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定性检测的样本量估算常用单组目标值法和抽样误差法，《体外诊断试剂临床试验技术指导原则》（2017年第72号）中提到：当评价指标P接近100%时，这两种样本量估算方法可能不适用，应考虑更加适宜的方法进行样本量估算和统计学分析，如精确概率法。
PASS 软件提供的 Test for One Proportion 模块提供了精确概率法的选项，在 Power Calculation Method 中选择Binomial Enumeration 即可。SAS 软件的 PROC POWER 过程则不支持精确概率法。
例如：某试剂的阳性符合率预期值为98%，目标值为95%，取显著性水平α=0.05，检验效能1-β=0.8，试估计所需样本量。
由于98%接近100%，因此采用精确概率法计算样本量。在 PASS 软件中设置相关参数，计算所需样本量为312。
需要注意的是：PASS软件通过迭代寻找满足检验效能高于0.8的样本量，当找到一个满足条件的样本量时，PASS即中止迭代，然而此时的样本量有可能并不是保守的。下面将展示这种“不保守”的现象。
在PASS软件中，我们设定求解目标为Power，样本量取值为区间[310, 370]，绘制功效曲线如下：
可以发现：检验效能并非随着样本量增加而单调增加，而是显示出“锯齿状”（saw-toothed），即使样本量高于PASS软件计算出的312，也存在检验效能低于0.8的情况，当且仅当样本量≥338时，才能保证检验效能稳定在0.8以上。造成此现象的原因是二项分布的离散性。
以下SAS宏代码可用于计算给定参数下的精确概率法的最保守样本量，供参考。
程序的基本思路如下：
Step1. 使用 PROC POWER 过程的近似正态法计算一个粗略的样本量n1
Step2. 在n1 附近找一个区间，区间上下界通过参数lbound_rate 和ubound_rate 控制
Step3. 使用 PROC POWER 过程计算样本量在区间 [lbound_rate *n1,ubound_rate *n1] 的检验效能
Step4. 判断区间 [lbound_rate *n1,ubound_rate *n1] 内是否存在满足任意 n>n0，使得 power(n) > 0.8 且 n0 之后的第一个波谷满足 power > 0.8 的 n0
Step5. 如 Step 4 找到了满足条件的n0，则输出样本量计算结果；否则，根据参数expand_step 扩展区间上界，重复 Step1-Step4
/* 宏程序功能：单组目标值-精确概率法，计算最保守样本量，计算结果未考虑脱落率。 */ %macro SampleSize_ExactBinomial(p0, p1, alpha = 0.05, power = 0.8, lbound_rate = 0.8, ubound_rate = 1.2, expand_step = 1, OutDataSet = SampleSize_ExactBinomial, DetailInfo = DetainInfo, PowerPlot = Y); /* --------------宏参数----------------- p0: 目标值 p1: 预期值 alpha: 显著性水平 power: 检验效能 lbound_rate: 寻值区间下界比例 ubound_rate: 寻值区间上界比例 expand_step: 扩展区间步长 OutDataSet: 输出样本量估算结果的数据集名称 DetailInfo: 输出样本量估算细节的数据集名称 PowerPlot: 是否绘制功效图 ----------------宏变量--------------- ntotal_normal: 正态近似法估算的样本量 ntotal_lbound: 寻值区间下界 ntotal_ubound: 寻值区间上界 IsLocalFindFirst: 是否找到首次满足检验效能的不保守样本量 IsGlobalFind: 是否找到稳定满足检验效能的最保守样本量 LooseMinSampleSize: 首次满足检验效能的不保守样本量 StrictMinSampleSize:稳定满足检验效能的最保守样本量 ActualPower: 最保守样本量下的实际检验效能 */ /*近似正态法求得一个粗略的样本量*/ ods output output = output_normal; proc power; onesamplefreq test = z method = normal alpha = &alpha power = &power nullproportion = &p0 proportion = &p1 ntotal = .; run; proc sql noprint; select ntotal into: ntotal_normal from output_normal; /*提取正态近似样本量*/ quit; %let ntotal_lbound = %sysfunc(floor(%sysevalf(&lbound_rate*&ntotal_normal))); /*寻值区间下界*/ %if %sysevalf(&ntotal_lbound < 5) %then %do; %let ntotal_lbound = 1; %let lbound_rate = %sysevalf(1/&ntotal_normal); %end; %let ntotal_ubound = %sysfunc(ceil(%sysevalf(&ubound_rate*&ntotal_normal))); /*寻值区间上界*/ %if %sysevalf(&ntotal_ubound < 5) %then %do; %let ntotal_ubound = 20; %let ubound_rate = %sysevalf(20/&ntotal_normal); %end; /*在区间[&ntotal_lbound, &ntotal_ubound]内多次求Power*/ ods output output = output_exact; proc power; onesamplefreq test = exact alpha = &alpha power = . nullproportion = &p0 proportion = &p1 ntotal = &ntotal_lbound to &ntotal_ubound by 1; %if &PowerPlot = Y %then %do; plot x = n min = &ntotal_lbound max = &ntotal_ubound step = 1 yopts = (ref = &power) xopts = (ref = &ntotal_normal); %end; run; /*左邻点*/ data power_exact_left; if _n_ = 1 then do; ntotal = &ntotal_lbound; power_left = .; output; end; set output_exact(keep = ntotal power rename = (power = power_left) firstobs = 1 obs = %eval(&ntotal_ubound - &ntotal_lbound)); ntotal = ntotal + 1; label power_left = "左邻点"; output; run; /*目标点*/ data power_exact_mid; set output_exact(keep = ntotal power rename = (power = power_mid)); label power_mid = "目标点"; run; /*右邻点*/ data power_exact_right; set output_exact(keep = ntotal power rename = (power = power_right) firstobs = 2 obs = %eval(&ntotal_ubound - &ntotal_lbound + 1)); ntotal = ntotal - 1; label power_right = "右邻点"; output; if _n_ = %eval(&ntotal_ubound - &ntotal_lbound) then do; ntotal = &ntotal_ubound; power_right = .; output; end; run; /*实际检验效能*/ data alpha_exact; set output_exact(keep = ntotal