04.4.1 应用的基本条件
在临床研究中，混杂偏倚（Confounding Bias）是阻碍我们发现真实因果关系的重大障碍。在构建“双维融合的精准分层诊疗体系”中，针对患者群体的不同预后特征（如肿瘤分期、年龄分段等）进行分层卡方检验（Cochran-Mantel-Haenszel 检验，CMH 检验），可以帮助我们剥离混杂偏倚，看清治疗方案的“本质疗效”。
CMH 检验主要用于分析两个二分类变量（自变量与因变量）之间的关联性，同时控制一个或多个分类混杂因素的影响。
A. 必须满足的基本条件
观测独立性：每个患者只能归属于交叉表中的一个格子（无重复计数）。
变量属性：
自变量为二分类（如：治疗A组 / 治疗B组）。
因变量为二分类（如：无复发 / 复发）。
分层混杂变量为分类变量（如：临床I期 / 临床II期）。
样本量要求：各分层内的 2×2 交叉表总样本量不宜过小（建议各层 N ≥40）。
B. 满足条件的正面示例：
研究背景：在“双维融合的精准分层诊疗体系”中，研究团队拟评价两套靶向维持治疗方案（方案A vs 方案B）对非小细胞肺癌（NSCLC）患者1年无复发状态（无复发/复发）的实际效果。
数据情况：由于入组患者包含“早期（临床I期）”与“进展期（临床II期）”两类群体，且两组间分期比例分布不均（分期会同时影响方案选择和复发结局，属于典型的分类混杂因素）。自变量（方案）为二分类，因变量（复发转归）为二分类，分层变量（分期）为二分类。
判定：完全符合 CMH 检验的应用条件，可通过分层消除分期带来的混杂干扰。
C. 不满足条件的负面示例（因果剖析与统计取舍）：
在实际临床分析中，如果混杂因素不具备分类特征或样本结构不合理，强行套用 CMH 检验将导致严重错误：
反面案例 1：混杂因素为连续性变量（如：年龄、连续的生物标志物浓度）
研究背景：评估新药与老药对患者1年存活率（生存/死亡）的差异，需要控制患者的连续年龄（如20-80岁，未分组）这一混杂因素。
错用因果：CMH 检验只能处理分类分层。如果将未分组的连续年龄直接作为分层变量，SPSS 会将每一个具体的年龄值（如 41岁、42岁、43岁...）强制识别为一个独立的层，从而产生几十个极度稀疏的“空壳层”。每一层内仅包含 1-2 例受试者，导致卡方公式在计算期望频数时分母趋近于零，系统报错或估算出的 OR 值产生严重偏倚（失真）。
取舍策略：
方案一（推荐）：放弃分层卡方，直接采用二元 Logistic 回归（Binary Logistic Regression），将药物分组（分类）和连续年龄（协变量）同时纳入模型进行多因素校正。
方案二：根据临床指南将年龄转化为等级分类变量（如：<60岁为中青年组，≥60岁为老年组），再采用标准 CMH 检验。
反面案例 2：小样本下过度分层（导致多层内出现零细胞，即“稀疏数据”）
研究背景：在一项小样本（N = 45）的临床探索性试验中，对比两组患者的疗效（有效/无效）。研究者为了追求完美，试图同时控制“性别（2层）”、“肿瘤病理类型（3层）”和“吸烟史（2层）”三个混杂因素。
错用因果：CMH 的分层总数等于所有分层水平的乘积。本例的分层总数为 2×3×2 = 12层。45 例患者被分配到 12 个分层后，平均每层只有不到 4 人。进入 2×2列表后，大部分格子的人数和理论频数都变为了 0。此时不仅 Breslow-Day 齐性检验由于方差不齐无法运行，CMH 加权算法也会因为大量格子频数为 0 导致加权权重失效，无法得出可信的合并 OR。
取舍策略：
方案一：合并或精简分层。在不违背临床专业逻辑的前提下，只保留最核心的一个分类混杂因素（如仅保留病理类型），删除或忽略次要混杂，使每层内样本充盈。
方案二：如果样本量确实无法增加，应采用精确 Logistic 回归（Exact Logistic Regression）或使用 Firth 惩罚最大似然估计进行多因素校正，而非强行分层。
04.4.2 核心概念深度剖析：为什么必须控制混杂？
A. 什么是混杂？
假设在总体数据中，治疗A组的无复发率显著高于治疗B组。但深入分析后发现，治疗A组里分配了大量的“临床I期（预后极好）”受试者，而治疗B组里大部分是“临床II期（预后极差）”受试者。 此时，“临床分期”同时影响了患者的方案选择和临床转归，这就是混杂偏倚。直接合并算出的 P 值和 OR值会产生虚假的放大或缩小。
B. 辛普森悖论（Simpson's Paradox）
这是医学统计中最著名的“视觉魔术”：在分层分析时，每个分层中都是方案 A 优于方案 B；但是一旦把所有层的数据简单粗暴地合并到一起，竟然得出了方案 B 优于方案 A 的相反结论。这就是不加控制的混杂偏倚导致的统计学灾难。
C. CMH 检验的解决方案
CMH 检验在后台分别计算每个层（Stratum）的卡方值、实际频数和理论频数，最后通过加权合并的方式，计算出一个排除分层干扰的加权合并 OR值（Common Odds Ratio）。
04.4.3 SPSS实战案例
A. 数据录入
第一步：数据录入
第二步：进入交叉表多层模块
点击顶部菜单：分析 (Analyze) ──► 描述统计 (Descriptive Statistics) ──► 交叉表 (Crosstabs...)。
变量多维布局（核心教学点：Layer 的使用）
将 治疗方案 Group（自变量）选入 行 (Row) 框中。
将 1年无复发状态 Outcome（因变量）选入 列 (Column) 框中。
【分层核心】 将 基线临床分期Stratum（分层混杂变量）选入 层 1 (Layer 1 of 1) 框中。
第三步：勾选 CMH 统计量，设置百分比与运行
点击右侧 “统计 (Statistics...)” 按钮。
勾选 卡方 (Chi-square)。
【核心动作】 勾选最下方的 Cochran's 和 Mantel-Haenszel 统计量 (Cochran's and Mantel-Haenszel statistics)。
在其右侧自动激活的 检验公共几率比为 (Test common odds ratio equals) 输入框中，保持默认数值 1 即可。
点击右侧 “单元格 (Cells...)” 按钮。
在“百分比 (Percentages)”中，勾选 行 (Row)。
点击 继续 (Continue)，再点击 确定 (OK)。
04.4.4 结果解读与论文汇报规范
A. 频数表与卡方检验表
运行后，SPSS 输出结果除了给出“每个分层单独的普通卡方表格”外，最重要的是给出了以下两张判定整体疗效的灵魂表格：
