Application To Genetics
Suppose that there are three possible genotypes at some locus, and we refer to these as aa, Aa and AA. The distribution of genotype counts can be put in a 2 × 3 contingency table. For example, consider the following data, in which the genotype frequencies vary linearly in the cases and are constant in the controls:
| Genotype aa | Genotype Aa | Genotype AA | Sum | |
|---|---|---|---|---|
| Controls | 20 | 20 | 20 | 60 |
| Cases | 10 | 20 | 30 | 60 |
| Sum | 30 | 40 | 50 | 120 |
In genetics applications, 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. For complex diseases, the underlying genetic model is often unknown. In genome-wide association studies, the additive (or codominant) version of the test is often used.
In the numerical example, the standardized test statistics for various weight vectors are
| Weights | Standardized test statistic |
|---|---|
| 1,1,0 | 1.85 |
| 0,1,1 | −2.1 |
| 0,1,2 | −2.3 |
and the Pearson chi-squared test gives a standardized test statistic of 2. Thus, we obtain a stronger significance level if the weights corresponding to additive (codominant) inheritance are used. Note that for the significance level to give a p-value with the usual probabilistic interpretation, the weights must be specified before examining the data, and only one set of weights may be used.
Read more about this topic: Cochran-Armitage Test For Trend
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