Contents
How is a Poisson regression similar to a logistic regression?
The Poisson regression model takes a very similar form to the logistic regression model (Chapter 30), each having a (usually) linear combination of explanatory variables on the right-hand side of the equation.
How to calculate event rate using Poisson regression?
We can manipulate the Poisson regression equation to estimate the event rate for an individual with a particular combination of values of x1, …, xk. For each set of covariate values for x1, …, xk, we calculate Then, the event rate for that individual is estimated as ez.
How is logistic regression used to estimate relative risk?
The logistic model can be used to estimate an odds ratio that, with sufficiently low disease prevalence, approximates a relative risk. Other regression techniques that directly estimate it, like binomial regression, have convergence issues that can easily derail a new student.
Can a Poisson model be used to estimate relative risk?
However, a logistic model is also well applied with rare outcomes: the odds ratio is approximately a risk ratio, even with outcome dependent sampling as with case control studies. The same cannot be said of relative risk or Poisson models.
Why do we use Poisson regression in cross sectional studies?
The only reason to choose Poisson regression is because you are doing a large cross-sectional study, which means the total sample including all cases and controls is a random variable following Poisson distribution, as opposed to the binomial (number of either exposed or diseased fixed) or multinomial model (total sample size fixed).
What is the Poisson distribution of a GLM model?
Poisson regression is a type of a GLM model where the random component is specified by the Poisson distribution of the response variable which is a count. Before we look at the Poisson regression model, let’s quickly review the Poisson distribution.