power.nb.test {MKmisc}

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: 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 [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)