個⼈化成本效益分析:運⽤⾙⽒推理之隨機過程

Personalized Cost-Effectiveness Analysis with Bayesian Reasoning-based Stochastic Process

楊昆澈(Kuen-Cheh Yang)

指導教授 ： 陳秀熙

國立臺灣大學/公共衛生學院/流行病學與預防醫學研究所/博士(2016年)

https://doi.org/10.6342/NTU201601310

摘要

背景
隨著以隨機分派試驗(RCT)為基礎之實證醫學(EBM)演進以及個人化預防醫學與治療策略之發展，精確醫學(precision medicine)在近年來益發受到矚目並顯現其重要性。作為實證醫學中重要一環，對於包含現有以及新近發展之醫療方法與技術之經濟評估(成本-效益分析, cost-effectiveness analysis (CEA))亦趨向於個人化之發展。然而在發展個人化經濟評估(individually-tailored CEA, ITCEA)上，需克服兩個重要的議題：對於效益以及成本之考量，特別是多面向(multi-dimensional)之結果，無法僅利用隨機分派試驗所得到之資訊進行個人層面之推論；以及缺乏可運用於個人之成本效益推論與評估方法。這些問題的最佳解決方法為運用隨機過程建構出如同隨機分派試驗一般的對照組並結合貝氏方法進行個人化之策略評估與推論。

目標
為發展ITCEA，本論文之主要目的在於
• 發展貝氏多項模式(phase-type model)以釐清多階段疾病進程之時序發展以利運用ITCEA於初段(預防性)介入；
• 發展貝氏寇斯多項模式(Coxian phase-type model)以釐清多階段疾病進程之時序發展並運用ITCEA於次段(疾病篩檢)介入策略；
• 進而發展貝氏多項模式(phase-type model)於多階段疾病進展結合ITCEA於具有多面向(multi-dimention)效益以及成本考量之三段(治療)介入。
• 本研究將上述發展之貝氏模式結合ITCEA實際運用於下述之實證資料:
• 運用所發展之第一項統計模式(多項隨機過程(phase-type stochastic process))於以系統性文獻回顧萃取之關於運用疫苗預防阿茲海默症(Alzheimer’s disease,AD)對於包含性別與年齡從輕度到死亡之實證結果；
• 以系統性文獻回顧萃取包含分子生物以及臨床與人口學層面之多種乳癌風險因子之實證結果以整合科學方法產生以乳癌攝影篩檢之實證資料並以第二項統計模式結合貝氏寇斯多項模式將各個風險因子作用於正常到臨床症前期(PCDP)以及由臨床症前期到臨床期(CP)之效果納入模型考量發展ITCEA；
• 運用整合科學產生巴金森氏症(Parkinson’s disease)治療策略中包含三個面向之效益(死亡人數、生活品質，以及unified Parkinson's disease rating scale (UPDRS)動作分數)以及成本之實證資料，結合貝氏多項模式(phase-type model)於多階段疾病進展發展多面向之ITCEA。