alpha); run; /*寻找最保守的样本量*/ %let IsLocalFindFirst = 0; %let IsGlobalFind = 0; data &DetailInfo; merge power_exact_left power_exact_mid power_exact_right alpha_exact; label ntotal = "当前样本量" power_left = "左侧点效能" power_mid = "当前点效能" power_right = "右侧点效能" alpha = "实际Alpha" min_sample_size = "已知最低样本量" is_local_find_first = "首次局部最优解" is_local_find = "局部最优解" is_global_find = "全局最优解" peak = "波峰" trough = "波谷"; format power_left 8.6 power_mid 8.6 power_right 8.6; retain min_sample_size 0 is_local_find 0 is_local_find_first 0 is_global_find 0; if ntotal > &ntotal_lbound and ntotal < &ntotal_ubound then do; if power_left < power_mid and power_right < power_mid then peak = "Yes"; if power_left > power_mid and power_right > power_mid then trough = "Yes"; if power_mid > &power and is_local_find = 0 then do; /*局部最优解，标记到达检验效能的样本量*/ min_sample_size = ntotal; is_local_find = 1; if is_local_find_first = 0 then do; /*首次达到局部最优解，可视为不保守的样本量估算结果*/ is_local_find_first = 1; call symput("LooseMinSampleSize", min_sample_size); call symput("IsLocalFindFirst", is_local_find_first); end; end; if power_mid < &power and is_local_find = 1 then do; /*局部最优解的破坏，锯齿状的波谷导致此时的检验效能无法稳定在所需大小之上*/ min_sample_size = .; is_local_find = 0; end; if (power_mid > &power and trough = "Yes" or power_mid = 1) and is_local_find = 1 and is_global_find = 0 then do; /*全局最优解，此时即便是波谷也能达到所需的检验效能，可视为最保守的样本量估算结果; 当检验效能=1时也可视为达到全局最优解*/ is_global_find = 1; call symput("StrictMinSampleSize", min_sample_size); call symput("ActualPower", power_mid); call symput("IsGlobalFind", is_global_find); end; end; run; %if &IsLocalFindFirst = 1 and &IsGlobalFind = 1 %then %do; /*输出样本量估算结果*/ data &OutDataSet; label P0 = "目标值" P1 = "预期值" ALPHA = "显著性水平" POWER = "检验效能" Normal = "正态近似" Exact1 = "精确概率法（不保守）" Exact2 = "精确概率法（最保守）"; P0 = &p0; P1 = &p1; ALPHA = α POWER = &power; Normal = &ntotal_normal; Exact1 = &LooseMinSampleSize; Exact2 = &StrictMinSampleSize; run; /*删除数据集*/ proc delete data = output_exact output_normal power_exact_left power_exact_mid power_exact_right alpha_exact; run; /*输出日志*/ %put NOTE: 参数：&=p0, &=p1, &=alpha, &=power; %put NOTE: 正态近似法求得最低样本量为&ntotal_normal; %put NOTE: 精确概率法求得首次达到检验效能的最低样本量为 %sysfunc(strip(&LooseMinSampleSize)) （不保守）; %put NOTE: 精确概率法求得最保守的样本量为 %sysfunc(strip(&StrictMinSampleSize))，实际检验效能为 %sysfunc(strip(&ActualPower)); %end; %else %do; %SampleSize_ExactBinomial(p0 = &p0, p1 = &p1, alpha = &alpha, power = &power, lbound_rate = &lbound_rate, ubound_rate = %sysevalf(&ubound_rate + &expand_step), expand_step = &expand_step, OutDataSet = &OutDataSet, DetailInfo = &DetailInfo, PowerPlot = &PowerPlot); %end; %mend; /*Examples %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98); %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98, alpha = 0.1); %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98, alpha = 0.1, power = 0.9); %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98, alpha = 0.1, power = 0.9, lbound_rate = 0.8, ubound_rate = 1.3); %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98, OutDataSet = SS); %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98, OutDataSet = SS, DetailInfo = Info); %SampleSize_ExactBinomial(p0 = 0.94, p1 = 0.98, OutDataSet = SS, DetailInfo = Info, PowerPlot = N); data param; n = 1; do p1 = 0.940 to 0.980 by 0.002; call execute('%nrstr(%SampleSize_ExactBinomial(p0 = 0.90, p1 = '||p1||', lbound_rate = 0.6, ubound_rate = 1.2, OutDataSet = SS'||strip(put(n, best.))||', PowerPlot = N))'); n = n + 1; output; end; run; data SS; set SS1-SS21; run; */参考文献：
- Vezzoli S, CROS NT V. Evaluation of Diagnostic Agents: a SAS Macro for Sample Size Estimation Using Exact Methods[C]//SAS Conference Proceedings: Pharmaceutical Users Software Exchange. 2008: 12-15.
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