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统计方法在循证医学中的应用
《循证医学》统计方法 在循证医学中的应用仇玉兰 上海交通大学医学院公共卫生学院QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine医学统计学是以数理统计方法和 概率论为理论基础的应用学科。 统计学方法选择的条件： 分析目的、临床研究设计方法、 数据资料类型、数据资料分布特 征、数理统计条件QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine数据资料类型：数值变量（定量变量） 变 量 分类变量 有序分类QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine二项分类 无序分类 多项分类(1)数值变量（定量资料）：其变量 值是定量的，表现为数值大小， 一般有度量衡单位。 (2)分类变量：其变量值是定性的， 表现为互不相容的类别或属性。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine无序分类（分类资料）： ① 二项分类－为两类间互相对立的 结果。如结果为阳性和阴性。 ② 多项分类－结果为互不相容的多 个类别。如人群的血型分布。 有序分类（等级资料）：各类之间 有程度的差别，给人以&半定量&的慨 念。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine统计描述 定量资料 参数估计 假设检验 单 变 量 统计描述 定性资料（无序分类）参数估计 假设检验等级资料（有序分类）假设检验－－非参数 秩和检验QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两变量关联性分析 简单回归分析多变量多元线性回归与相关 Logistic回归分析QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine数据资料分布特征：1. 正态分布： 正态曲线（normal curve）是一条高峰位 于中央，两侧逐渐下降并完全对称，曲线 两端永不与横轴相交的钟型曲线。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine2. 偏态分布： (1) 正偏态分布――集中位置偏向数 值小的一侧 (2) 负偏态分布――集中位置偏向数 值大的一侧QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine数理统计条件：统计学方法所涉及的数理统计公式 都是在一定的条件下推导和建立 的，即都有一定的应用条件。 临床研究数据分析中最常涉及的应 用条件如数据的分布、数据的变异 度（方差齐同或同质性）、数据资 料类型、线性问题、共线性问题等。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine参数估计的概念：参数估计是指用样本指标（统计量） 估计总体指标（参数）。参数估计 有点估计 ( point estimation ) 和区 间估计 ( interval estimation ) 两种。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（一）点估计用样本统计量直接作为总体参数的点估计 值，即直接用随机样本的样本均数作为总 体均数的点估计值，用样本频率 P 作为总 体概率π的点估计值。 点估计方法简单，但没有考虑抽样误差， 无法评价估计值与真值之间的差距。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（二）区间估计 结合样本统计量和标准误可以确定一 个具有较大置信度的包含总体参数的 区间，该区间称为总体参数的 1 - α 置信区间（ confidence interval , Cl ）。 α值一般取 0.05 或 0.01 , 故 1 - α为 0.95 或 0.99 。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine习惯上用总体均数（或总体率）的 95%（或99%）可信区间，表示该区 间包含总体均数μ（或总体率π）的 概率为 95% （或99%），用此范围 估计总体平均数或总体平均率，表示 100次抽样中，有95（99）次包含总 体均数或总体率。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine通常用样本均数和均数的标准误估 计总体均数的置信区间，或用样本 频率及其标准误估计总体概率的置 信区间。如果没有特别说明，一般 作双侧的区间估计。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine置信水平由 95％提高到 99％ ，置 信区间由窄变宽，估计的精度下降。 若要提高置信水平，又要估计的精 度好，就必须缩小 S 或加大 n 。 S 反映客观存在的个体差异，通常无 法缩小，但可加大样本量。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine假设检验与区间估计的关系：1. 置信区间具有假设检验的主要功能（1）双侧检验 某儿科采用静脉注射人血丙种球蛋白治 疗小儿急性毛细支气管炎。用药前后患 儿血清中免疫球蛋白IgG（mg/dl）含量 如下表。请问用药前后IgG有无变化？QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineH 0 : μ d = 0, H 1 : μ d ≠ 0, α = 0.05 n = 12, ∑ d = 5707.95, ∑ d 2 = , ∑ d 5707.95 d= = = 475.66 n 12 sd = (∑ d ) ∑d ? n n?12 2=(