| Group * Outcome * Stratum Crosstabulation | Group * Outcome * Stratum Crosstabulation | Group * Outcome * Stratum Crosstabulation | Group * Outcome * Stratum Crosstabulation | Group * Outcome * Stratum Crosstabulation | Group * Outcome * Stratum Crosstabulation | Group * Outcome * Stratum Crosstabulation |
|---|---|---|---|---|---|---|
| Stratum | Stratum | Stratum | Stratum | Outcome | Outcome | Total |
| Stratum | Stratum | Stratum | Stratum | 0 | 1 | Total |
| 1 | Group | 1 | Count | 6 | 24 | 30 |
| 1 | Group | 1 | Expected Count | 9.0 | 21.0 | 30.0 |
| 1 | Group | 1 | % within Group | 20.0% | 80.0% | 100.0% |
| 1 | Group | 2 | Count | 12 | 18 | 30 |
| 1 | Group | 2 | Expected Count | 9.0 | 21.0 | 30.0 |
| 1 | Group | 2 | % within Group | 40.0% | 60.0% | 100.0% |
| 1 | Total | Total | Count | 18 | 42 | 60 |
| 1 | Total | Total | Expected Count | 18.0 | 42.0 | 60.0 |
| 1 | Total | Total | % within Group | 30.0% | 70.0% | 100.0% |
| 2 | Group | 1 | Count | 15 | 15 | 30 |
| 2 | Group | 1 | Expected Count | 18.0 | 12.0 | 30.0 |
| 2 | Group | 1 | % within Group | 50.0% | 50.0% | 100.0% |
| 2 | Group | 2 | Count | 21 | 9 | 30 |
| 2 | Group | 2 | Expected Count | 18.0 | 12.0 | 30.0 |
| 2 | Group | 2 | % within Group | 70.0% | 30.0% | 100.0% |
| 2 | Total | Total | Count | 36 | 24 | 60 |
| 2 | Total | Total | Expected Count | 36.0 | 24.0 | 60.0 |
| 2 | Total | Total | % within Group | 60.0% | 40.0% | 100.0% |
| Total | Group | 1 | Count | 21 | 39 | 60 |
| Total | Group | 1 | Expected Count | 27.0 | 33.0 | 60.0 |
| Total | Group | 1 | % within Group | 35.0% | 65.0% | 100.0% |
| Total | Group | 2 | Count | 33 | 27 | 60 |
| Total | Group | 2 | Expected Count | 27.0 | 33.0 | 60.0 |
| Total | Group | 2 | % within Group | 55.0% | 45.0% | 100.0% |
| Total | Total | Total | Count | 54 | 66 | 120 |
| Total | Total | Total | Expected Count | 54.0 | 66.0 | 120.0 |
| Total | Total | Total | % within Group | 45.0% | 55.0% | 100.0% |
| Chi-Square Tests | Chi-Square Tests | Chi-Square Tests | Chi-Square Tests | Chi-Square Tests | Chi-Square Tests | Chi-Square Tests |
|---|---|---|---|---|---|---|
| Stratum | Stratum | Value | df | Asymptotic Significance (2-sided) | Exact Sig. (2-sided) | Exact Sig. (1-sided) |
| 1 | Pearson Chi-Square | 2.857c | 1 | .091 | ||
| 1 | Continuity Correctionb | 1.984 | 1 | .159 | ||
| 1 | Likelihood Ratio | 2.899 | 1 | .089 | ||
| 1 | Fisher's Exact Test | .158 | .079 | |||
| 1 | Linear-by-Linear Association | 2.810 | 1 | .094 | ||
| 1 | N of Valid Cases | 60 | ||||
| 2 | Pearson Chi-Square | 2.500d | 1 | .114 | ||
| 2 | Continuity Correctionb | 1.736 | 1 | .188 | ||
| 2 | Likelihood Ratio | 2.521 | 1 | .112 | ||
| 2 | Fisher's Exact Test | .187 | .094 | |||
| 2 | Linear-by-Linear Association | 2.458 | 1 | .117 | ||
| 2 | N of Valid Cases | 60 | ||||
| Total | Pearson Chi-Square | 4.848a | 1 | .028 | ||
| Total | Continuity Correctionb | 4.074 | 1 | .044 | ||
| Total | Likelihood Ratio | 4.883 | 1 | .027 | ||
| Total | Fisher's Exact Test | .043 | .022 | |||
