Cochran-Mantel-Haenszel Test

The Cochran-Mantel-Haenszel test assesses the association between a binary exposure and a binary outcome across several strata, controlling for the stratifying variable and estimating a common odds ratio.

Cochran-Mantel-Haenszel 검정은 여러 층에 걸쳐 층 변수를 통제한 상태에서 이분 노출과 이분 결과의 연관을 검정하고 공통 오즈비를 추정한다.

Is treatment associated with recovery after accounting for differences between hospitals?

병원 간 차이를 고려한 뒤에도 치료가 회복과 관련이 있나요?

The Cochran-Mantel-Haenszel test sums observed minus expected counts across the 2 × 2 tables of each stratum and compares the result with its variance. The Mantel-Haenszel odds ratio summarizes the common association, and the Breslow-Day test checks whether the odds ratios are homogeneous across strata.

When to use Cochran-Mantel-Haenszel Test

• A 2 × 2 association must be adjusted for a categorical confounder.
• Data come from several centers, sites or age bands.
• A pooled odds ratio across strata is required.

When to use something else

• Odds ratios differ markedly between strata; report stratum-specific odds ratios or fit a logistic regression with an interaction.
• Several confounders, including continuous ones, need adjustment; use logistic regression.

Assumptions and requirements

• Observations are independent.
• The common odds ratio summary assumes similar odds ratios across strata, which the Breslow-Day test checks.
• The combined sample is large enough for the chi-square approximation.

What the analysis reports

• CMH chi-square statistic and p value
• Mantel-Haenszel common odds ratio with confidence interval
• Breslow-Day homogeneity test
• Stratum-specific 2 × 2 tables and odds ratios

How to report it

A Cochran-Mantel-Haenszel test controlling for [stratum] indicated a significant association between [exposure] and [outcome], χ²_MH(1) = [chi2], p = [p], OR_MH = [OR], 95% CI [[lower], [upper]].

Related methods

• Chi Square Test
• Binary Logistic Regression
• Fisher's Exact Test

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