Use of max and min scores for trend tests for association when the genetic model is unknown

In case-control studies, the Cochran-Armitage (CA) trend test is powerful for detection of an association between a risk allele and a marker. To apply this test, a score should be assigned to the genotypes based on the genetic model. When the underlying genetic model is unknown, the trend test statistic is a function of the score. In this paper, simple procedures are given to obtain two scores (max and min), which respectively maximize and minimize the CA trend test statistics for genetic associations. These two scores can be used to examine the effect of the choice of scores on the test of no association. When the CA trend test statistic with the max (or min) score is less (or greater) than a prespecified value, the conclusion is clear: we will accept (or reject) the null hypothesis of no association for any scores used. When this value is less than the CA trend test statistic with the max score but greater than the one with the min score, the decision of whether or not to reject the null hypothesis depends on the choice of scores. In this situation, the CA trend test with a prespecified score cannot be used without careful scientific justification of the choice of scores. The use of max and min scoring schemes is applied to a real data set.