。在比較穴位按摩及物理治療緩解下背痛的案例中，每增加一單位人年之成本效用比為新台幣12,490(95%CI:5,465-40,560)元。在願付額為新台幣12,000元下，具成本效益的機率為51%(95%CI:0.48-0.54)。 針對370位有下背痛經驗的患者，透過面訪及使用競標法問卷來了解患者在使用新療法下對不同緩解程度(25%(81人)、50%(112人)、75%(78人)、100%(99人))之願付額。願付額會隨著緩解程度增加而增加，當緩解程度達25%時，願付額為新台幣3,764元、達50%時，願付額為新台幣10,866元、達75%時，願付額為新台幣11,962元、達100%時，願付額為新台幣16,167元。當更進一步調整年齡、性別、收入、當前疼痛分數後，緩解疼痛程度依然是顯著影響願付額度的因素。其中，較年長、高收入、疼痛分數較高以及男性患者，有較高的願付額度。而當單次療程花費為新台幣200元、500元及1000元時，具成本效益的機率分別為84%(95%CI:0.82-0.86)、43%(0.41-0.45)、和16%(0.15-0.18)。另一方面，在單次療程花費為新台幣200元、500元及1000元時，欲使具成本效益之機率大於50%，願付額度需達新台幣122元(95%CI:-339-588)、4,781元(95%CI:4,485-5,129)、及13,092元(95%CI:11,900-14,539)。這些描述能夠讓決策者了解在此治療下有那些人是可負擔的。 本研究進一步考量相關因素下以多變量廻歸模型發展及預測接受願付額分數(affordable score)。當成本效益機率為50%時，相對穴位按摩治療，當願付額為12,000元下，接受願付額分數為84.2分。而當願付額為12,500元時(95%信賴區間上限)，接受願付額分數則增加為86.4分，超過這分數的群體，我們可視為接受願付額之樂觀主義者。相對地，若願付額為11,500元時(95%信賴區間下限)，接受願付額分數亦為84.2分，顯示小於84.2分下的群體可視為接受願付額之保守主義者。 結論 新穎的貝氏有向非循環圖模型分析於經濟評估的發展可應用於估計因人而異之願付額成本效益下成本效益可接受曲線的可信區間(不確定性)。透過本研究所估計之個人化願付額可用於評估個人在此付費額下個別的負擔能力。

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.