Order‐restricted hypothesis tests for nonlinear mixed‐effects models with measurement errors in covariates

Abstract

Order‐restricted hypothesis testing problems frequently arise in practice, including studies involving regression models for longitudinal data. These tests are known to be more powerful than tests that ignore such restrictions. In this article, we consider order‐restricted tests for nonlinear mixed‐effects models with measurement errors in time‐dependent covariates. We propose to use a multiple imputation method to address measurement errors, since this approach allows us to use existing complete‐data methods for order‐restricted tests. Some theoretical results are presented. We evaluate our proposed methods via simulation studies that demonstrate they are more powerful than either a competing naive method or a two‐step approach to testing hypotheses. We illustrate the use of our proposed approach by analyzing data from an HIV/AIDS study.