Comparison of Two Nonparametric Regression Curves: Test of Superiority and Noninferiority

• Activity Number: 325
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Council of Chapters
• Author(s): Mervyn Joseph Silvapulle*+
• Companies: Monash University
• Keywords: Constrained inference ; Noninferiority ; Order restricted inference ; Superiority

Abstract

Tests are developed for detecting differences between two univariate nonparametric regression curves. The objective of the new method is to establish that a treatment is noninferior to another for the whole population and also that it is superior at least for a part of the population, when the treatment effect is represented by a nonparametric regression curve. The inference problem is formulated as test against the alternative hypothesis which says that (a) the regression curve for population 1 does not fall below that for population 2 by more than a specified small amount at any value of the covariate, and (b) the former exceeds the latter, at some values of the covariate, by more than a specified amount. The test statistic is easy to compute and also apply using a table of asymptotic critical values. Because this test is conservative, a less conservative bootstrap test is proposed and is shown to be asymptotically valid. In a simulation study, we observed that the type I error rates for these tests were close to the nominal level, and the bootstrap test exhibited higher estimated power, as expected.