材料與方法
本研究運用包含多項過程(phase-type process) 與 寇斯多項過程 (Coxian phase-type process) 之隨機模型建構阿茲海默症、乳癌以及巴金森氏症之疾病自然進程。藉由此一疾病自然進程，本研究進而以模擬對照組對初段預防策略、次段預防策略以及三段於防策略之效益進行評估。疾病自然之建構亦採用多項分佈(multinomial distribution)結合多項式回歸(polytomous regression)以將個人可量測之變異納入模型考量中。研究中亦運用隨機效應模式(random effect model)已將個人無法量測之變異納入。基於貝氏架構下發展個人化成本效益分析(ITCEA)並且以增量成本效益比(ICER)作為評估指標，除此之外，研究中更運用重參數化來建構淨貨幣效益 (net monetary benefit (NMB))， NMB (λ)=λΔe-Δc， 並據以發展貝氏成本效益接受曲線(CEAC)作為成本效益評估方法。
再者，本論文提出多維淨效益的概念用在結果的評量超過一個面向的狀況，以主要結果所對應的付費意願上限比率為主，並計算其他面向結果相對於主要結果的付費意願上限比率比。然而，由於成本參數往往呈現極端的右偏分佈，再者其數值範圍與效益差距頗大，因此我們進一步利用付費意願對數轉換上限比率得到淨效益與增加對數轉換成本及增加對數轉換效益之關係。我們利用貝氏非循環圖形模式及馬可夫蒙地卡羅模擬方法得到多變量常態分佈淨效益的模擬結果。
本研究利用所發展之ITCEA以及貝氏架構於阿茲海默症疫苗策略、以乳房攝影之乳癌篩檢以及巴金森氏症之經濟評估。
對於阿茲海默症疫苗策略評估，本研究模擬一包含50%輕度狀態與50%中度狀態之族群。資料中亦藉由文獻資料將年齡以及性別分佈納入考量。研究比較疫苗施打策略與無疫苗施打之個人化成本效益。
藉由整合科學方法模擬包含不同影響疾病發生與進展之生物風險因子與腫瘤特性因子之族群，本研究進行貝氏機率性個人化成本效益評估，比較統一進行每年篩檢、每兩年、每三年、四年以及六年一次之篩檢計畫)以及與個人化之篩檢策略與不進行篩檢做比較。
晚期巴金森氏症治療方法之成本效益分析，考慮的治療方法包括多巴胺用藥、腦深層電刺激術及延遲治療，效益面的評量則是多維的，包括巴金森症狀衡量表第三部份(UPDRS III)動作分數、生命調整人年(QALY)及死亡。本論文利用馬可夫鏈蒙地卡羅電腦模擬方法在考慮參數的不確定性及個人隨機誤差之下，模擬一個5332名H-Y分期第四期以上的巴金森氏症個案於十年內在不同治療策略下的累積成本及累積效益。

結果
運用疫苗預防阿茲海默症之個人化成本效益分析，以一般頻率統計方法調整年齡及性別後，與完全無疫苗施打介入相比較，每增加一個人年其增加成本效益比為$17,604。以貝氏統計方法估計，其以隨機效應模式及無隨機效應模式分析，每增加一個人年之增加成本效益比分別為$19,270 (95% CI: -33,320-44,400)及$19,330 (95% CI: -32,570-44,320)。進一步利用貝氏分析且調整年齡及性別後，其每增加一個人年之增加成本效益比將從$19,330增加至$37,680(95% CI: 14,460-78,560)。
根據貝氏觀點而言，以貝氏隨機效應模式進行分析，成本效益機率為50%時，其願付額為$30,000；如果以一般頻率統計方法進行分析，則願付額為$23,800。以一般頻率統計方法，其成本效益機率為95%時，其願付額為$46,300。在我們的研究中，一般頻率統計方法與貝氏方法，個人化成本效益之增加成本效果比及接受曲線確實有顯著差異存在。然而，不論是一般頻率方法或貝氏統計方法，在阿茲海默症疫苗研究中皆顯示在女性及較年輕族族較為具有成本效益。
以乳癌篩檢為例，個人化篩檢策略結合不同篩檢時間間隔，每增加一人年 (life year, LY)其增加成本效益比(ICER)為$51,742 ($50,634 - $52,850)， 該增加成本效益比都比兩年一篩($63,777/LY)、三年篩檢一次($55,593/LY)及每年篩檢($82,514/LY)都低，且與四年篩檢一次的增加成本效益比相當接近($53,165/LY)；但比起六年篩檢一次的高($43,781/LY)。利用貝氏方法進行估計，其產生結果與一般頻率估計方法相近。然而，在付費意願為$47,000情況下，個人化成本效益接受曲線(CEAC)與每六年篩檢一次區線相交叉，研究結果顯示具有成本效益之機率為0.7。
在末段治療的例子中，本論文比較多巴胺用藥、腦深層電刺激術及延遲治療對晚期巴金森氏症的成本與效益，其中效益的評量是多維的，包括巴金森症狀衡量表第三部份(UPDRS III)動作分數、生命調整人年(QALY)及死亡。結果發現相較於延遲治療，多巴胺用藥有機會是成本節約(Cost-saving)的策略，腦深層電刺激術在每減少一分UPDRS III、每增加一個QALY及每避免一個死亡所需的平均增加成本效益比分別為$102-$1,208, $1,147-$9,490及$10,414-$102,749。若與多巴胺用藥相比，則腦深層電刺激術相對應的平均增加成本效益比則分別增加至$1,069-$5,751、$11,635-$38,607， 和$109,524-$469, 299。
若將三種結果測量同時考慮，則以上三種可能的策略比較組合在成本效益接受曲線(cost-effectiveness acceptability curve, CEAC)上均較單一結果測量平緩。當付費意願對數轉換上限比率達6以上，腦深層電刺激術會較多巴胺用藥具成本效益。相較於延遲治療，具成本效益的比率欲達到50%的付費意願對數轉換上限比率在多巴胺用藥及腦深層電刺激術分別為4.4及5.3。而與多巴胺用藥相比，腦深層電刺激術的付費意願對數轉換上限比率則需達6.2。

