twoCoprimary (version 1.0.0)

power2MixedCountContinuous: Power Calculation for Two Co-Primary Endpoints (Count and Continuous)

Description

Calculates 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).

Usage

power2MixedCountContinuous(
  n1,
  n2,
  r1,
  r2,
  nu,
  t,
  mu1,
  mu2,
  sd,
  rho1,
  rho2,
  alpha
)

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

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)

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 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
)

# 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
)