twoCoprimary (version 1.0.0)

ss1Count: Sample Size Calculation for a Single Count Endpoint (Negative Binomial)

Description

Calculates the required sample size for a two-arm superiority trial with a single overdispersed count endpoint following a negative binomial distribution, as described in Homma and Yoshida (2024).

Usage

ss1Count(r1, r2, nu, t, r, alpha, beta)

Value

A data frame with the following columns:

r1

Mean rate for treatment group

r2

Mean rate for control group

nu

Dispersion parameter

t

Follow-up time

r

Allocation ratio

alpha

One-sided significance level

beta

Type II error rate

n1

Required sample size for treatment group

n2

Required sample size for control group

N

Total sample size (n2 + n1)

Arguments

r1

Mean rate (events per unit time) for the treatment group

r2

Mean rate (events per unit time) for the control group

nu

Common dispersion parameter for the negative binomial distribution (nu > 0)

t

Common follow-up time period

r

Allocation ratio (treatment:control = r:1, where r > 0)

alpha

One-sided significance level (typically 0.025 or 0.05)

beta

Target type II error rate (typically 0.1 or 0.2)

Details

The test statistic for the negative binomial rate ratio is: $$Z_1 = \frac{\hat{\beta}_1}{\sqrt{Var(\hat{\beta}_1)}}$$ where \(\hat{\beta}_1 = \log(\bar{Y}_1) - \log(\bar{Y}_2)\) and the variance is: $$Var(\hat{\beta}_1) = \frac{1}{n_2}\left[\frac{1}{t}\left(\frac{1}{r_2} + \frac{1}{r \cdot r_1}\right) + \frac{1+r}{\nu \cdot r}\right]$$

This is equation (8) in Homma and Yoshida (2024).

References

Homma, G., & Yoshida, T. (2024). Sample size calculation in clinical trials with two co-primary endpoints including overdispersed count and continuous outcomes. Pharmaceutical Statistics, 23(1), 46-59.

Examples

# Sample size for count endpoint with nu = 0.8
ss1Count(r1 = 1.0, r2 = 1.25, nu = 0.8, t = 1, r = 1,
         alpha = 0.025, beta = 0.1)

# Unbalanced design with 2:1 allocation
ss1Count(r1 = 1.0, r2 = 1.5, nu = 1.0, t = 1, r = 2,
         alpha = 0.025, beta = 0.2)

# Higher dispersion
ss1Count(r1 = 1.5, r2 = 2.0, nu = 3.0, t = 1, r = 1,
         alpha = 0.025, beta = 0.1)