Monte Carlo methods are employed to compare the effectiveness of pair-matched and independent stratified samples for estimating relative risk in the presence of bias. Three approximations to the maximum likelihood estimator for stratified samples suggested by Woolf, Mantel and Haenszel and Birch, respectively [25, 17, 2], are also compared. The sampling model is modified to approximate the practical choices for a researcher and to allow for the loss of unmatchable sample units. The mean square error is always largest for the matched-pairs estimator, while of the stratified estimators, Woolf's consistently produces the smallest MSE, equaled only by Birch's when the samples are equal.