? 12 = 84.2747 12 ? 1QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicined d 475.66 = = = 19.552 t= sd sd / n 84.2747 / 12ν = n ? 1 = 12 ? 1 = 11t 0.05(11) = 2.201, t = 19.552 & t 0.05(11) , P & 0.05 在α＝0.05的水准上拒绝H 0，可以认为用 药后小儿IgG增高QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine95%可信区间： 84.2747 d ± t 0.05(11) sd = 475.66 ± 2.201 × 12 = (422.114,529.206)( mg / dl ) H 0 : μ d = 0不在上述的可信区间范围内， 即不接受H 0，这与假设检验中的P & 0.05 的结论是一致的。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（2）单侧检验 已知北方农村儿童前囟门闭合月龄 为14.1。某研究者从东北某县抽取 36名儿童，前囟门闭合月龄均值为 14.3，标准差为5.08。问该县儿童 前囟门闭合月龄的均数是否大于一 般儿童？（假设该县儿童前囟门闭 合月龄不会低于一般儿童）QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineH 0 : μ = μ 0 , H 1 : μ＞μ 0 , α = 0.05 x ? μ 0 14.3 ? 14.1 t= = = 0.236 sx 5.08 / 36 ν = n ? 1 = 36 ? 1 = 35, t 0.05( 35 ) = 1.69 t = 0.236 & t 0.05( 35 ) , p & 0.05 按α＝0.05水准，不拒绝H 0，可以认为 该县儿童前囟门闭合月龄不大于一般 儿童。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine95％单侧可置信区间上限：5.08 x + t 0.05( 35 ) s x = 14.3 + 1.69 × = 15.73 36 H 0 : μ = 14.3在上述的可信区间范围内， 即接受H 0，这与假设检验中的P & 0.05 的结论是一致的。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine2. 置信区间可提供假设检验没有提 供的信息 置信区间在回答差别有无统计学 意义的同时，还可以提示差别是 否具有实际意义QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine3. 假设检验提供，而置信区间不提供 的信息 （1）在统计推断结论为拒绝 H0 时， 假设检验可以报告确切的 P 值，从而较为精确地说明检验 结论的概率保证。但置信区间 只是在一定的置信水平上进行 推断。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（2）不拒绝 H0 时，假设检验可以对 检验功效作出估计，即评价是 否由于识别差别的能力较弱而 不拒绝 H0 ，而置信区间不行。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine循证医学中的常用统计指标一、分类资料的指标 EER , CER 及可信区间 EER (experimental event rate)－ 试验组中某事件的发生率 CER (control event rate , CER)－ 对照组中某事件的发生率QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine总体概率的置信区间： 根据样本含量 n 和样本频率 p 的 大小，可以采用查表法和正态近 似法计算总体概率的置信区间。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine1. 查表法 当样本含量 n 较小，比如 n ≤ 50， 特别是 p 很接近 0 或 100％时，可 以通过查相应统计用表，确定总体 概率的置信区间。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine2. 正态近似法 当 n 足够大，且样本频率 p 和 （ 1 - p）均不太小时，如 np 与 n ( 1 Cp）均大于 5 时， P 的抽样 分布接近正态分布，此时可按下 列公式求总体概率的置信区间。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine( p ? uα SE , p + uα SE )或缩写为：p ± uα SE u0.05 = 1.96；u0.01 = 2.58 SE为频率P的标准误， SE = p(1 ? p ) nQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine例：用某种仪器检查已确诊的乳腺 癌患者 120 名，检出乳腺癌患者 94 例，检出率为 78.3％。估计该 仪器乳腺癌总体检出率的 95％置 信区间。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine本例n较大，np = 94，n(1 ? p ) = 26， 均大于5，故用下式计算： p ± Zα S p = p ± Z 0.05 p(1 ? p ) n0.783 × (1 ? 0.783) = 0.783 ± 1.96 × 120 = 0.709 ~ 0.857QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine该仪器乳腺癌总体检出率的95％置 信区间为（70.9％，85.7％）。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine率差及可信区间两个发生率的差即为率差，也称危 险差 (rate difference, risk difference) ，其大小可反映试验效 应的大小，其可信区间可用于推断 两个率有无差别。