結論
本研究為首篇運用貝氏多項模式以及寇斯多項模式將包含時序訊息之疾病多階段進程納入考量並且進一步據以發展對於初段預防(疫苗預防策略)、次段預防(篩檢)以及三段預防(治療)且涵蓋多面向效益與成本之個人化經濟評估分析方法(ITCEA)。本研究在貝氏架構下運用前述兩種隨機模式結合個人化經濟評估方法，以增量成本效益比(ICER)、成本效益平面圖(C-E plane)，以及成本效益接受曲線(CEAC)評估在不同次族群(以個人層級變項區分)、除變項外之個人變異(random effect)以及不同的事前分佈於評估施打疫苗之策略對於減少阿茲海默症之個人化成本效益。本研究亦展現了如何運用系統性文獻回顧結合整合科學方法產生具有包含不同風險因子訊息之乳癌疾病進展與乳房攝影篩檢實證資料，並據以獲得對於不同篩檢間隔策略下之個人化篩檢策略以及運用整合科學方法產生對於巴金森氏症治療策略之多面向之效益(死亡人數、生活品質，以及UPDRS動作分數)以及成本之實證資料並據以進行多面向之成本效益分析。

關鍵字

隨機過程 ； ⾙⽒分析 ； 成本效益分析 ； 個⼈化醫療 ； 阿茲海默症 ； 乳癌篩檢 ； 巴⾦森⽒症

並列摘要

Background
Precision medicine has gained momentum under the context of individually-tailored preventive and therapeutic strategies evolving from evidence-based medicine that mainly relies on randomized controlled trial (RCT). Economic appraisal (cost-effectiveness analysis (CEA)), one of main elements of EBM, of the existing and the newly proposed interventions has been also diverted toward client-oriented values. There are two main obstacles for personalized CEA, including inability to merely rely on data on effectiveness and costs from RCT, particularly multi-dimensional costs and efficacies, and lacking of individualized-reasoning-based statistical methods. The panacea for tackling these issues related to individually-tailored CEA (ITCEA) is the better use of stochastic process to create pseudo-control group similar to the control group from RCT and Bayesian reasoning method for individual inference.
Objectives
To achieve statistical aims in ITCEA, this thesis were to
• develop a Bayesian phase-type model to delineate temporal course of multi-state disease progression for ITCEA on primary (prophylactic) prevention;
• develop a Bayesian Coxian phase-type model to delineate temporal course of multi-state disease progression for ITCEA on secondary (screening) prevention;
• develop a Bayesian phase-type model to delineate temporal course of multi-state disease progression for ITCEA on tertiary (therapeutic) prevention considering multi-dimensional costs and efficacies.
• To demonstrate how to apply the proposed Bayesian models to ITCEA, we aimed to:
• retrieve empirical data on age-gender-specific clinical course, costs and efficacy of vaccination in ameliorating the progression of Alzheimer’s disease from systematic literature review to illustrate the first statistical aim by building up a phase-type stochastic process from mild to death;
• synthesize various empirical data sources on risk profiles from bench to bedside and costs of breast cancer with mammography screening from systematic literature review to illustrate the second statistical aim by building up a Coxian phase-type stochastic process from the pre-clinical detectable phase (PCDP) to the clinical phase (CP) with the incorporation stage-specific covariates;
• synthesize various clinical data sources on three dimensional outcomes (number of death, quality of life years, and unified Parkinson's disease rating scale (UPDRS) motor score) and costs of treating Parkinson’s disease (PD) by building up a phase-type stochastic process from mild to severe Hoehn-Yahr (H-Y) of PD.

