sizePoisson: Sample size calculation for simple Poisson regression

In powerMediation: Power/Sample Size Calculation for Mediation Analysis

Description

Sample size calculation for simple Poisson regression. Assume the predictor is normally distributed. Two-sided test is used.

Usage

sizePoisson(
    beta0, 
    beta1, 
    mu.x1, 
    sigma2.x1, 
    mu.T = 1, 
    phi = 1, 
    alpha = 0.05, 
    power = 0.8)

Arguments

beta0	intercept
beta1	slope
mu.x1	mean of the predictor
sigma2.x1	variance of the predictor
mu.T	mean exposure time
phi	a measure of over-dispersion
alpha	type I error rate
power	power

Details

The simple Poisson regression has the following form:

Pr(Y_i = y_i | mu_i, t_i) = exp(-mu_i t_i) (mu_i t_i)^{y_i}/ (y_i!)

where

mu_i=exp(beta_0+beta_1 x_{1i})

We are interested in testing the null hypothesis beta_1=0 versus the alternative hypothesis beta_1=theta_1. Assume x_1 is normally distributed with mean mu_{x_1} and variance sigma^2_{x_1}. The sample size calculation formula derived by Signorini (1991) is

N=phi{[z_{1-alpha/2}sqrt{V(b_1 | beta_1=0)} +z_{power}sqrt{V(b_1 | beta_1=theta_1)}]^2}/ {mu_T exp(beta_0) theta_1^2}

where phi is the over-dispersion parameter (var(y_i)/mean(y_i)), alpha is the type I error rate, b_1 is the estimate of the slope beta_1, beta_0 is the intercept, mu_T is the mean exposure time, z_a is the 100*a-th lower percentile of the standard normal distribution, and V(b_1|beta_1=theta) is the variance of the estimate b_1 given the true slope beta_1=theta.

The variances are

V(b_1 | beta_1 = 0)=1/{sigma^2_{x_1}}

and

V(b_1 | beta_1 = theta_1)=1/{sigma^2_{x_1}} exp[-(theta_1 mu_{x_1} + theta_1^2sigma^2_{x_1}/2)]

Value

total sample size

Note

The test is a two-sided test. For one-sided tests, please double the significance level. For example, you can set alpha=0.10 to obtain one-sided test at 5% significance level.

Author(s)

Weiliang Qiu <[e-mail]>

References

Signorini D.F. (1991). Sample size for Poisson regression. Biometrika. Vol.78. no.2, pp. 446-50

See Also

See Also as powerPoisson

Examples

# sample size = 28
print(sizePoisson(
  beta0 = 0.1, 
  beta1 = 0.5,
  mu.x1 = 0, 
  sigma2.x1 = 1,
  mu.T = 1, 
  phi = 1,
  alpha = 0.05, 
  power = 0.8))

powerMediation documentation built on March 24, 2021, 1:06 a.m.