  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.
