I would fit a Poisson model to the dose-response data with offsets for the baseline expecteds.
Sent from my iPhone > On Jan 8, 2014, at 10:49 AM, "Wollschlaeger, Daniel" > <wollschlae...@uni-mainz.de> wrote: > > My question is how I can fit linear relative rate models (= excess relative > risk models, ERR) using R. In radiation epidemiology, ERR models are used to > analyze dose-response relationships for event rate data and have the > following form [1]: > > lambda = lambda0(z, alpha) * (1 + ERR(x, beta)) > > * lambda is the event rate > * lambda0 is the baseline rate function for non-exposed persons and depends > on covariates z with parameters alpha > * ERR is the excess relative risk function for exposed persons and depends on > covariates x (among them dose) with parameters beta > * lambda/lambda0 = 1 + ERR is the relative rate function > > Often, the covariates z are a subset of the covariates x (like sex and age). > lambda is assumed to be log-linear in lambda0, and ERR typically has a linear > (or lin-quadratic) dose term as well as a log-linear modifying term with > other covariates: > > lambda0 = exp(alpha0 + alpha1*z1 + alpha2*z2 + ...) > ERR = beta0*dose * exp(beta1*x1 + beta2*x2 + ...) > > The data is often grouped in form of life tables with the observed event > counts and person-years (pyr) for each cell that results from categorizing > and cross-classifying the covariates. The counts are assumed to have a > Poisson-distribution with mean mu = lambda*pyr, and the usual > Poisson-likelihood is used. The interest is less in lambda0, but in inference > on the dose coefficient beta0 and on the modifier coefficients beta. > > In the literature, the specialized Epicure program is almost exclusively > used. Last year, a similar question on R-sig-Epi [2] did not lead to a > successful solution (I contacted the author). Atkinson & Therneau in [3] > discuss excess risk models but get lambda0 separately from external data > instead of fitting lambda0 as a log-linear term. Some R packages sound > promising to me (eg., gnm, timereg) but I currently don't see how to > correctly specify the model. > > Any help on how to approach ERR models in R is highly appreciated! > With many thanks and best regards > > Daniel > > [1] Preston DL. Beyond Dose Response: Describing Long-Term Health Effects of > Radiation Exposure. > http://isi.cbs.nl/iamamember/CD2/pdf/519.PDF > > [2] https://stat.ethz.ch/pipermail/r-sig-epi/2012-January/000265.html > > [3] Atkinson et al. 2008. Poisson models for person-years and expected rates. > http://www.mayo.edu/research/documents/biostat-81pdf/DOC-10026981 > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
