Cochran-Armitage Trend Test

The Cochran-Armitage Trend Test Operation will be performed along with a report and 2 charts. Only Markers and Samples that have passed the basic Matrix QA and the Hardy-Weinberg test, filtered by specified missingness thresholds, HW equilibrium conformity as well as non-mismatching markers status will be considered in this test.

You may find further details on how to perform basic statistical analysis in a population-based genetic association case-control study in this Nature Protocls article.

Using the recount of Genotypes done at the Genotype Frequency count, a 3×2 contingency table is considered for each marker as in the following example:

Observed AA Aa aa Row Total
Case 110 85 15 210
Control 90 72 48 210
Column Total 200 157 63 420

The Cochran-Armitage Trend Test introduces a suspected ordering of effects depending on the dosage of alleles. Thus 3 models are possible: dominant, co-dominant and recessive.
The Trend test is calculated as follows:


Trend Test = weight1 × ((ControlTot / SampleNb) × CaseAA -
    (CaseTot / SampleNb) × ControlAA) +
    weight2 × ((ControlTot / SampleNb) × CaseAa -
    (CaseTot / SampleNb) × ControlAa) +
    weight3 × ((ControlTot / SampleNb) × Caseaa -
    (CaseTot / SampleNb) × Controlaa)

The weights are selected according to the suspected mode of inheritance. For example, in order to test whether allele a is dominant over allele A, the choice t = (1, 1, 0) is locally optimal. To test whether allele a is recessive to allele A, the optimal choice is t = (0, 1, 1). To test whether alleles a and A are codominant, the choice t = (0, 1, 2) is locally optimal. In genome-wide association studies, the additive (or codominant) version of the test is used.

Next The Variance of the Trend Test has to be calculated:


Trend Test Variance = CaseTot ×
        ControlTot ×
        ((
          (
              (weight²1×(AATot×(SampleNb-AATot)))
              +
              (weight²2×(AaTot×(SampleNb-AaTot)))
              +
              (weight²3×(aaTot×(SampleNb-aaTot)))
          )
          -
          (
              2 × (
              (weight²1×weight²2×AATot×AaTot)
              +
              (weight²2×weight²3×AaTot×aaTot)
              )
          )
        )
        /
        SampleNb³)

From these values GWASpi calculates the X² value as follows:


X² = Trend Test² / Trend Test Variance;

From this X² value, a p-value can be calculated for a X² distribution with 1 degree of freedom.

See Association Test Reports section for details on table displays and charts.