Biometrics 68, 990–991 September 2012 DOI: 10.1111/j.1541-0420.2012.01804.x CORRESPONDENCE Letter to the Editor “Comment on Proschan et al. (2011), Out of the Frying Pan and in to the Fire?” From: Vance W. Berger, PhD Biometry Research Group, National Cancer Institute, Executive Plaza North, Suite 3131, 6130 Executive Boulevard, MSC 7354, Bethesda, MD 20892-7354, U.S.A. email: vb78c@nih.gov I read with great interest the recent paper by Proschan, Brittain, and Kammerman (2011) that argues, correctly and articulately, that in the cases considered true or standard ran- domization is preferable to minimization. But if wearing a seat belt is a good idea when driving in inclement weather, then is it not also a good idea when driving in any type of weather? Though this point did not seem to be made explicitly, the ar- guments presented in favor of true randomization in the cases considered extend also to other cases, and for brevity, these arguments will not be repeated here. There is, however, an ad- ditional argument that favors true randomization, and that is that minimization, by its very nature, precludes the possi- bility of allocation concealment and almost ensures selection bias (Berger, 2005, 2010). As noted in this latter reference: “Investigators using minimization can determine the group to which a prospective subject would be allocated, and then decide if this is a good thing or a bad thing, in terms of creating an imbalance with respect to some key predictor of outcome not considered in the imbalance function.” Strict minimization, which is deterministic, will allow in- vestigators to know for sure. But any minimization that uses biasing probabilities extreme enough to force balance will also allow investigators to be reasonably certain of the next allo- cation for a prospective patient, and this is enough to bias the trial. If, on the other hand, the biasing probabilities are sufficiently close to 50%, then this defeats the purpose of us- ing minimization, as balance will then not be assured even with respect to the covariates used in the imbalance func- tion. Clearly, then, minimization is not ideal. But even among “standard” randomization methods, some are better than others. The authors used the specific method of permuted blocks as an example of true or standard randomization. It is true that the permuted block method does constitute one type of true randomization, and a particularly popular type at that, but let us not confuse popularity with appropriateness. Attempts at masking are almost never completely and demonstrably successful, even in trials labeled as “masked” or “blinded”. Unless the trial is not only planned as masked but also per- fectly masked, the more restrictive a randomization scheme, the more it compromises efforts at allocation concealment. Therefore, like minimization, although not to the same ex- tent, the permuted block method is susceptible to prediction and selection bias (Berger, Ivanova, and Deloria-Knoll, 2003; Berger, 2005). So using the permuted block method instead of minimiza- tion represents jumping out of the frying pan and into the fire. Fortunately, there is a better way. The maximal proce- dure (Berger et al., 2003; Berger, 2005) matches the permuted blocks procedure on control of chronological bias while of- fering better control of selection bias. Moreover, it does not introduce additional research costs, so, in the terminology of game theory, one might say that the permuted blocks method is inadmissible, and the dominating (uniformly better) proce- dure not only exists, but also can be identified explicitly and put into practice. Clinical trials are too important, in terms of their influence on medical practice, to use any research methods but the best available. Acknowledgement The author thanks the review team for helpful comments that resulted in a much-improved final version. References Berger, V. W. (2005). Selection Bias and Covariate Imbalances in Ran- domized Clinical Trials, Chichester, UK: John Wiley & Sons. Berger, V. W. (2010). Minimization, by its nature, precludes al- location concealment and invites selection bias, Contemporary Clinical Trials 31, 406. Berger, V. W., Ivanova, A., and Deloria-Knoll, M. (2003). Minimizing predictability while retaining balance through the use of less re- strictive randomization procedures, Statistics in Medicine 22(19), 3017–3028. Proschan, M., Brittain, E., and Kammerman, L. (2011). Minimize the use of minimization with unequal allocation, Biometrics. The authors replied as follows: We thank Dr. Berger for his correspondence about an is- sue we omitted—selection bias. He raises a very good point that susceptibility to selection bias is another reason to prefer randomization to minimization. Selection bias is a key issue 990 C  2012, The International Biometric Society No Claim to original US government works