Testing hypotheses under covariate-adaptive randomisation and additive models

Abstract

Covariate-adaptive randomisation has a long history of applications in clinical trials. Shao, Yu, and Zhong [(2010). A theory for testing hypotheses under covariate-adaptive randomization. Biometrika, 97, 347–360] and Shao and Yu [(2013). Validity of tests under covariate-adaptive biased coin randomization and generalized linear models. Biometrics, 69, 960–969] showed that the simple t-test is conservative under covariate-adaptive biased coin (CABC) randomisation in terms of type I error, and proposed a valid test using the bootstrap. Under a general additive model with CABC randomisation, we construct a calibrated t-test that shares the same property as the bootstrap method in Shao et al. (2010), but do not need large computation required by the bootstrap method. Some simulation results are presented to show the finite sample performance of the calibrated t-test.

Keywords

• biased coin
• clinical trials
• robust test
• t-test
• type i error
• variance estimator