The foundations of confounding in epidemiology

AbstractA statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented. Confounding by a covariate C in the presence of data on C is distinguished from confounding in the absence of data on C. A covariate C is defined to be a nonconfounder in the absence of data on C if the population parameter of interest can be unbiasedly estimated (asymptotically) absent data on C. Under this definition, C may be a confounder for some parameters of interest and a nonconfounder for others. If C is a confounder for a parameter of interest that has a causal interpretation, we call C a causal confounder. When data on C are available, C is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through C. Bayesians, frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render C a non-confounder. In particular C will in general be a nonconfounder precisely when the crude data ignoring C are S-sufficient for the parameter of interest. The intuitive view held by many practicing epidemiologists that confounding by C represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori