![]() We also modify the Blackwell-Hodges model to allow for selection bias only when the investigator is able to discern the next assignment with certainty. Further, this bias is not eliminated by the use of random block sizes. In an unmasked trial, the permuted-block design provides substantial potential for selection bias in the comparison of treatments due to the predictability of the assignments that is induced by the requirement of balance within blocks. The Blackwell-Hodges model is used to assess the potential for selection bias induced by investigator attempts to guess which treatment is more likely to be assigned to each incoming patient. An alternative strategy that requires no assumptions is to perform the analysis using only the subset of complete blocks in which no observations are missing. ![]() This provides a basis for the analysis when responses from some patients are assumed to be missing-at-random. Permutation tests are also presented for the case of stratified analyses within one or more subgroups of patients defined post hoc on the basis of a covariate. Thus, if there is a positive intrablock correlation, which is more likely than not for m greater than 1, an analysis ignoring blocking will be unduly conservative. For blocks of common length 2m, the range of R is from -1/(2m-1) to 1. For these tests, it is shown that the size of a test obtained from an analysis incorporating the blocking (say T), versus an analysis ignoring the blocking (say TI), is related to the intrablock correlation coefficient (R) as TI = T(1-R). It is common, however, to ignore the blocking in the analysis. These include the block-stratified Mantel-Haenszel chi-square test for binary data, the blocked analysis of variance F test, and the blocked nonparametric linear rank test. ![]() Under a permutation model for statistical tests, proper analyses should employ tests that incorporate the blocking used in the randomization. This article describes some of the important statistical properties of the commonly used permuted-block design, also known simply as blocked-randomization. ![]()
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