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两率差为 0 时，两组的某事件发 生率没有差别，而两率差的可信 区间不包含 0 （上下限均大于 0 或上下限均小于 0 ）； 反之，两率差的可信区间包含 0 ，则差别无统计学意义。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两率差的可信区间：( p1 ? p2 ) ± uα SE ( p1 ? p2 )两率差的标准误：SE ( p1 ? p2 ) = p1 (1 ? p1 ) p2 (1 ? p2 ) + n1 n2QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine例：阿司匹林治疗心肌梗死治疗组梗死率EER＝12％ 对照组梗死率CER＝25％ SE ( p1 ? p2 ) = = p1 (1 ? p1 ) p2 (1 ? p2 ) + n1 n20.12(1 ? 0.12) 0.25(1 ? 0.25) + = 0.049 125 120QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两率差的95％可信区间：( p1 ? p2 ) ± uα SE ( p1 ? p2 ) = (0.12 ? 0.25 ) ± 1.96 × 0.049 = (? 0.23,?0.03 )QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两率差的可信区间为(-0.23，-0.03) 上下限均小于 0 （不包含 0 ），两 率有差别。阿司匹林治疗心肌梗死 的病死率 EER = 12 % ，对照组的 病死率 CER = 25 % ，阿司匹林可 降低心肌梗死的病死率。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineRR 及可信区间 相对危险度RR (relative risk) ，也 叫危险比 (risk ratio)或率比(rate ratio)。是暴露组发病（死亡）率与 非暴露组发病（死亡）率的比值， 简称RR。 RR = EER CERQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineRR说明暴露组发病或死亡为非暴 露组的倍数。RR&1说明暴露因素 与疾病为正联系，暴露可能是危险 因素；RR&1说明暴露因素与疾病 为负联系，暴露可能具有保护意 义； RR=1说明暴露因素与疾病无 关联。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine相对危险度与联系强度RR大小 0.9~1.0 1.0~1.1 0.7~0.8 1.2~1.4 0.4~0.6 1.5~2.9 0.1~0.3 3.0~9.9 &0.1 10~ 联系强度 无 弱 中等 强 很强QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine相对危险度95％可信区间：Woolf法1 1 1 1 Var ( InRR ) = + + + a b c dlnRR的95%可信区间：InRR ± 1.96 Var ( InRR )其反自然对数即为RR的95%可信区间QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine例：阿司匹林治疗心肌梗死 治疗组的病死率 p1=15/125=0.12 对照组的病死率 p2=30/120=0.25 RR 和可信区间为：RR = EERCER= 0 . 120 . 25= 0 . 48QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine1 1 1 1 Var ( InRR ) = + + + a b c d 1 1 1 1 = + + + = 0.12 15 110 30 90InRR ± 1.96 Var ( InRR ) = In0.48 ± 1.96 × 0.12 = ?0.734 ± 0.679 = (? 1.413,?0.055)QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineRR的95%可信区间为其反自然对 数，即为： exp( -1.413，-0.055 ) = ( 0.243，0.946 ) RR 的 95％可信区间为（0.243， 0.946），该区间小于 1 ，可以认 为阿司匹林可降低心肌梗死病死率QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineOR 及可信区间 比值比 (odds ratio，OR) 如某因素与某疾病存在联系，则 估计其联系的强度，联系强度可 用比值比(odds ratio，OR)估计QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine比值(odds)－－指某事物发生的概 率与不发生的概率之比a 病例组的暴露比值＝ cb 对照组的暴露比值 = d(a + c ) (a + c )(b + d ) (b + d )a = cb = dQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine病例组的暴露比值与对照组的暴 露比值之比称为比值比ad c = OR = b bc dQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicinea比值比的含义是指暴露组的疾病危 险性为非暴露组的多少倍。当 OR&1时，说明病例组的暴露概率 大于对照组，即暴露有较高的发病 危险性；反之，当OR&1时，说明 病例组的暴露概率低于对照组，即 暴露有保护作用。疾病与暴露联系 愈密切，比值比的数值愈大。