Estimation and Inference Concerning Ordered Means in Analysis of Covariance Models with Interactions

• Activity Number: 320
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jason Leonard Morrissette*+ and Michael Paul McDermott
• Companies: University of Rochester and University of Rochester
• Keywords: order constrained inference ; likelihood ratio test ; Johnson-Neyman procedure ; quadratic programming

Abstract

We present methods for estimating the parameters of an analysis of covariance model under pre-specified order restrictions on the mean response across the levels of a grouping variable. The order restriction is assumed to hold across all levels of categorical covariates and across pre-specified ranges of continuous covariates, each of which may interact with the grouping variable. The estimation procedure involves solving a quadratic programming minimization problem with a carefully specified constraint matrix. A likelihood ratio test for equality of the ordered group mean responses is developed and the null distribution of the test statistic is described. A Johnson-Neyman-type procedure for identifying regions of the covariates which correspond to significant group differences is also formulated. The proposed methods are demonstrated using data from a clinical trial of the dopamine agonist pramipexole for the treatment of early Parkinson's disease.