Impact of Stratification Imbalance on Probability of Type I Error

The impact of ignoring the stratification effect on the probability of a Type I error is investigated. The evaluation is in a clinical setting where the treatments may have different response rates among the strata. Deviation from the nominal probability of a Type I error, α, depends on the stratification imbalance and the heterogeneity in the response rates; it appears that the latter has a larger impact. The probability of a Type I error is depicted for cases in which the heterogeneity in the response rate is present but there is no stratification imbalance. Three-dimensional graphs are used to demonstrate the simultaneous impact of heterogeneity in response rates and of stratification imbalance.