| Total | Linear-by-Linear Association | 4.808 | 1 | .028 | ||
| Total | N of Valid Cases | 120 | ||||
| a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 27.00. |
| b. Computed only for a 2x2 table | b. Computed only for a 2x2 table | b. Computed only for a 2x2 table | b. Computed only for a 2x2 table | b. Computed only for a 2x2 table | b. Computed only for a 2x2 table | b. Computed only for a 2x2 table |
| c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. | c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. | c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. | c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. | c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. | c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. | c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 9.00. |
| d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. | d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. | d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. | d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. | d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. | d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. | d. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.00. |
B. 层间几率比均一性检验（Breslow-Day 齐性检验）
这是我们在解读 CMH 前必须通过的“预检验”。
| Tests of Homogeneity of the Odds Ratio | Tests of Homogeneity of the Odds Ratio | Tests of Homogeneity of the Odds Ratio | Tests of Homogeneity of the Odds Ratio |
|---|---|---|---|
| Chi-Squared | df | Asymptotic Significance (2-sided) | |
| Breslow-Day | .028 | 1 | .867 |
| Tarone's | .028 | 1 | .867 |
🎯 读表决策要领（核心教学点）：
读取 Breslow-Day 的 P值：本案例中 P = 0.867 > 0.05。
统计学意义：这证明两层（早期和进展期）中的治疗效应大小（即两层的 OR值 2.67 与 2.33）是同质、无显著差异的（Homogeneous）。
下阶段动作：既然两层效应方向和大小高度一致，允许我们合并这两层的数据，直接进入下一步读取合并后的 CMH 疗效。
(避坑：如果 Breslow-Day 的 P < 0.05，代表临床分期 and 治疗方案之间存在强烈的交互作用，合并OR毫无意义，必须分别独立汇报早期 and 进展期的不同疗效。)
Mantel-Haenszel 统计量与合并效应量（合并 OR估算）
| Tests of Conditional Independence（独立性检验） | Tests of Conditional Independence（独立性检验） | Tests of Conditional Independence（独立性检验） | Tests of Conditional Independence（独立性检验） |
|---|---|---|---|
| Chi-Squared | df | Asymptotic Significance (2-sided) | |
| Cochran's | 5.333 | 1 | .021 |
| Mantel-Haenszel | 4.407 | 1 | .036 |
| Under the conditional independence assumption, Cochran's statistic is asymptotically distributed as a 1 df chi-squared distribution, only if the number of strata is fixed, while the Mantel-Haenszel statistic is always asymptotically distributed as a 1 df chi-squared distribution. Note that the continuity correction is removed from the Mantel-Haenszel statistic when the sum of the differences between the observed and the expected is 0. | Under the conditional independence assumption, Cochran's statistic is asymptotically distributed as a 1 df chi-squared distribution, only if the number of strata is fixed, while the Mantel-Haenszel statistic is always asymptotically