Multiparameter one‐sided tests for nonlinear mixed effects models with censored responses

Nonlinear mixed‐effects (NLME) models are commonly used in longitudinal studies such as pharmacokinetics and HIV viral dynamics studies. NLME models are often derived based on underlying data‐generating mechanisms, therefore the parameters in these models often have natural physical interpretations that may suggest reasonable constraints on certain parameters. For example, the HIV viral decay rates for populations receiving anti‐HIV treatments may be reasonably expected to be nonnegative. Hypothesis testing for these parameters should incorporate practically reasonable constraints to increase statistical power. Motivated from HIV viral dynamic models, in this article we propose multiparameter one‐sided or constrained tests for NLME models with censored responses, for example, viral dynamic models with viral loads subject to lower detection limits. We propose approximate likelihood‐based tests that are computationally efficient. We evaluate the tests via simulations and show that the proposed tests are more powerful than the corresponding two‐sided or unrestricted tests. We apply the proposed tests to two AIDS datasets with new findings.