率的等效性檢驗方法的比較

1、◇設(shè)計與統(tǒng)計◇中國臨床藥理學(xué)與治療學(xué)中國藥理學(xué)會主辦CN3421206ΠRISSN100922501:ΠΠwww.DrugChina.2004Mar9(3):3543572003211203收稿2004202206修回陳峰通訊作者男博士教授博士生導(dǎo)師研究方向:醫(yī)學(xué)現(xiàn)場研究中的統(tǒng)計理論與方法。Tel:025286862754E2mail:dr.chenfeng@163.com率的等效性檢驗方法的比較呂靜靜于浩1陳峰1山東省疾病預(yù)防控制中心

2、濟(jì)南250014山東1南京醫(yī)科大學(xué)公共衛(wèi)生學(xué)院流行病與衛(wèi)生統(tǒng)計學(xué)系南京210029江蘇摘要目的:對10種率的等效性檢驗方法的Ⅰ型誤差和檢驗效能進(jìn)行比較并據(jù)此選擇較好的方法估計樣本含量以便實際工作者應(yīng)用。方法:采用MonteCarlo模擬試驗。結(jié)果:10種方法中以Dun2t2Gent方法為最佳并按該方法估計了樣本含量。模擬試驗表明率的等效性檢驗所需要的樣本含量非常大當(dāng)試驗組和參考組各只有100例時任何等效性檢驗方法的檢驗效能均較低。結(jié)論:

3、按目前國家食品藥品監(jiān)督管理局規(guī)定的最低樣本含量100對相應(yīng)的檢驗效能很低建議用統(tǒng)計學(xué)方法進(jìn)行估計。關(guān)鍵詞百分率等效性檢驗檢驗效能樣本含量MonteCarlo中圖分類號:R311文獻(xiàn)標(biāo)識碼:A文章編號:100922501(2004)0320354204有效率的臨床等效性(clinicalequivalence)檢驗應(yīng)該用相應(yīng)的等效性統(tǒng)計檢驗方法(statisticalap2proachestoestablishingequivalence

4、)來評價這一觀點廣大臨床試驗工作者已達(dá)成共識。但率的等效性檢驗方法很多到底選用何種方法進(jìn)行評價各種方法的檢驗效能如何需進(jìn)行研究。本文通過Monte2Car2lo模擬對十種藥物有效率的等效性檢驗方法進(jìn)行比較研究從而推薦較好的方法并據(jù)此估計等效性檢驗所需樣本含量以方便臨床使用。1方法1.1率的等效性檢驗可以從三個不同角度去考慮:(1)基于率差(ratedifferenceRD)的檢驗:直接比較兩個率之差差值接近于0則認(rèn)為等效(2)基于優(yōu)勢比

5、(oddsratio)的檢驗:接近于1則認(rèn)為等效(3)基于率比(relativeriskRR)的檢驗:RR接近于1則認(rèn)為等效。本試驗精選三類(RDRR)中10種方法進(jìn)行模擬研究比較它們在等效性檢驗中的Ⅰ型誤差和檢驗效能(power)并據(jù)此選擇較好的方法估計樣本含量。假設(shè)在一隨機(jī)、雙盲的臨床等效性試驗中試驗組接受治療的病人數(shù)為NT陽性對照組接受治療的病人數(shù)為NRXT、XR分別是兩組治療有效(或治愈)的人數(shù)不失一般性設(shè)XT、XR服從二項分布

6、兩組的樣本率記為pT和pR對應(yīng)的總體率分別記為PT和PR選10種方法(表1)。1.2模擬試驗設(shè)計的基本原理為了使各方法間具有可比性應(yīng)選擇對應(yīng)的等效區(qū)間。不妨設(shè)兩總體率之差在(π0π0)內(nèi)則認(rèn)為兩總體率等效。據(jù)此可得率差的等效區(qū)間為:(πl(wèi)πu)=(π0π0)對應(yīng)的優(yōu)勢比的等效區(qū)間為:(ΨlΨu)=[(1PR)(PRπ0)(PR(1PRπ0)(1PR)(PRπ0)(PR(1PRπ0)]對應(yīng)的率比的等效區(qū)間為:(δlδu)=(1π0PR1π

7、0PR)假設(shè)檢驗中為真(“兩藥物不等效”)而推斷結(jié)論為“兩藥物等效”這種錯誤稱Ⅰ型誤差其概率記為α。H1為真(“兩藥物等效”)而推斷結(jié)論為“兩藥物不等效”這種錯誤稱Ⅱ型誤差其概率為β相應(yīng)地推斷正確的概率是:1β稱為檢驗效能。1.3參數(shù)設(shè)置取等效區(qū)間(π0π0)=(0.10.1)PT=PRππ分別取0.100.0500.050.10NT=NR=N分別取100120200PR分別取453?19952005TsinghuaTongfangOp

