Abstract:
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Covariate-adaptive randomization mainly includes two families of procedures: stratified randomization and minimization. While the balance properties of the two families have been extensively studied in literature, the theory of inference following such randomization has drawn less attention. Recently, Shao et al. (2010) showed that the 2-sample t-test under stratified randomization is conservative, provided that the restricted randomization applied to any stratum is able to achieve a balance rate of Op(1). Hence, Efron's (1975) biased coin design satisfies this condition, whereas Wei's (1978) urn design and Smith's (1984) generalized coin design, with a balance rate of Op(n^0.5), do not. In our paper we showed that the conservativeness also holds for the latter two procedures, and even more generally, for any restricted randomization that is more balanced than complete randomization. We derived the asymptotic variance of the t-statistic when such restricted randomization is employed. We also used simulation to compare the degree of conservativeness under the above-mentioned procedures, and then adopted Shao et al.'s bootstrap method to restore the correct significance level.
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