distributed as a 1 df chi-squared distribution. Note that the continuity correction is removed from the Mantel-Haenszel statistic when the sum of the differences between the observed and the expected is 0. | Under the conditional independence assumption, Cochran's statistic is asymptotically distributed as a 1 df chi-squared distribution, only if the number of strata is fixed, while the Mantel-Haenszel statistic is always asymptotically distributed as a 1 df chi-squared distribution. Note that the continuity correction is removed from the Mantel-Haenszel statistic when the sum of the differences between the observed and the expected is 0. | Under the conditional independence assumption, Cochran's statistic is asymptotically distributed as a 1 df chi-squared distribution, only if the number of strata is fixed, while the Mantel-Haenszel statistic is always asymptotically distributed as a 1 df chi-squared distribution. Note that the continuity correction is removed from the Mantel-Haenszel statistic when the sum of the differences between the observed and the expected is 0. |
| Mantel-Haenszel Common Odds Ratio Estimate（公共几率比估算） | Mantel-Haenszel Common Odds Ratio Estimate（公共几率比估算） | Mantel-Haenszel Common Odds Ratio Estimate（公共几率比估算） | Mantel-Haenszel Common Odds Ratio Estimate（公共几率比估算） |
|---|---|---|---|
| Estimate | Estimate | Estimate | .403 |
| ln(Estimate) | ln(Estimate) | ln(Estimate) | -.909 |
| Standard Error of ln (Estimate) | Standard Error of ln (Estimate) | Standard Error of ln (Estimate) | .398 |
| Asymptotic Significance (2-sided) | Asymptotic Significance (2-sided) | Asymptotic Significance (2-sided) | .022 |
| Asymptotic 95% Confidence Interval | Common Odds Ratio | Lower Bound | .185 |
| Asymptotic 95% Confidence Interval | Common Odds Ratio | Upper Bound | .879 |
| Asymptotic 95% Confidence Interval | ln(Common Odds Ratio) | Lower Bound | -1.689 |
| Asymptotic 95% Confidence Interval | ln(Common Odds Ratio) | Upper Bound | -.129 |
| The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed under the common odds ratio of 1.000 assumption. So is the natural log of the estimate. | The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed under the common odds ratio of 1.000 assumption. So is the natural log of the estimate. | The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed under the common odds ratio of 1.000 assumption. So is the natural log of the estimate. | The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed under the common odds ratio of 1.000 assumption. So is the natural log of the estimate. |
🎯 最终指标抓取：
控制混杂后的净效应 P 值：
读取第一行 Cochran's 对应的渐进显著性：P = 0.021。
临床意义：在排除、控制了基线临床分期的干扰后，治疗 A 组的1年无复发率仍然显著优于治疗 B 组（调整后 P = 0.021 < 0.05）。
控制混杂后的净效应量（合并 OR值）：
读取表格中的 Common Odds Ratio：估算值为 0.403，其 95% 置信区间（95%CI）为 [0.185, 0.879]。
临床意义：排除分期干扰后，接受治疗 A 组的患者在 1 年内的复发几率仅为 B 组的 0.403倍。由于 OR < 1 且置信区间上限未跨越 1（[0.185, 0.879]），证明治疗 A 具有极其显著的临床防复发增效作用。