A General formulation for standardization of rates as a method to control confounding by measured and unmeasured disease risk factors

Abstract

Standardization, a common approach for controlling confounding in population-studies or data from disease registries, is defined to be a weighted average of stratum specific rates. Typically, discussions on the construction of a particular standardized rate regard the strata as fixed, and focus on the considerations that affect the specification of weights. Each year the data from the SEER cancer registries are analyzed using a weighting procedure referred to as ``direct standardization for age.'' To evaluate the performance of direct standardization, we define a general class of standardization operators. We regard a particular standardized rate to be the output of an operator and a given data set. Based on the functional form of the operators, we define a subclass of standardization operators that controls for confounding by measured risk factors. Using the fundamental disease probability paradigm for inference, we establish the conclusions that can be drawn from year-to-year contrasts of standardized rates produced by these operators in the presence of unmeasured cancer risk factors. These conclusions take the form of falsifying specific assumptions about the conditional probabilities of disease given all the risk factors (both measured and unmeasured), and the conditional probabilities of the unmeasured risk factors given the measured risk factors. We show the one-to-one correspondence between these falsifications and the inferences made from the contrasts of directly standardized rates reported each year in the Annual Report to the Nation on the Status of Cancer.