Sample Size Calculation for a Single Continuous Endpoint

Calculates the required sample size for a two-arm superiority trial with a single continuous endpoint using the standard formula for normally distributed outcomes.

Usage

ss1Continuous(delta, sd, r, alpha, beta)

Arguments

delta: Mean difference between treatment groups (treatment effect)
sd: Common standard deviation for the continuous endpoint
r: Allocation ratio of group 1 to group 2 (group 1:group 2 = 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)

Value

A data frame with the following columns:

delta: Mean difference (treatment effect)
sd: Common standard deviation
r: Allocation ratio
alpha: One-sided significance level
beta: Type II error rate
n1: Required sample size for group 1
n2: Required sample size for group 2
N: Total sample size (n1 + n2)

Details

The required sample size for group 2 is calculated using the standard formula: $$n_2 = \left\lceil \frac{(1 + 1/r) \sigma^2 (z_\alpha + z_\beta)^2}{\delta^2} \right\rceil$$ where $z_\alpha$ and $z_\beta$ are the quantiles of the standard normal distribution corresponding to the one-sided significance level $\alpha$ and type II error rate $\beta$, respectively. The sample size for group 1 is $n_1 = \lceil r \times n_2 \rceil$.

Examples

# Balanced design with 1:1 allocation
ss1Continuous(delta = 0.4, sd = 1, r = 1, alpha = 0.025, beta = 0.1)
#> 
#> Sample size calculation for single continuous endpoint
#> 
#>              n1 = 132
#>              n2 = 132
#>               N = 264
#>           delta = 0.4
#>              sd = 1
#>      allocation = 1
#>           alpha = 0.025
#>            beta = 0.1
#> 

# Unbalanced design with 2:1 allocation
ss1Continuous(delta = 0.5, sd = 1.2, r = 2, alpha = 0.025, beta = 0.2)
#> 
#> Sample size calculation for single continuous endpoint
#> 
#>              n1 = 136
#>              n2 = 68
#>               N = 204
#>           delta = 0.5
#>              sd = 1.2
#>      allocation = 2
#>           alpha = 0.025
#>            beta = 0.2
#> 

# Large treatment effect
ss1Continuous(delta = 0.8, sd = 1, r = 1, alpha = 0.025, beta = 0.1)
#> 
#> Sample size calculation for single continuous endpoint
#> 
#>              n1 = 33
#>              n2 = 33
#>               N = 66
#>           delta = 0.8
#>              sd = 1
#>      allocation = 1
#>           alpha = 0.025
#>            beta = 0.1
#>