On the consequences of overstratification

It is common, in particular in observational studies in epidemiology, to impose stratification to adjust for possible effects of age and other variables on the binary outcome of interest. Overstratification may lower the precision of the estimated effects of interest. Understratification risks bias. These issues are studied analytically. Asymptotic results show that loss of efficiency depends on the true effect and on a measure of the average imbalance across strata between exposed and unexposed individuals. Bias depends on the correlation between stratum-specific size imbalances and event rates in the unexposed. Approximate results are also given. An example is used.