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine优势比与联系强度OR大小 0 ～ 0.3 0.4 ～ 0.5 0.6 ～ 0.8 0.9 ～ 1.1 1.2 ～ 1.6 1.7 ～ 2.5 &= 2.6 关联意义 高度有益 中度有益 微弱有益 不产生影响 微弱有害 中度有害 高度有害QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineOR的95%可信区间：1 1 1 1 Var ( InOR ) = + + + a b c d 上述值的反自然对数即InOR 95 % C . I . = InOR ± 1 .96 Var ( InOR 为 OR 的可信区间)QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineOR可信限的作用： 1. 有助于估计变异范围的大小 2. 有助于检验OR值的判断意义， 可信区间中不包括1.0，即可认 为该OR值在0.05或0.01水平上 有显著性QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine例：阿司匹林治疗心肌梗死，估计 其 OR 的 95 ％可信区间15 × 90 ad = 0.41 = OR = bc 30 × 110QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineOR的95%可信区间：1 1 1 1 Var ( InOR ) = + + + a b c d 1 1 1 1 = + + + = 0 .12 15 110 30 90InOR 95 % C . I . = InOR ± 1 .96 Var ( InOR)= In 0 .41 ± 1 .96 × 0 .12 = ? 0 .892 ± 0 .678 = (? 1 .57 , ? 0 .214 ) exp (? 1 .57 , ? 0 .214 ) = (0 .21 ,0 .81 )QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineOR 的 95％可信区间为（0.21， 0.81） ，该区间小于 1 ，可以认 为阿司匹林治疗心肌梗死有效。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineRRR 及可信区间 相对危险度减少率（relative risk reduction , RRR） ，其计算公式 为： CER ? EER RRR = = 1 ? RR CER RRR 可反映试验组与对照组某病发 生率增减的相对量QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineARR 及可信区间 绝对危险度减少率（absolute risk reduction , ARR），其计算公式为： ARR = CER C EER 反映试验组与对照组某病发生率增 减的绝对量QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineNNT 及可信区间 NNT 的临床含义：对患者采用某 种防治措施处理，得到一例有利结 果需要防治的病例数（the number of patients who need to be treated to achieve one additional favorable outcome, NNT）。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineThe Number Needed to Treat (NNT) is the number of patients you need to treat to prevent one additional bad outcome (death, stroke, etc.).QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine计算公式为：1 1 NNT = = CER ? EER ARRNNT 的值越小，该防治效果就越 好，其临床意义也就越大。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineNNT 95％可信区间的下限：1 的上限值 ARRNNT95 ％可信区间的上限：1 的下限值 ARRQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineNNH 及可信区间 NNH 的临床含义：对患者采用某种 防治措施处理，出现一例副作用需 要处理的病例数（the number needed to harm one more patients from the therapy, NNH）。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineNNH为绝对危险度增加(absolute risk increase，ARI)的倒数1 NNH = ARINNH 的值越小，某治疗措施引起 的副反应就越大。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineARI 绝对危险度增加率（absolute risk increase , ARI） 即试验组中某不利结果发生率 EERb 与对照组某不利结果发生率 CERb 的 差值，不利结果（bad outcomes） 如死亡、复发、无效等，其计算公式 为：ARI = EERb C CERbQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineABI 绝对受益增加率（absolute benefit increase ，ABI） 即试验组中某有益结果发生率 EERg 与对照组某有益结果发生率 CERg 的 差值，有益结果（good outcomes） 如治愈、显效、有效等，其计算公式 为：ABI = EERg C CERgQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineRRI 相对危险度增加率 （ relative risk increase , RRI ) 试验组中某不利结果的发生率为 