Quote from
bmoroz82 on 06/18/2025, 7:19 am
Per our statisticians and epidemiologists…
Dear Dr. Osipov,
Many thanks for your question. You are correct that analyses using DATAB-generated rate files are not calculating relative risks based on cumulative case and non-case counts in exposed and unexposed groups (i.e. the classic (a/(a+b)…) notation) as is done in cross-sectional or many cohort studies. Instead, AMFIT uses Poisson regression to model variation in the (hazard) rates (cases/person-time) as a function of age, dose, and other factors. The variation in rates associated with different levels of some exposure (”doses”) can be described using relative rates (RRs), excess relative rates (ERRs) or differences in rates (EARs). Ignoring the dependence of rates on other factors (such as sex , smoking, or birth cohort) the rate at age [latex]\alpha[/latex] in a population exposed to dose [latex]d[/latex] can be written as [latex]\lambda(\alpha, d)[/latex] with [latex]\lambda(\alpha, 0)[/latex] as the baseline rate. We then have
[latex]RR(d) = \frac{\lambda(\alpha, d)}{\lambda(\alpha, 0)}[/latex]
[latex]EAR(d) = \lambda(\alpha, d) - \lambda(\alpha, 0)[/latex], and
[latex]ERR(d) = RR(d) - 1 = \frac{EAR(d)}{\lambda(\alpha, 0)}[/latex]
The Cox proportional hazards model assumes that the rate can be written as
[latex]\lambda(\alpha, d) = \lambda(\alpha, 0) \rho(d)[/latex], where [latex]\rho(d) = exp(\beta d)[/latex]
With this model, the RR does not depend on the baseline rate. Cox regression estimates the relative rate parameters without specification of a baseline rate model. While parameter estimation is based on differences in the dose distributions within risk sets consisting of the cases and non-cases at each distinct event time, the time values for the risk sets are superfluous. Epicure’s PEANUTS module can be used to estimate RR and ERR proportional hazard model parameters.
We note that, while the last “R” in ‘RR’ and ‘ERR’ is often defined as “risk”, in analyses of survival data one is actually comparing “rates”. Thus, for survival data analyzed using either Poisson regression (AMFIT) or Cox regression (PEANUTS) it is best to define RR and ERR as relative rates and excess relative rates, respectively.
The suite of Epicure modules can model all these scenarios. For a more technical discussion and examples of how to specify and fit such models, please review these pages of the manual available here:
https://hirosoft.com/wp-content/uploads/nethelp/NetHelp/index.html#!Documents/analysisofalargecohortstudyradiationandbreastcancer1.htm
Many thanks for your question. We hope this explanation is helpful. Let us know if you have other questions!
Hirosoft International, L.L.C.
Per our statisticians and epidemiologists…
Dear Dr. Osipov,
Many thanks for your question. You are correct that analyses using DATAB-generated rate files are not calculating relative risks based on cumulative case and non-case counts in exposed and unexposed groups (i.e. the classic (a/(a+b)…) notation) as is done in cross-sectional or many cohort studies. Instead, AMFIT uses Poisson regression to model variation in the (hazard) rates (cases/person-time) as a function of age, dose, and other factors. The variation in rates associated with different levels of some exposure (”doses”) can be described using relative rates (RRs), excess relative rates (ERRs) or differences in rates (EARs). Ignoring the dependence of rates on other factors (such as sex , smoking, or birth cohort) the rate at age 
in a population exposed to dose 
can be written as 
with 
as the baseline rate. We then have
, and
The Cox proportional hazards model assumes that the rate can be written as
, where 
With this model, the RR does not depend on the baseline rate. Cox regression estimates the relative rate parameters without specification of a baseline rate model. While parameter estimation is based on differences in the dose distributions within risk sets consisting of the cases and non-cases at each distinct event time, the time values for the risk sets are superfluous. Epicure’s PEANUTS module can be used to estimate RR and ERR proportional hazard model parameters.
We note that, while the last “R” in ‘RR’ and ‘ERR’ is often defined as “risk”, in analyses of survival data one is actually comparing “rates”. Thus, for survival data analyzed using either Poisson regression (AMFIT) or Cox regression (PEANUTS) it is best to define RR and ERR as relative rates and excess relative rates, respectively.
The suite of Epicure modules can model all these scenarios. For a more technical discussion and examples of how to specify and fit such models, please review these pages of the manual available here:
https://hirosoft.com/wp-content/uploads/nethelp/NetHelp/index.html#!Documents/analysisofalargecohortstudyradiationandbreastcancer1.htm
Many thanks for your question. We hope this explanation is helpful. Let us know if you have other questions!
Hirosoft International, L.L.C.
