ABSTRACT
Multiple strategies exist for using covariate information in randomized treatment allocation schemes. Since most clinical trials cannot be repeated, reliance on balance in expectation may be considered insufficient. Hence, “Block what you can and randomize what you cannot”1 is the wisdom often invoked for clinical trial design. Kalish and Begg2 review a comprehensive list of treatment allocation strategies. The most common and straightforward method for using covariates is stratified randomization, an algorithm that applies permuted blocks to individual strata.3 When the ratio of sample size to strata is small, however, stratified randomization may actually increase the imbalance for given covariates. For these settings, minimization methods that dynamically balance the treatment assignment marginally for each factor have been proposed.4-6
Use of covariates in the analysis of randomized experiments often is guided by our understanding of linear models. In this setting, covariates are not needed to produce an unbiased estimate of effect or a test of appropriate size but may be used to improve power by reducing the residual variance. In nonlinear models, however, omitting covariates may reduce efficiency because the treatment effect estimators are biased toward zero.7-10
Data analysis is made more complicated by randomization methods that use covariates.11-13 Green and Byar demonstrated that an unstratified analysis of binary data generated from a trial using important prognostic covariates in a stratified treatment allocation rule yields a conservative test with noticeably reduced power. A stratified analysis in this setting preserves the nominal size of a test.14 For more complex randomization strategies, such as the adaptive designs, however, there is no direct link between the covariate structure in the design and the test statistic.