EERb ，对照组某不利结果的发生 率为 CERb , RRI 可按下式计算：EERb ? CERb RRI = CERbQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineRBI 相对获益增加率（relative benefit increase , RBI） 试验组中某有益结果的发生率为 EERg ，对照组某有益结果的发生 率为 CERg，RBI 可按下式计算：RBI =EERg ? CERg CERgQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineLHH 防治性措施受益与危害的似 然比（ likelihood of being helped vs harmed , LHH ) 其计算公式为：1 NNT NNH LHH = = 1 NNH NNTQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineLHH 反映了防治措施给受试者带来 的受益与危害的比例， LHH & 1 （NNH＞NNT ），利大于弊；反 之， LHH & l 时（NNH＜NNT ）， 弊大于利。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine二、数值资料的指标 数值变量资料常用的统计描述指标 1.平均水平指标 （1）均数（mean, x ）：表示对称 分布资料的平均水平。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（2）中位数（median, M）：可用 于各种分布，一般多用于描 述偏态分布或数据一端无界 资料的平均水平。 （3）几何均数（geometric mean, G）：适用于数据呈对数正态 分布。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine2. 离散度（变异度variation）指标 （1）标准差（standard deviation, S）：用来表示对称分布资料 的个体变异度。同类资料比较 时，标准差越大，表示个体间 的变异越大。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（2）四分位间距（quartile range, Q）： 是两个特定的百分位数之差，即第 75百分数P75（上四分位数QU）和 第25百分位数P25（下四分位数QL） 之差，用Q表示，适用于任何分布 的定量资料，尤其适用于偏态分布 的资料（不宜用标准差表示离散度）QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine（3）变异系数（coefficient of variation, CV）：当单位不同，或单位相同但 是均数相差较大时，用标准差表示 变量值的变异度不太合理，用变异 系数更好。变异系数是一种相对的 离散程度指标，它无单位，其计算 公式为：CV = S × 100 % XQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine总体均数的置信区间 1. t 分布方法 若将置信度定为（1 - α），则总 体均数μ的（1 - α）置信区间的 一般计算式为：(X ? t ( ) ? SανX, X + tα (ν ) ? S X )或缩写为：X ± tα (ν ) ? S XQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine公式中 tα(ν) 为 t 分布双侧尾部面 积 α对应的 t 临界值； tα (ν ) ? S X 称为置信区间的精度，它等于置信 区间宽度的一半，意指置信区间的 两端点离样本均数 X 有多远。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine置信水平由 95％提高到 99％ ，置 信区间由窄变宽，估计的精度下降。 若要提高置信水平，又要估计的精 度好，就必须缩小 S 或加大 n 。S 反映客观存在的个体差异，通常无 法缩小，但可加大样本量。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine2. 正态分布近似方法 当σ未知，但n足够大（n & 50），t分布的极限分布是标准正态分布，可 用Zα 代替t分布法公式中tα，则总体均 数的双侧置信区间为：( X ? Zα SX, X + Zα S X )或缩写为：X ± Zα S X Z 0.05 = 1.96；Z 0.01 = 2.58QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两均数差及可信区间 两个均数差的可信区间可用于两个均 数的比较，由于两个均数差等于 0 时 为无统计学意义。如果两个均数差的 可信区间不包含 0 （上下限均大于 0 或上下限均小于 0），则两个均数差 差别有统计学意义；反之，两个均数 差的可信区间包含 0 ，则差别无统计 学意义。QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine两个均数差的95％可信区间：d = x1 ? x 2S X1 ? X 2 =(n1 ? 1)S+ (n2 ? 1)S ? 1 1 ? ×? + ? ?n n ? n1 + n2 ? 2 2 ? ? 12 1 2 2(d ? t0.05 ,ν? S X 1 ? X 2 , d + t 0.05 ,ν ? S X 1 ? X 2)QIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of MedicineQIU Yu-lan Shanghai Jiao Tong University School of Medicine QIU Yu-lan Shanghai Jiao Tong University School of Medicine
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