- 學位論文
成本效益分析之總健康效益的不偏估計量
Unbiased Estimator of Net Health Benefit for the Analysis of Uncertainty in the Cost-Effectiveness Analysis
摘要
最近幾年，在保健問題上有2個重要的概念，Heitjan及O'Brien提供成本效益比(cost-effectiveness ratio)的詳細概念，Stinnett和Mullahy在成本效益分析(cost-eff-ectiveness analysis)上提出總健康效益(net health benefit)這個新概念。令y表示成本，z代表效益。考慮一組大小為n的成本與效益的隨機樣本{(y1,z1),(y2,z2),...,(yn,zn)}且其期望值為μy 和μz。定義成本效益比λ=μy/μz。定義總健康效益μNHB=μy-λμz，其中λ為常數且其意義為開端的成本效益比。因此總健康效益代表的是實際的花費減去在給定的λ水準下，實際的效益在理論上的花費。所以總健康效益的值越小越好。在成本效益分析上，對於增加成本效益比(incremental cost-effectiveness ratio)與增加總健康效益(incremental net health benefit)有更多的關注。考慮2組隨機樣本，新的試驗組{(y1i,z1i)| i=1, 2, ..., n}與標準試驗組{(y2j,z2j)| j=1, 2, ..., m}並定義為μy1新試驗組成本的期望值、μy2為標準試驗組成本的期望值、μz1為新試驗組效益的期望值、μz2為標準試驗組效益的期望值。定義λINHB=(μy1-μy2)/(μz1-μz2)，為上述的ICER。定義μINHB=(μy1-μy2)-λ(μz1-μz2)，為上述的INHB，其中的λ為一常數，其意義為全部的花費的期望值除以全部的效益的期望值。如果ICER為負值，則會有2種完全相反地情形導致產生一個錯誤的決策。一種是分子為負且分母為正則新試驗較標準試驗好，另一種是分子為正且分母為負則標準試驗較新試驗好。增加總健康效益是兩組總健康效益的差異，且如果增加總健康效益是負值則新試驗組優於標準試驗組。更多的文獻專注在如何找成本效益比、總健康效益、增加成本效益比、增加總健康效益的信賴區間。Chaudhary與Polsky提供了一些方法去尋找信賴區間，諸如盒子法(box method)、Fieller法(Fieller's method)或拔靴法(bootstrap method)，但是這些方法都沒有一個適當的點估計值去測量這些參數。我們利用最小平方法(least square method)和製造一個線性模型去找總健康效益及增加總健康效益的最小平方估計量(least square estimators)，在特殊的情況下也可以找到成本效益比的最小平方估計量。不幸的是，因為模型的假設是建構在總健康效益的概念上，所以我們沒辦法估計增加成本效益比。因為成本效益比、總健康效益、增加總健康效益的估計量的變異數非常難以計算，拔靴法提供了一種估計量估計成本效益比、總健康效益、增加總健康效益的估計量的變異數。
並列摘要
In a recent year, we have two central conception of health care problem, Heitjan and O'Brien give the detailed conception of cost-effectiveness ratio (CER), Stinnett and Mullahy propose a new conception net health benefit (NHB) in the cost-effectiveness analysis. Let y represent for cost, z stands for effectiveness. Consider one random sample {(y1,z1),(y2,z2),...,(yn,zn)} with size n of cost and effectiveness with mean μy, μz, respectively. Define cost-effectiveness ratio to be λ=μy/μz. Define net health benefit is μNHB=μy-λμz, where λ is a constant which means the threshold cost-effectiveness ratio. Therefore NHB means the actual cost minus theoretically cost in actual effectiveness on a given λ level. Hence the value of NHB is smaller well. Most attention on the incremental cost-effectiveness ratio (ICER) and incremental net health benefit (INHB) in the cost-effectiveness analysis. Consider two random sample, new treatment {(y1i,z1i)| i=1, 2, ..., n} and standard treatment {(y2j,z2j)| j=1, 2, ..., m} with μy1 is the mean of cost of the new treatment, μy2 is the mean of cost of the standard treatment, μz1 is the mean of effectiveness of the new treatment, μz2 is the mean of effectiveness of the standard treatment. Define λICER=(μy1-μy2 )/(μz1-μz2) be above ICER. Define μINHB=(μy1-μy2)-λ(μz1-μz2) be above INHB, where λ is a constant which means the total mean of cost divide by total mean of effectiveness. If ICER is negative then there are two completely adverse conditions such that a mistaken decision occur. One is that numerator is negative and denominator is positive, then new treatment is better than standard treatment; another is that numerator is positive and denominator is negative, then standard treatment is better than new treatment. INHB is the difference of the two NHBs and the new treatment is superior to the standard treatment if the INHB is negative. Most research have focused on how to find the confidence interval (CI) for CER, NHB, ICER, INHB. Chaudhary and Polsky offer some method to find those CI such as box method, Fieller's method or bootstrap method, but they have no advisable point estimator to measure those parameters. We use least square method (LSM) and make a linear model to find the least square estimators (LSE) for NHB and INHB, in special case we can find the LSE for CER. Unfortunately, since the model assumption is according to the conception of NHB, we can not estimate ICER. Since the variance of the estimator for CER, NHB and INHB are very difficulty to find, bootstrap method provides a kind of estimator to estimate the variance of the estimator for CER, NHB and INHB.