If I use a Poisson model to explain an event, I have coefficients from analysis. How can we calculate epidemiological rates and ratios from these coefficients? Especially, is there a common way to automatize these calculations in R software?
More especially, if my dependent variable is discrete, which is a good rate or ratio to explain associations with independent variables? In cross-sectional studies, specially.
You can use log-binomial regression or poisson regression with robust variance estimation to directly estimate prevalence ratios from cross-sectional studies. This is often preferred to logistic regression since odds ratios overestimate the prevalence ratio, particularly when the outcome is not rare. See https://www.ncbi.nlm.nih.gov/pubmed/14567763
I haven't used R much, but the code for SAS is available at:
http://aje.oxfordjournals.org/content/162/3/199.full
R: If "model" is your glm, you can use predict(model, newdata, type="response") to get predicted counts or rates for the given combination of predictor values in newdata.
Hi Marcos. If you have a continuous outcome, you will be unable to estimate prevalence ratios. Prevalence ratios must be estimated for binary outcomes only.
Regarding the estimation of prevalence ratios via Poisson regression, you can interpret the Incidence Rate Ratio as a prevalence ratio if you are working with a binary outcome. To get IRR output, instead of the coefficients, you should use the option "irr" after adjusting your model in Stata. I do not use R, but maybe my report about Stata can help you to find out how to do the same in R.
You can use log-binomial regression or poisson regression with robust variance estimation to directly estimate prevalence ratios from cross-sectional studies. This is often preferred to logistic regression since odds ratios overestimate the prevalence ratio, particularly when the outcome is not rare. See https://www.ncbi.nlm.nih.gov/pubmed/14567763
I haven't used R much, but the code for SAS is available at:
http://aje.oxfordjournals.org/content/162/3/199.full
Why are you using Poisson instead of logistic regression to estimate prevalence?
How do you do a Poisson regression on a continuous dependent variable? (For now I will assume that you have a count of positive integers as dependent variable.)
James D Mancuso is right that odds ratios are overestimates of the risk ratio. However, you can use predicted probabilities to get the absolute values for prevalence in each of the groups you want to compare.
If you want to continue with Poisson regression, I'd think that you need to use prectied lambdas as Jochen Wilhelm mentioned but you need to convert them to predicted probabilities for a result of least 1, which would be: 1 - exp( - lambda).
First, I thank all you for answers. These have been all useful for me.
Second, and also too important. I committed a mistake at my asking. My dependent variable is DISCRETE, not continuous as I firstly wrote. Sorry for this. I have already corrected it above.
I have found the following to solve my problem.
Prevalence ratio is calculated as following:
RP = (prevalence on exposed) / (prevalence on unexposed)
This is possible only if we have dependent and independent binary variables. Using a Poisson regression model, we can use:
RP = exp(coefficient in Poisson model)
This rate standardize coefficients, so we can compare explaining variables among them in same scale. This is important for me (and so I think it is for many epidemiologists).
Regarding to Cauane's contributing, I must apologize firstly for my mistake asking about a continuous variable. In fact, my dependent variable is discrete. Also, I can inform that incidence density ratio (IDR) can be calculated on R using package "epiDisplay", command "idr.display". Therefore, it demands an offset. I have tested in my models and there are differences between IDR and RP calculated from same models.
I have adapted a function in R to calculate prevalence ratio using robust variance for confidence intervals and p-value. You must have "sandwich" package installed in your R. Use it just defining your "glm" model and call:
RP.Poisson(model)
The function is:
#####################
RP.Poisson
It's true for PR CAN BE ESTIMATED FROM BOTH POISSON AND GLM IN STATA BUT WHEN YOU SEND THE OUTPUTS TO PUBLICATION TABLES IN WORD, UNLIKE FOR POISSON MODEL THE GLM SAVED COEFFICIENTS OTHER THAN THE PR.
You can use a model based on the the glm family, library(broom), with the glm family you can use Poisson/Quasipoisson Regression
Your Outcome in Poisson model will be rate and not prevalence. If you are looking for a prevalence ratio then use logistic regression model.
You can simply exponentiate the coefficients to get the prevalence ratio from Poisson regression.
In SPSS, we can use GLM to conduct Poisson regression with appropriate data distribution and link function.
Analyze -> Generalized Linear Models -> Generalized Linear Models -> Tab: Type of model (Count - Poisson loglinear) -> Tab: Response -> Tab: Predictor -> Tab: Estimation: Robust estimator -> Tab: Statistics: Include Exponentiate parameter estimates.
Hope this can help
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