Order-restricted scores test for the evaluation of population-based case-control studies when the genetic model is unknown.

The Cochran-Armitage (CA) linear trend test for proportions is often used for genotype-based analysis of candidate gene association. Depending on the underlying genetic mode of inheritance, the use of model-specific scores maximises the power. Commonly, the underlying genetic model, i.e. additive, dominant or recessive mode of inheritance, is a priori unknown. Association studies are commonly analysed using permutation tests, where both inference and identification of the underlying mode of inheritance are important. Especially interesting are tests for case-control studies, defined by a maximum over a series of standardised CA tests, because such a procedure has power under all three genetic models. We reformulate the test problem and propose a conditional maximum test of scores-specific linear-by-linear association tests. For maximum-type, sum and quadratic test statistics the asymptotic expectation and covariance can be derived in a closed form and the limiting distribution is known. Both the limiting distribution and approximations of the exact conditional distribution can easily be computed using standard software packages. In addition to these technical advances, we extend the area of application to stratified designs, studies involving more than two groups and the simultaneous analysis of multiple loci by means of multiplicity-adjusted p-values for the underlying multiple CA trend tests. The new test is applied to reanalyse a study investigating genetic components of different subtypes of psoriasis. A new and flexible inference tool for association studies is available both theoretically as well as practically since already available software packages can be easily used to implement the suggested test procedures.