I was planning to calcualtecalculate the incidence rate ratio (IRR) incidence, i.e. incidence rate group B/ incidence rate group A
And, and then test if this rate it equalequals to 1/calcualte, and finally calculate 95% CI intervals for the IRR.
I found a method frofor calculation the 95% CI in a book (Rosner "Fundamentals of Biostatistics"Rosner's Fundamentals of Biostatistics):
exp[log(IRR) +/- 1.96√((1/a1)+(1/a2))]
$$\exp\left[\log(\text{IRR}) \pm 1.96\sqrt{(1/a_1)+(1/a_2)}\right]$$
where a1$a_1$ and a2$a_2$ are the number of events. But this approximation is only valid for large enough sample sizes and i think the numer of event iI have is to small (maybe for the total comparison its okeit's okay.)
So iI think iI should use an otheranother method.
Im using R and the exactciexactci package and found that iI could maybe use poisson.testpoisson.test(). But this function has 3 methods for defining the two sided p-values. Central: central, minlike and blaker.
So my questionsmy questions are:
The manual of exactci says:
central: is 2 times the minimum of the one-sided p-values bounded above by 1. The name `central' is motivated by the associated inversion con dence intervals which are central intervals, i.e., they guarantee that the true parameter has less than =2 probability of being less (more) than the lower (upper) tail of the 100(1 .. )% con dence interval. This is called the TST (twice the smaller tail method) by Hirji (2006).
minlike: is the sum of probabilities of outcomes with likelihoods less than or equal to the observed likelihood. This is called the PB (probability based) method by Hirji (2006).
blaker: combines the probability of the smaller observed tail with the smallest probability of the opposite tail that does not exceed that observed tail probability. The name 'blaker' is motivated by Blaker (2000) which comprehensively studies the associated methodvignette for con dence intervals. This is called the CT (combined tail) method by Hirji (2006).exactci says:
central: is 2 times the minimum of the one-sided p-values bounded above by 1. The name 'central' is motivated by the associated inversion con dence intervals which are central intervals, i.e., they guarantee that the true parameter has less than $\alpha/2$ probability of being less (more) than the lower (upper) tail of the 100(1-$\alpha$)% confidence interval. This is called the TST (twice the smaller tail method) by Hirji (2006).
minlike: is the sum of probabilities of outcomes with likelihoods less than or equal to the observed likelihood. This is called the PB (probability based) method by Hirji (2006).
blaker: combines the probability of the smaller observed tail with the smallest probability of the opposite tail that does not exceed that observed tail probability. The name 'blaker' is motivated by Blaker (2000) which comprehensively studies the associated method for con dence intervals. This is called the CT (combined tail) method by Hirji (2006).
