Cochran-Armitage Trend Test
Jinjiang Fan
Introduction
The Cochran-Armitage Trend Test is a statistical method used to detect a dose-related trend in binary outcomes (e.g., positive/negative responses) across ordered groups. It assesses whether the proportion of positive responses increases (or decreases) with increasing dose levels. In genotoxicity testing, such as the in vitro micronucleus test, it helps determine whether higher concentrations of a test substance lead to a statistically significant rise in micronucleated cells. The test assumes a linear trend and is more powerful than general chi-square tests for trend detection. It is commonly recommended in regulatory guidelines like OECD TG 487.
Using your actual micronucleus assay data with varying cell counts per concentration:
Data Setup (4 dose levels):
You can substitute the green sections with your own data. If your dose levels differ, adjust the range from dose = 0:4 to dose = 0:# accordingly.
R Code Implementation
—----------------------------------------------------------------------------------------------------
# Cochran-Armitage Test
library(DescTools)
# IVM: Dose vs MN
# 5 Dose levels - Dose: 0 1 2 3 4
# Cases:
# nMn 20046, 19987, 19927, 19813, 19560
# Mn 203, 315, 328, 387, 591
# So: real data: Study No.##
dose <- matrix(c(
20046, 19987, 19927, 19813, 19560, 203, 315, 328, 387, 591
), byrow=TRUE, nrow=2, dimnames=list(mn=0:1,
dose=0:4))
Desc(dose)
CochranArmitageTest(dose, alternative="increasing")
CochranArmitageTest(dose)
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Copy / past the codes to: Run R code online or R or RStudio.
Expected Output Interpretation
The `Desc(dose)` command will provide descriptive statistics including:
- Cell counts in each group
- Proportions of micronuclei at each dose level
- Overall summary statistics
The `CochranArmitageTest(dose, alternative="increasing")` will test specifically for an increasing trend, which is appropriate for genotoxicity studies.
The `CochranArmitageTest(dose)` will provide a two-sided test.
Results Summary
Based on your data pattern, you should expect:
- Very high Z-statistic (likely > 10)
- Extremely significant p-value (p < 0.001)
- Strong positive dose-response relationship
- Clear evidence of genotoxicity
Data Pattern Analysis
Your data shows clear dose-response:
Dose 0: 203/20249 (1.00%) micronuclei
Dose 1: 315/20302 (1.55%) micronuclei
Dose 2: 328/20255 (1.62%) micronuclei
Dose 3: 387/20200 (1.92%) micronuclei
Dose 4: 591/20151 (2.93%) micronuclei
This shows approximately **3-fold increase** in micronuclei frequency from control to highest dose, indicating strong genotoxic potential.
E.g.
-----------------------------------------------------------------------------
dose (matrix, array)
Summary:
n: 101'157, rows: 2, columns: 5
Pearson's Chi-squared test:
X-squared = 231.12, df = 4, p-value < 2.2e-16
Log likelihood ratio (G-test) test of independence:
G = 222.57, X-squared df = 4, p-value < 2.2e-16
Mantel-Haenszel Chi-squared:
X-squared = 203.51, df = 1, p-value < 2.2e-16
Phi-Coefficient 0.048
Contingency Coeff. 0.048
Cramer's V 0.048
dose 0 1 2 3 4 Sum
mn
0 freq 20'046 19'987 19'927 19'813 19'560 99'333
perc 19.8% 19.8% 19.7% 19.6% 19.3% 98.2%
p.row 20.2% 20.1% 20.1% 19.9% 19.7% .
p.col 99.0% 98.4% 98.4% 98.1% 97.1% .
1 freq 203 315 328 387 591 1'824
perc 0.2% 0.3% 0.3% 0.4% 0.6% 1.8%
p.row 11.1% 17.3% 18.0% 21.2% 32.4% .
p.col 1.0% 1.6% 1.6% 1.9% 2.9% .
Sum freq 20'249 20'302 20'255 20'200 20'151 101'157
perc 20.0% 20.1% 20.0% 20.0% 19.9% 100.0%
p.row . . . . . .
p.col . . . . . .
Cochran-Armitage test for trend
data: dose
Z = -14.266, dim = 5, p-value < 2.2e-16
alternative hypothesis: increasing
Cochran-Armitage test for trend
data: dose
Z = -14.266, dim = 5, p-value < 2.2e-16
alternative hypothesis: two.sided
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