wp.poisson: Statistical Power Analysis for Poisson Regression

In WebPower: Basic and Advanced Statistical Power Analysis

Statistical Power Analysis for Poisson Regression

Description

This function is for Poisson regression models. Poisson regression is a type of generalized linear models where the outcomes are usually count data. Here, Maximum likelihood methods is used to estimate the model parameters. The estimated regression coefficent is assumed to follow a normal distribution. A Wald test is used to test the mean difference between the estimated parameter and the null parameter (tipically the null hypothesis assumes it equals 0). The procedure introduced by Demidenko (2007) is adopted here for computing the statistical power.

Usage

wp.poisson(n = NULL, exp0 = NULL, exp1 = NULL, alpha = 0.05,
  power = NULL, alternative = c("two.sided", "less", "greater"),
  family = c("Bernoulli", "exponential", "lognormal", "normal", "Poisson",
  "uniform"), parameter = NULL, subdivisions=200L,
  i.method=c("numerical", "MC"), mc.iter=20000)

Arguments

n	Sample size.
exp0	The base rate under the null hypothesis. It always takes positive value. See the article by Demidenko (2007) for details.
exp1	The relative increase of the event rate. It is used for calculatation of the effect size. See the article by Demidenko (2007) for details.
alpha	significance level chosed for the test. It equals 0.05 by default.
power	Statistical power.
alternative	Direction of the alternative hypothesis ("two.sided" or "less" or "greater"). The default is "two.sided".
family	Distribution of the predictor ("Bernoulli","exponential", "lognormal", "normal", "Poisson", "uniform"). The default is "Bernoulli".
parameter	Corresponding parameter for the predictor's distribution. The default is 0.5 for "Bernoulli", 1 for "exponential", (0,1) for "lognormal" or "normal", 1 for "Poisson", and (0,1) for "uniform".
subdivisions	Number of divisions for integration
i.method	Integration method
mc.iter	Number of iterations for Monte Carlo integration

Value

An object of the power analysis.

References

Demidenko, E. (2007). Sample size determination for logistic regression revisited. Statistics in medicine, 26(18), 3385-3397.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

Examples

#To calculate the statistical power given sample size and effect size:
wp.poisson(n = 4406, exp0 = 2.798, exp1 = 0.8938, alpha = 0.05,
                 power = NULL, family = "Bernoulli", parameter = 0.53)
#  Power for Poisson regression
#
#       n     power alpha  exp0   exp1    beta0      beta1 paremeter
#    4406 0.9999789  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#
#  URL: http://psychstat.org/poisson

#To generate a power curve given a sequence of sample sizes:
res <- wp.poisson(n = seq(800, 1500, 100), exp0 = 2.798, exp1 = 0.8938,
      alpha = 0.05, power = NULL, family = "Bernoulli", parameter = 0.53)
res
#  Power for Poisson regression
#
#       n     power alpha  exp0   exp1    beta0      beta1 paremeter
#     800 0.7324097  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#     900 0.7813088  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#    1000 0.8224254  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#    1100 0.8566618  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#    1200 0.8849241  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#    1300 0.9080755  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#    1400 0.9269092  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#    1500 0.9421344  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#
#  URL: http://psychstat.org/poisson

#To plot the power curve:
plot(res) 

#To calculate the required sample size given power and effect size:
wp.poisson(n = NULL, exp0 = 2.798, exp1 = 0.8938, alpha = 0.05,
            power = 0.8, family = "Bernoulli", parameter = 0.53)
#  Power for Poisson regression
#
#           n power alpha  exp0   exp1    beta0      beta1 paremeter
#    943.2628   0.8  0.05 2.798 0.8938 1.028905 -0.1122732      0.53
#
#  URL: http://psychstat.org/poisson

WebPower documentation built on Oct. 14, 2023, 1:06 a.m.