Empirical Power for Negative Binomial Comparison

Estimates empirical power to detect a relative risk either above or below a specified boundary, depending on the direction of the alternative hypothesis. Simulates count data with over dispersion, fits a model with glm.nb, and evaluates the power to reject the null hypothesis using a negative binomial model.

Usage

sim_power_nbinom(
  n1,
  n2,
  ir1,
  tm,
  rr,
  boundary,
  dispersion,
  alpha,
  nsim,
  conf.level = 0.95
)

Arguments

n1: Integer. Number of participants in group 1.
n2: Integer. Number of participants in group 2.
ir1: Numeric. Incidence rate in group 1.
tm: Numeric. Average exposure time per subject (assumed equal across subjects).
rr: Numeric. True relative risk between groups (group 2 rate = rr × group 1 rate).
boundary: Numeric. Relative risk boundary under the null hypothesis.
dispersion: Numeric. Dispersion parameter (\(\phi\)) for the negative binomial distribution.
alpha: Numeric. Type I error rate (two-sided).
nsim: Integer. Number of simulation iterations.
conf.level: Numeric. Confidence level for the empirical power estimate

Value

An S3 object of class empirical_power_result, which contains the estimated empirical power and its confidence interval. The object can be printed, formatted, or further processed using associated S3 methods. See also empirical_power_result.

Note

Uses the alternative parameterization of the negative binomial: mu is the mean, and size = 1/dispersion. In glm.nb, dispersion is estimated as theta. The 'boundary' parameter defines the relative risk under the null hypothesis. When rr < 1, rejection occurs if the upper limit of the confidence interval is below the boundary. When rr > 1, rejection occurs if the lower limit is above the boundary.

The alpha parameter is two-sided as it is used to estimate two-sided confidence intervals

Author

Chris Gast

John J. Aponte

Examples

# \donttest{
sim_power_nbinom(
 n1 = 150, n2 = 150,
 ir1 = 0.55, tm = 1.7,
 rr = 0.6, boundary = 1,
 dispersion = 2,
 alpha = 0.05,
 nsim = 1000
)
#> Empirical Power Result
#> ----------------------- 
#> Power:       0.6960
#> 95% CI:      [0.6664, 0.7244]
#> Simulations: 1000
# }