8、ticalDiscCo.Ltd.Allrightsreserved.續(xù)上表PRPTRDclahacmldgewctbRRrrlogrr0.70.600.0000.0000.0000.0000.0000.0080.0090.0080.0000.0000.650.0000.0000.0000.0000.0000.0070.0120.0070.0010.0020.700.0000.0000.0000.0000.0000.0020.0030.0

9、030.0070.0150.750.0010.0000.0010.0010.0000.0000.0000.0000.0220.0290.800.0000.0000.0000.0010.0000.0000.0000.0000.0120.0160.80.700.0000.0000.0000.0000.0250.0410.0410.0410.0010.0040.750.0080.0000.0080.0180.0520.1000.1040.09

10、90.0140.0220.800.0370.0110.0350.0540.0850.1620.1750.1590.0450.0850.850.0850.0450.0770.1010.0410.1190.1340.1150.0850.1120.900.0330.0230.0290.0410.0020.0140.0170.0090.0310.0480.90.800.0350.0220.0260.0370.0180.0310.0310.027

11、0.0220.0350.850.1950.1390.1670.2070.1220.1780.1780.1680.1410.2030.900.4550.3600.4060.4630.4430.5040.5050.5030.3690.461e、w、c和tb分別代表直接概率法、Woolf法、Cnfield法、test2based法cla、hac、ml和dg分別代表的經(jīng)典可信區(qū)間法、Hauck2erson法、最大似然法、Dunt2Gent法rr

12、、logrr分別代表經(jīng)典可信區(qū)間法、對數(shù)變換法表310種方法的模擬試驗的Ⅰ型誤差與檢驗效能(delta=0.1N=NT=NR=200)PRPTRDclahacmldgewctbRRrrlogrr0.50.400.0320.0320.0320.0320.0200.0320.0320.0320.0210.0210.450.1540.1540.1540.1540.0920.1540.1540.1540.1430.1540.500.2280.2

13、280.2280.2280.1510.2280.2280.2280.2550.2560.550.1570.1570.1570.1570.0950.1570.1570.1570.1600.1600.600.0420.0420.0420.0420.0360.0460.0460.0460.0300.0310.60.500.0420.0420.0420.0420.0360.0460.0460.0460.0300.0310.550.1440.14

14、30.1460.1460.1220.1620.1640.1620.1530.1620.600.2630.2440.2720.2790.2240.3020.3070.3020.2810.2870.650.1830.0490.1870.1870.1290.1820.1850.1820.1790.1850.700.0430.0340.0430.0430.0240.0350.0360.0350.0470.0500.70.600.0340.027

15、0.0350.0360.0300.0360.0360.0360.0280.0320.650.2050.1760.2050.2070.1760.2140.2140.2140.1950.2050.700.3830.3580.3830.3920.3670.4250.4280.4210.3680.3870.750.2240.1960.2240.2270.1890.2490.2520.2470.2140.2220.800.0520.0430.05

16、20.0530.0340.0450.0450.0450.0540.0560.80.700.0370.0330.0370.0380.0340.0420.0420.0420.0360.0370.750.2910.2650.2880.3020.2230.2530.2530.2530.2970.3090.800.6000.5530.5920.6070.5590.6100.6110.6100.5820.5970.850.3380.3110.331

17、0.3460.4080.4610.4750.4610.2940.3090.900.0520.0450.0470.0520.0280.0390.0430.0390.0470.0550.90.800.0370.0290.0300.0390.0320.0370.0460.0370.0340.0390.850.4480.4130.4260.4510.2450.2780.3000.2780.4560.4910.900.9070.9000.9030

18、.9130.7150.7750.7760.7750.8810.905e、w、c和tb分別代表直接概率法、Woolf法、Cnfield法、test2based法cla、hac、ml和dg分別代表的經(jīng)典可信區(qū)間法、Hauck2erson法、最大似然法、Dunt2Gent法rr、logrr分別代表經(jīng)典可信區(qū)間法、對數(shù)變換法表4Dunt2Gent法樣本含量估計PRPT～PR0.020.0100.010.020.50480446425443480

19、0.554774354204404730.604654314104214570.654424003753904310.704113813553713950.753693353253253500.803182872602762950.852572302102152300.901861651551601553討論利用來檢驗率的等效性直接概率法的檢驗效能總低于其他方法這與傳統(tǒng)的認(rèn)識恰好相反。對于Ⅰ型誤差直接概率法的實際Ⅰ型誤差也總低于名義水準(zhǔn)