Adjustments to the Mantel-Haenszel test for data from stratified multistage surveys

The usual form of the Mantel-Haenszel test statistic assumes independent observations. This is inappropriate for data from a stratified multistage survey. Two alternative adjustments to the test statistic are developed to deal with this: (a) a modification of the effective sample size for each row of each table, using the design effects, extending a method proposed by Donald and Donner for familial aggregation studies; (b) a Taylor series approximation to the variance of the square root of the numerator of the Mantel-Haenszel statistic. Both methods are evaluated by application to both simulated and real data. The two methods perform equally well, and offer a considerable improvement over the unadjusted test statistic when observations from the same cluster are highly correlated. A simplified adjustment is also considered, as is the need for correction to the variance of the odds ratio estimator.