Power Calculation for Two Co-Primary Endpoints (Count and Continuous)
Source:R/power2MixedCountContinuous.R
power2MixedCountContinuous.RdCalculates the power for a two-arm superiority trial with one overdispersed count co-primary endpoint and one continuous co-primary endpoint, as described in Homma and Yoshida (2024).
Arguments
- n1
Sample size for group 1 (test group)
- n2
Sample size for group 2 (control group)
- r1
Mean rate (events per unit time) for the treatment group (count endpoint)
- r2
Mean rate (events per unit time) for the control group (count endpoint)
- nu
Common dispersion parameter for the negative binomial distribution (nu > 0)
- t
Common follow-up time period
- mu1
Mean for group 1 (continuous endpoint)
- mu2
Mean for group 2 (continuous endpoint)
- sd
Common standard deviation for the continuous endpoint
- rho1
Correlation between count and continuous outcomes for treatment group
- rho2
Correlation between count and continuous outcomes for control group
- alpha
One-sided significance level (typically 0.025 or 0.05)
Value
A data frame with the following columns:
- n1
Sample size for group 1
- n2
Sample size for group 2
- r1
Mean rate in group 1 for count endpoint
- r2
Mean rate in group 2 for count endpoint
- nu
Dispersion parameter
- t
Follow-up time
- mu1
Mean in group 1 for continuous endpoint
- mu2
Mean in group 2 for continuous endpoint
- sd
Standard deviation for continuous endpoint
- rho1
Correlation for group 1
- rho2
Correlation for group 2
- alpha
One-sided significance level
- powerCount
Power for the count endpoint alone
- powerCont
Power for the continuous endpoint alone
- powerCoprimary
Power for both co-primary endpoints
Details
The test statistics are (equation 7 in Homma and Yoshida 2024): $$Z_1 = \frac{\hat{\beta}_1}{\sqrt{Var(\hat{\beta}_1)}}, \quad Z_2 = \frac{\hat{\delta}}{\sigma\sqrt{(1+\kappa)/(\kappa n_0)}}$$
The joint distribution of (Z1, Z2) follows an asymptotic bivariate normal distribution with correlation gamma (equation 11): $$\gamma = \sum_{j=0,1} \frac{n_0 \rho_j \sqrt{1+\lambda_j/\nu}} {n_j \sqrt{\lambda_j V_a} \sqrt{(1+\kappa)/\kappa}}$$
where \(\lambda_j = r_j \times t\).
The correlation bounds are automatically checked using corrbound2MixedCountContinuous.
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
# Power calculation with moderate correlation
power2MixedCountContinuous(
n1 = 300,
n2 = 300,
r1 = 1.0,
r2 = 1.25,
nu = 0.8,
t = 1,
mu1 = -50,
mu2 = 0,
sd = 250,
rho1 = 0.5,
rho2 = 0.5,
alpha = 0.025
)
#>
#> Power calculation for mixed count and continuous co-primary endpoints
#>
#> n1 = 300
#> n2 = 300
#> sd = 250
#> rate = 1, 1.25
#> nu = 0.8
#> t = 1
#> mu = -50, 0
#> rho = 0.5, 0.5
#> alpha = 0.025
#> powerCont = 0.687765
#> powerCount = 0.461715
#> powerCoprimary = 0.389192
#>
# Power calculation with no correlation
power2MixedCountContinuous(
n1 = 350,
n2 = 350,
r1 = 1.0,
r2 = 1.5,
nu = 1,
t = 1,
mu1 = -40,
mu2 = 0,
sd = 200,
rho1 = 0,
rho2 = 0,
alpha = 0.025
)
#>
#> Power calculation for mixed count and continuous co-primary endpoints
#>
#> n1 = 350
#> n2 = 350
#> sd = 200
#> rate = 1, 1.5
#> nu = 1
#> t = 1
#> mu = -40, 0
#> rho = 0, 0
#> alpha = 0.025
#> powerCont = 0.753576
#> powerCount = 0.977329
#> powerCoprimary = 0.736492
#>
# Unbalanced design
power2MixedCountContinuous(
n1 = 400,
n2 = 200,
r1 = 1,
r2 = 1.25,
nu = 1,
t = 1,
mu1 = -50,
mu2 = 0,
sd = 250,
rho1 = 0.6,
rho2 = 0.6,
alpha = 0.025
)
#>
#> Power calculation for mixed count and continuous co-primary endpoints
#>
#> n1 = 400
#> n2 = 200
#> sd = 250
#> rate = 1, 1.25
#> nu = 1
#> t = 1
#> mu = -50, 0
#> rho = 0.6, 0.6
#> alpha = 0.025
#> powerCont = 0.636619
#> powerCount = 0.470483
#> powerCoprimary = 0.393625
#>