power.nb.test: Power Calculation for Comparing Two Negative Binomial Rates

In MKpower: Power Analysis and Sample Size Calculation

Power Calculation for Comparing Two Negative Binomial Rates

Description

Compute sample size or power for comparing two negative binomial rates.

Usage

power.nb.test(n = NULL, mu0, mu1, RR, duration = 1, theta, ssize.ratio = 1,
              sig.level = 0.05, power = NULL, alternative = c("two.sided", "one.sided"),
              approach = 3)

Arguments

n	Sample size for group 0 (control group).
mu0	expected rate of events per time unit for group 0
mu1	expected rate of events per time unit for group 1
RR	ratio of expected event rates: mu1/mu0
duration	(average) treatment duration
theta	theta parameter of negative binomial distribution; see rnegbin
ssize.ratio	ratio of sample sizes: n1/n where n1 is sample size of group 1
sig.level	Significance level (Type I error probability)
power	Power of test (1 minus Type II error probability)
alternative	one- or two-sided test
approach	1, 2, or 3; see Zhu and Lakkis (2014).

Details

Exactly one of the parameters n and power must be passed as NULL, and that parameter is determined from the other.

The computations are based on the formulas given in Zhu and Lakkis (2014). Please be careful, as we are using a slightly different parametrization (theta = 1/k).

Zhu and Lakkis (2014) based on their simulation studies recommend to use their approach 2 or 3.

Value

Object of class "power.htest", a list of the arguments (including the computed one) augmented with a note element.

Author(s)

Matthias Kohl [e-mail]

References

H. Zhu and H. Lakkis (2014). Sample size calculation for comparing two negative binomial rates. Statistics in Medicine, 33:376-387.

See Also

rnegbin, glm.nb

Examples

## examples from Table I in Zhu and Lakkis (2014)
## theta = 1/k, RR = rr, mu0 = r0, duration = mu_t
power.nb.test(mu0 = 0.8, RR = 0.85, theta = 1/0.4, duration = 0.75, power = 0.8, approach = 1)
power.nb.test(mu0 = 0.8, RR = 0.85, theta = 1/0.4, duration = 0.75, power = 0.8, approach = 2)
power.nb.test(mu0 = 0.8, RR = 0.85, theta = 1/0.4, duration = 0.75, power = 0.8, approach = 3)

power.nb.test(mu0 = 1.4, RR = 1.15, theta = 1/1.5, duration = 0.75, power = 0.8, approach = 1)
power.nb.test(mu0 = 1.4, RR = 1.15, theta = 1/1.5, duration = 0.75, power = 0.8, approach = 2)
power.nb.test(mu0 = 1.4, RR = 1.15, theta = 1/1.5, duration = 0.75, power = 0.8, approach = 3)


## examples from Table II in Zhu and Lakkis (2014) - seem to be total sample sizes
## can reproduce the results with mu_t = 1.0 (not 0.7!)
power.nb.test(mu0 = 2.0, RR = 0.5, theta = 1, duration = 1.0, ssize.ratio = 1,
              power = 0.8, approach = 1)
power.nb.test(mu0 = 2.0, RR = 0.5, theta = 1, duration = 1.0, ssize.ratio = 1,
              power = 0.8, approach = 2)
power.nb.test(mu0 = 2.0, RR = 0.5, theta = 1, duration = 1.0, ssize.ratio = 1,
              power = 0.8, approach = 3)

power.nb.test(mu0 = 10.0, RR = 1.5, theta = 1/5, duration = 1.0, ssize.ratio = 3/2,
              power = 0.8, approach = 1)
power.nb.test(mu0 = 10.0, RR = 1.5, theta = 1/5, duration = 1.0, ssize.ratio = 3/2,
              power = 0.8, approach = 2)
power.nb.test(mu0 = 10.0, RR = 1.5, theta = 1/5, duration = 1.0, ssize.ratio = 3/2,
              power = 0.8, approach = 3)


## examples from Table III in Zhu and Lakkis (2014)
power.nb.test(mu0 = 5.0, RR = 2.0, theta = 1/0.5, duration = 1, power = 0.8, approach = 1)
power.nb.test(mu0 = 5.0, RR = 2.0, theta = 1/0.5, duration = 1, power = 0.8, approach = 2)
power.nb.test(mu0 = 5.0, RR = 2.0, theta = 1/0.5, duration = 1, power = 0.8, approach = 3)


## examples from Table IV in Zhu and Lakkis (2014)
power.nb.test(mu0 = 5.9/3, RR = 0.4, theta = 0.49, duration = 3, power = 0.9, approach = 1)
power.nb.test(mu0 = 5.9/3, RR = 0.4, theta = 0.49, duration = 3, power = 0.9, approach = 2)
power.nb.test(mu0 = 5.9/3, RR = 0.4, theta = 0.49, duration = 3, power = 0.9, approach = 3)

power.nb.test(mu0 = 13/6, RR = 0.2, theta = 0.52, duration = 6, power = 0.9, approach = 1)
power.nb.test(mu0 = 13/6, RR = 0.2, theta = 0.52, duration = 6, power = 0.9, approach = 2)
power.nb.test(mu0 = 13/6, RR = 0.2, theta = 0.52, duration = 6, power = 0.9, approach = 3)


## see Section 5 of Zhu and Lakkis (2014)
power.nb.test(mu0 = 0.66, RR = 0.8, theta = 1/0.8, duration = 0.9, power = 0.9)

MKpower documentation built on Sept. 9, 2025, 5:37 p.m.