where
Grouped Data Poisson Regression.
The second and third
approaches use Poisson regression methods [9,10,11,12]
to describe the joint effect of several risk factors on cause-
specific mortality. The general form of the regression function is
represents the unknown mortality rate, 
is the number of deaths, and 
denotes the person-years at
risk in the 
cell of an ADS. The i subscript refers to
age, the j subscript indicates the dimensions of the ADS that
correspond to factors of secondary interest (e.g., birth-cohort, SES)
and the k subscript indicates exposure related covariates that are
of primary interest, i.e. facility, internal exposure, and external
exposure. The ''external/internal" model is used---[12],
chapter 4---in which the baseline rates 
are
proportional to known external standard rates 
, and
the 
are treated as observed values of Poisson variates with
expectation given by Eq. 1. For a given cell in the ADS, the value
of 
will also depend on birth cohort. This approach has
two advantages. First, it is not necessary to provide a parametric
description of the age component of the baseline rates, and second the
''intercept" terms (when all explanatory variables are at their
reference level) provide estimates of the SMRs for the internal
control group.