Material and Methods
By using the stochastic models including the phase-type process and the Coxian phase-type process, the natural history of multistate disease progression for diseases including Alzheimer’s disease (AD), breast cancer, and Parkinson’s disease were constructed. Based on the pseudo-control group derived from disease natural history the efficacies of primary prevention, secondary prevention, and tertiary prevention strategies were evaluated. The disease progression was modelled using multinomial distributions and also in conjunction with polytomous regression to incorporate the heterogeneity of measured covariates. A random-effect model was also applied to capture the individual unobserved variation. The ITCEA with Bayesian cost-effectiveness analysis underpinning using incremental cost-effectiveness ratio (ICER) were then illustrated. The ITCEA was further evaluated using the net monetary benefit (NMB) derived from reparameterization of NMB (λ)=λ∆e-∆c which was further summarized Bayesian acceptability curve, A (λ)=P(NMB (λ>0| y).
In order to cope with the scenario that outcome measure could be multiple dimensions, we proposed the idea of multiple-dimension net monetary benefit (NMB) considering the ceiling ratio of willingness to pay (WTP) for the main measure of effectiveness (λ1) and relative weight of further measures of effectiveness (λ2/λ1, λ3/λ1,…,λk/λ1 ), which refers to that an increase one unit in the secondary effectiveness is equivalent to an increase of λ2⁄λ1. Because cost is often a skewed distribution and generally greater than effectiveness, we further proposed the transformed ICER (β), and correlate the NMB to willingness to pay, incremental logarithm function of cost, and incremental logarithm function of effectiveness. We used Bayesian directed acyclic graphic model (DAG) with Markov Chain Monte Carlo (MCMC) method to simulate NMB (yij), which follows a multivariate normal distribution, with data on incremental logarithm function of cost and effectiveness given a series of βj.
The synthesis of various data sources on the effectiveness of ITCEA were applied to the vaccination for AD, screening for breast cancer with mammography, and therapeutic strategies for Parkinson’s disease.
For the illustration of AD, we simulated a cohort consisted of 50% mild state and 50% moderate state. Data on age and gender were also generated to test the ITCER with and without adjustment for age and sex, and random effects. The intervention of active immunization was compared with the unvaccinated group.
The probabilistic CEA for mammography screening was performed to a hypothetical female cohort with heterogeneous risks profiles due to varying combination of risk genes, tumor phenotype and conventional biological factors, either acting as initiators or promoters. The alternative strategies included universal screening program (annual, biennial, triennial, four-yearly, and six-yearly program) and personalized screening compared to no screening.
The therapeutic strategies for treating severe Parkinson’s disease included deep brain stimulation of sub thalamic nucleus (DBS-STN), medication, and delayed treatment. The outcomes were measured in terms of the unified Parkinson's disease rating scale (UPDRS) III motor score, quality-adjusted life year (QALY) and death. The accumulated cost and effectiveness were simulated using Markov Chain Monte Carlo methods considering the uncertainty of transition rates and cost.

