J.1 DOSE AND DOSE SURROGATES
The presumed effect on risk of the dose or dose surrogate variable, Di, in model is much simpler (involving only the ERR parameter, b) than the model for the background risk (involving many additional parameters a); however, Di will also vary in time. For example, if Di is cumulative dose from a particular nearby plant for representative individuals, then Di for all census tracts near that plant would be zero until the start of operations of that plant and would accumulate in time during operation. Even treatment of much simpler dose surrogates (exposed or not exposed according to distance) should reflect startup times of each plant or facility.
Other factors may also need to be considered in the calculation of Di; for example, if it is known that a population around a particular plant or facility has been highly mobile over the period of exposure then it would be desirable to incorporate that mobility into the calculation of Di in order to approximate the average cumulative dose to the individuals in each census tract for each time period considered. If distance is to be used as a dose surrogate then time-weighted distance could also be considered.
J.2 PERSON-YEAR CALCULATIONS
Another key issue in Poisson modeling is to adequately approximate person-years of exposure to some hazard, pyi, as well as counting the number of events Ni. For each cell in the tabulation of events cross-classified by geographical unit, race, age, and calendar time, census data are required in order to determine the population size for each table entry, i.e., the whole population must be classified according to these same variables. Data from each decennial census must be interpolated to the out years. The accuracy of person-year approximations affect the modeling of Ni using Poisson regression and inaccuracies in estimation of person-years is one (among many) reasons to assume that the Poisson model may not adequately capture the variability of the observed counts Ni.
It is likely that observed counts Ni will depart from the Poisson regression distribution in a way that must be adequately accommodated when fitting the regression models such as (5). If a random variable is distributed according to the Poisson distribution then the variance of Ni is also equal to mi. However, there are good reasons why we expect that the actual variability of Ni will be greater than that predicted by Poisson distribution. For example, as mentioned above, for the out years at least, the population size and hence person-years will not be known exactly. Even more importantly, however, is that other known and unknown risk factors that influence disease