AMFIT is a Poisson regression program with special features to
facilitate the analysis of rates. It is particularly useful for
dose-response analysis of rate (or event-time) tables created from cohort
follow-up data. Poisson regression analysis of rates is based on approximation
of the rate (hazard) function 
as piecewise constant on
fixed time intervals. Ordinarily the data are also grouped on covariate values.
When the piecewise constant hazard is modeled by stratification on time, the
analysis is closely related to the partial likelihood methods used by PEANUTS. In AMFIT the full hazard
function (including 
) can be modeled directly, which allows
for analyses different from those based on partial likelihood methods.
The formal model is that the number of events 
have a Poisson distribution with
means 
in conjunction with an EPICURE model 
. For grouped follow-up data the 
correspond to time at risk, for
example, person-years, and the to the number of events
within the time. In other applications of Poisson regression there is usually
some kind of “denominator”, , representing variations in
the means due to sampling period, area, volume, and so on.
Technically, because the 
values are not constants, the
number of cases in the cells of an event-time table do not follow a Poisson
distribution; however, because of the piecewise constant hazard function
assumption, the likelihood function for this survival data model is identical to
that for the Poisson model. The use of Poisson regression methods for cohort
data has been discussed by Breslow and Day(Breslow
and Day 1988) , Preston et al (Preston
1984), Frome (Frome
1983), Laird and Olivier (Laird and
Olivier 1981), and others.
For regression analyses of rates in a cohort, the rates are is
typically summarized in a cross-classification with one factor being intervals
of time and the other factors determining a cross-classification over the
(possibly time-dependent) covariate values. Each cell of this
cross-classification contains: the total time at risk 
, the number of events , and covariate values. We refer to
such a data summary as an event-time table. Making such tables involves complex
calculations that can be carried out easily and effectively with DATAB, which
was developed primarily for this purpose.