A method of assessing the sensitivity of the Cochran–Mantel–Haenszel test to an unobserved confounder

Observational studies, including the case-control design frequently used in epidemiology, are subject to a number of biases and possible confounding factors. Failure to adjust with them may lead to an erroneous conclusion about the existence of a causal relationship between exposure and disease. The Cochran-Mantel-Haenszel (CMH) test is widely used to measure the strength of the association between an exposure and disease or response, after stratifying on the observed covariates. Thus, observed confounders are accounted for in the analysis. In practice, there may be causal variables that are unknown or difficult to obtain. Hence, they are not incorporated into the analysis. Sensitivity analysis enables investigators to assess the robustness of the findings. A method for assessing the sensitivity of the CMH test to an omitted confounder is presented here. The technique is illustrated by re-examining two datasets: one concerns the effect of maternal hypertension as a risk factor for low birth weight infants and the other focuses on the risk of allopurinol on having a rash. The computer code performing the sensitivity analysis is provided in appendix A.