Results
In the example of individual-tailored cost-effectiveness analysis on primary prevention (vaccination) for AD, the ICER from frequentist approach with adjustment for age and gender was $17,604 per life-year gained for the vaccinated group against no vaccination group. By using Bayesian approach, the ICER were $19,270 (95% CI: -33,320-44,400) and $19,330 (95% CI: -32,570-44,320) per QALY gained for models with and without random effect, respectively. After adjustment for age and gender in Bayesian approach, ICERs increased from $19,330 to $37,680(95% CI: $14,460-$78,560).
Following Bayesian viewpoint, the values of ceiling ratio for 50% of probability of being cost-effectiveness were $30,000 for Bayesian approach with random effect. The corresponding value for frequentist approach was $23,800. Following frequentist viewpoint, the value of ceiling ratio for 95% of probability of being cost-effective was $46,300. The discrepancy between frequentist approach and Bayesian approach with the results of cost-effectiveness acceptability curve(CEAC) and ICER was remarkable in this example, but the vaccination for AD is obvious to be more cost-effective in women and younger subjects in both of frequentist and Bayesian approaches.
In the example of breast cancer screening, the ICER for the personalized screening strategy with various combinations of inter-screening intervals was $51,742 ($50,634 - $52,850) per additional life year (LY), which lower than the strategy of biennial ($63,777/LY), triennial ($55,593/LY) and annual screening ($82,514/LY). It was close to quadrennial ($53,165/LY) but higher than sexennial screening ($43,781/LY). In Bayesian approach, the order to be cost-effectiveness was almost the same to frequentist approach. However, the CEAC of personalized screening intersected 6-year interval screening at WTP of $47,000. The probability of being cost-effective was 0.71 at this intersection.
When comparing different therapeutic strategies (delayed treatment, medication, and DBS-STN) for severe Parkinson disease with outcome measured on unified Parkinson's disease rating scale (UPDRS) III motor score, quality-adjusted life-year (QALY), and death, we found that medication was likely to be cost-saving compared to the delayed treatment When comparing DBS-STN to the delayed treatment, the mean incremental cost-effectiveness ratio (ICER) ranged from $102 to $1,208 per UPDRS III score reduced, $1,147 to $9,490 per QALY gained, and $10,414 to $102,749 per death averted. When comparing DBS-STN to medication, the corresponding figures for per UPDRS III score reduced, QALY gained, and death averted were $1,069 to $5,751, $11,635 to $38,607, and $109,524 to $469, 299, respectively.
When considering all three outcome dimensions (joint approach), the curves for all three possible comparisons (medication versus delayed treatment, DBS-STN versus delayed treatment, and DBS-STN versus medication) were more flat than only considering UPDRS III (marginal approach). The curves for the three comparisons were not dependent on the unit of outcome measures (per score, per year, or per case). The results shows that DBS-STN was superior to medication comparing to delayed treatment when transformed ceiling ratio of WTP>6. The transformed ceiling ratio of 50% being cost-effectiveness (β50) for medication and DBS-STN compared to delayed treatment was 4.4 and 5.3, respectively. The β50 for DBS-STN comparing to medication was 6.2.
Conclusions
This thesis is the first study, to the best of knowledge, to develop a Bayesian phase-type and Coxian phase-type model to model temporal course of multi-state disease progression for economic appraisal of individualized-tailored cost-effectiveness analysis (ITCEA) on primary (prophylactic) prevention, secondary (screening) prevention and tertiary (therapeutic) prevention considering multi-dimensional costs and efficacies. With the application of both stochastic processes using Bayesian approach, this thesis shows various results of Bayesian ITCEA on ICER, C-E plane, and CEAC by different subgroups (covariates), individual variation beyond measured covariates (random effect), different priors while it was applied to the administration of vaccine for relieving AD. This thesis also demonstrates how to synthesize various empirical data sources on risk profiles from bench to bedside and costs of breast cancer with mammography screening from systematic literature review to give the results of personalized screening with various inter-screening interval and how to synthesize various clinical data sources on three dimensional outcomes (number of death, quality of life years, and UPDRS motor score) and costs of treating Parkinson’s disease (PD) to show the results of multi-dimensional efficacies of CEA.

並列關鍵字

Stochastic process ； Bayesian analysis ； Cost-effectiveness analysis ； Personalized medicine ； Alzheimer’s disease ； Breast cancer screening ； Parkinson’s disease

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