Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/functions_poisson.R
Power calculation for simple Poisson regression. Assume the predictor is normally distributed.
1 2 3 4 5 6 7 8 9 | powerPoisson(
beta0,
beta1,
mu.x1,
sigma2.x1,
mu.T = 1,
phi = 1,
alpha = 0.05,
N = 50)
|
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 |
N |
toal sample size |
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)]
power
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.
Weiliang Qiu <stwxq@channing.harvard.edu>
Signorini D.F. (1991). Sample size for Poisson regression. Biometrika. Vol.78. no.2, pp. 446-50
See Also as sizePoisson
1 2 3 4 5 6 7 8 9 10 | # power = 0.8090542
print(powerPoisson(
beta0 = 0.1,
beta1 = 0.5,
mu.x1 = 0,
sigma2.x1 = 1,
mu.T = 1,
phi = 1,
alpha = 0.05,
N = 28))
|
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