Score Tests for a Mixture Model Where Both the Response Rate and Response Mean are Linear Functions of the Covariate

• Activity Number: 108
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Xiaohui Luo*+ and Dennis Boos+ and Roy Tamura
• Affiliation(s): North Carolina State University and North Carolina State Unviersity and Eli Lilly and Company
• Keywords: score test ; nonresponder ; simple linear regression ; maximum statistic ; permutation test ; likelihood ratio test

Abstract

For a mixture model where both the response rate and the response mean are linear functions of the covariate (dose level), we propose new score test statistics for a treatment effect. If the linear coefficient for the response rate is $\beta$, and $d$ is the linear coefficient for the mean, then the score statistics are derived from $H_0^1: \beta = 0$ (assuming $d=0$), $H_0^2: d = 0$ (assuming $\beta=0$), and $H_0: \beta = 0, \, d = 0$, respectively. For $H_0$ we propose a two-degree-of-freedom score statistic and also the maximum of the individual score statistics for $H_0^1$ and $H_0^2$, respectively. Using permutation critical values, the tests are compared with simple linear regression and the likelihood ratio test. A simulation study shows that under most of the circumstances considered, the two-degree-of-freedom score statistic and the likelihood ratio test give the best performance, while the simple linear regression is competitive when $\beta$ is large. But the score test is much easier to compute than the likelihood ratio test. The six methods are also applied to several real data sets, and the two-degree-of-freedom score statistic provides satisfactory results.