# power.nb.test: Power calculation for comparing two negative binomial rates In stamats/MKpower: Power Analysis and Sample Size Calculation

## Description

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

## Usage

 ```1 2 3``` ```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: n/n1 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 [email protected]

## References

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

`rnegbin`, `glm.nb`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46``` ```## 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) ```