Magnitude and likelihood of loss resulting from non-stratified randomization

We investigate the power of detecting treatment differences by the stratified logrank test for balanced samples as compared to samples with unequal allocation to treatments within strata. Given non-stratified randomization to treatments, we relate power losses to their probability of occurrence. In addition, we evaluate the likelihood of zero cells. For power calculations, we employ an asymptotic formula and complement by Monte Carlo simulations to verify results in small samples. In the cases investigated, our results show that large power losses due to imbalance are relatively unlikely with 2 strata. Small strata, however, involve a non-negligible probability of wasting all observations because of zero cells or censoring.