# Modeling incidence rates in family-based cohort: Poisson vs Cox

I have a cohort made of family trios and affected sib pairs (probands have rheumatoid arthritis - RA). I would like to calculate some incidence densities (for example apparitions of RA, of disease 1, disease 2 and disease 3 in each individual) and compare them with ratios (that's the point: IRR or HR?). Of course, IR and IRR (or HR?) have to be adjusted for the effects of age and sex.

First for incidence densities, I calculate number of events observed divided by the time at risk of event during the observation period. Then to have CIs, I use Poisson distribution.

Then I would like to see if some groups have higher or lower risks to declare some diseases for example RA patients vs non RA patients ; RA patients in ASP families vs RA patients in family trios ; disease 1 in RA patients vs disease 2 in RA patients etc.

I have read some questions here and some articles and I think I have many options:

• running a Poisson regression (I'm using R) which seems appropriate for modeling count data. I would take the log of my follow-up time in the offset option of glm and I would adjust for the effect of age and sex by putting them in the model:

glm(status~offset(log(futime))+sex+age, data=mydata, family=poisson)

So I would have IRRs and IRR confidence levels by exponentiation. Considering the comparisons I want to see, I would have to just subsetting my data into groups of interest. However my data are very correlated and I'm confused how the regression would take account of the kinship of the patients. I was thinking about GEE: http://aje.oxfordjournals.org/content/157/4/364.full and using geepack https://cran.r-project.org/web/packages/geepack/vignettes/geepack-manual.pdf but I don't know if it's adaptated. Also should I keep age in a continuous variable or in classes (18-29 / 30-39 / 40-49 etc.)

• fitting a Cox model. But same problem. Should I use the cluster argument? coxph(Surv(time,status)~sex+age+cluster(families), data=mydata)

I have read that paper which uses 'coxme' package by T Therneau:

accounting for family correlations, by fitting Cox models with Gaussian random effects models to the data with the R package “coxme” Puéchal X, Génin E, Bienvenu T, Le Jeunne C, Dusser DJ (2014) Poor Survival in Rheumatoid Arthritis Associated with Bronchiectasis: A Family-Based Cohort Study. PLoS ONE 9(10): e110066.doi:10.1371/journal.pone.0110066

To resume, it is unclear if I have to use rather Poisson regression than Cox model. I get that the 2 models are based on different assumptions, Poisson on constant hazards and Cox on proportionnal hazards. Maybe I should verify first the assumption of constant hazards but how? I don't know which fits the better since I have a family based cohort. Also, does the length of the follow-up have an influence? I have noticed in several publications a more often use of Cox model when follow-up is up to like 5 years. What about for long time follow-up which is my case?