# Poisson power analysis

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Hi,

We're conducting a power analysis using wp.poisson to get the relative risk for different levels of a normally distributed predict (mean = 0, sd = 1). Our dependent variable is binary, but it was suggested that we use a poisson rather than logistic since the prevalence of the behavior we're observing is over 10% (22-40% has been observed in previous studies). The observed intercept in simulated data is -1.91, based on the 22% occurrence, so the IRR is 0.148. I used the relative risk for a small, medium and large effect as 1.22, 1.86, and 3.00, as suggested by Olivier et al (2017). I get an error when I try to run the medium and large effects of "non-finite function value." Here's my code:

medium <- wp.poisson(n = seq(40, 100, 10), exp0 = 0.15, exp1 = 1.86, alpha = 0.05, power = NULL, family = "normal", parameter = c(0, 1))

medium

Any suggestions for trouble shooting?

by johnny (3.3k points)
selected

Thanks for the question. This issue seemed to be related to the integration function we used. For certain parameters, the integration gave very off values. We will try to fix the issue in the next few days.
by thestepher (150 points)
by johnny (3.3k points)

We have fixed the integration issue but it will take some time to push it to CRAN. If you need to use it now, you can use the following. Thanks.

library(WebPower)

source("https://webpower.psychstat.org/R/poisson.R")

wp.poisson(n = 40, exp0 = 0.15, exp1 = 3, alpha = 0.05, power = NULL, family = "normal", parameter = c(0, 1))

Using your example, the output is below

Power for Poisson regression

n     power alpha exp0 exp1    beta0    beta1

40 0.9534119  0.05 0.15    3 -1.89712 1.098612

50 0.9825010  0.05 0.15    3 -1.89712 1.098612

60 0.9937320  0.05 0.15    3 -1.89712 1.098612

70 0.9978398  0.05 0.15    3 -1.89712 1.098612

80 0.9992791  0.05 0.15    3 -1.89712 1.098612

90 0.9997659  0.05 0.15    3 -1.89712 1.098612

100 0.9999257  0.05 0.15    3 -1.89712 1.098612

URL: http://psychstat.org/poisson