Model-robust designs for nonlinear quantile regression.

We construct robust designs for nonlinear quantile regression, in the presence of both a possibly misspecified nonlinear quantile function and heteroscedasticity of an unknown form. The asymptotic mean-squared error of the quantile estimate is evaluated and maximized over a neighbourhood of the fitted quantile regression model. This maximum depends on the scale function and on the design.

Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics.

Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well-being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate-adjusted response-adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well-being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial.