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Abstract:
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When a covariate in a regression analysis is ordered categorical, it is common to use one of the following simple strategies: (i) treat it as unordered, (ii) treat it as a numerical variable, (iii) collapse categories and treat it as a binary variable. All are unsatisfactory. As it is often reasonable to assume monotonicity, models can be fit by maximizing the likelihood subject to corresponding parameter constraints. Under the null hypothesis of no association and other usual assumptions, the usual F or chi-square statistic is distributed as a mixture of F or chi-square distributions with weights that can be determined analytically or by simulation and are dependent on the relative sample sizes of the categories. This work was motivated by analysis of gene expression levels in individuals who had normal cognition, mild cognitive impairment, and Alzheimer's disease. Of interest were genes that showed evidence of increased or decreased expression levels with cognitive decline. The results of applying the four analysis approaches to the Alzheimer's expression data will be shared. It is proposed that this approach be considered more often by applied statisticians.
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