Calculate sample size for negative binomial distribution

Estimation of required sample size as given by Cundill & Alexander (2015).

n_negbinom(
  mean0,
  effect,
  dispersion0,
  dispersion1 = dispersion0,
  alpha = 0.05,
  power = 0.9,
  q = 0.5,
  link = c("log", "identity"),
  two_sided = TRUE
)

Arguments

mean0: Mean in control group
effect: Effect size, \(1 - (\mu_1 / \mu_0)\), where \(\mu_0\) is the mean in the control group (mean0) and \(\mu_1\) is the mean in the treatment group.
dispersion0: Dispersion parameter in control group
dispersion1: Dispersion parameter in treatment group. Defaults to shape0, because GLM assumes equal shape across groups.
alpha: Type I error rate
power: 1 - Type II error rate
q: Proportion of observations allocated to the control group
link: Link function to use. Currently implement: 'log' and 'identity'
two_sided: logical, if TRUE the sample size will be calculated for a two-sided test. Otherwise, the sample size will be calculated for a one-sided test.

Value

Returns an object of class "sample_size". It contains the following components:

N: the total sample size
n0: sample size in Group 0 (control group)
n1: sample size in Group 1 (treatment group)
two_sided: logical, TRUE, if the estimated sample size refers to a two-sided test
alpha: type I error rate used in sample size estimation
power: target power used in sample size estimation
effect: effect size used in sample size estimation
effect_type: short description of the type of effect size
comment: additional comment, if there is any
call: the matched call.

References

Cundill, B., & Alexander, N. D. E. (2015). Sample size calculations for skewed distributions. BMC Medical Research Methodology, 15(1), 1–9. https://doi.org/10.1186/s12874-015-0023-0

Examples

n_negbinom(mean0 = 71.4, effect = 0.7, dispersion0 = 0.33,
           alpha = 0.05, power = 0.9)
#> Estimated sample size for group difference.
#> Generalized Regression, Negative Binomial Distribution, link: log 
#> 
#> N (total)		 88.74 
#> n0 (Group 0)		 44.37 
#> n1 (Group 1)		 44.37 
#> 
#> Effect size		 0.7 
#> Effect type		 1 - (mean1/mean0) 
#> Type I error		 0.05 
#> Target power		 0.9 
#> Two-sided		 TRUE 
#> 
#> Call: n_negbinom(mean0 = 71.4, effect = 0.7, dispersion0 = 0.33, alpha = 0.05, 
#>     power = 0.9)