Calculate Conditional or Predictive Power for Multiple Contrast Test

Calculates the predictive or conditional power for a multiple contrast test based on interim data, e.g. for a futility interim analysis. This function can also be applied to longitudinal endpoints, where at the time of interim analysis incomplete data is available.

Usage

powMCTInterim(
  contMat,
  mu_0t,
  S_0t,
  S_01,
  alpha = 0.025,
  type = c("predictive", "conditional"),
  mu_assumed = NULL,
  alternative = c("one.sided", "two.sided"),
  control = mvtnorm.control()
)

Arguments

contMat: Contrast matrix to use. The individual contrasts should be saved in the columns of the matrix
mu_0t: The first stage estimates
S_0t: The covariance matrix for the first stage estimates
S_01: The covariance matrix anticipated for the estimates at study end
alpha: Significance level to use
type: Whether predictive power (for a flat prior) or conditional power should be calculated. For conditional power mu_assumed needs to be specified.
mu_assumed: Mean vector to assume for the second stage (only used when type is conditional). If NULL (default), the first stage estimates mu_0t are used.
alternative: Character determining the alternative for the multiple contrast trend test.
control: A list specifying additional control parameters for the pmvnorm calls in the code, see also mvtnorm.control for details.

Value

Numeric containing the calculated power values

References

Bornkamp, B., Zhou, J., Xi, D. and Cao W. (2025). Futility analyses for the MCP-Mod methodology based on longitudinal models, arXiv:2406.19965

Examples


# Setup the scenario.
doses <- c(0, 0.5, 1, 2, 4, 8)
mods <- Mods(
  emax = c(0.5, 1, 2, 4),
  sigEmax = rbind(c(0.5, 3), c(1, 3), c(2, 3), c(4, 3)),
  quadratic = -0.1,
  doses = doses
)
w <- c(1, 0.5, 0.5, 0.5, 1, 1)
contMat <- optContr(models = mods, w = w)$contMat
sigma <- 0.3
n_final <- round(531 * w / sum(w))
n <- floor(n_final / 2)
S_0t <- diag(sigma^2 / n)
S_01 <- diag(sigma^2 / n_final)
## assumed interim estimate
mu_0t <- 0.05 * doses / (doses + 1) + rnorm(6, 0, 0.382 / sqrt(n))
## assumed mu (needed for conditional power)
mu_assumed <- 0.135 * doses / (doses + 1)

# Calculate predictive and conditional power.
powMCTInterim(
  contMat = contMat, S_0t = S_0t, S_01 = S_01, mu_0t = mu_0t,
  type = "predictive"
)
#> [1] 0.0006866183
#> attr(,"error")
#> [1] 2.387509e-06
#> attr(,"msg")
#> [1] "Normal Completion"
powMCTInterim(
  contMat = contMat, S_0t = S_0t, S_01 = S_01, mu_0t = mu_0t,
  type = "conditional", mu_assumed = mu_assumed
)
#> [1] 0.06110965
#> attr(,"error")
#> [1] 0.0008431539
#> attr(,"msg")
#> [1] "Normal Completion"
powMCTInterim(
  contMat = contMat, S_0t = S_0t, S_01 = S_01, mu_0t = mu_0t,
  type = "predictive", alternative = "two.sided"
)
#> [1] 0.5590982
#> attr(,"error")
#> [1] 0.0005531084
#> attr(,"msg")
#> [1] "Normal Completion"
powMCTInterim(
  contMat = contMat, S_0t = S_0t, S_01 = S_01, mu_0t = mu_0t,
  type = "predictive", control = mvtnorm.control(maxpts = 1e5)
)
#> [1] 0.0007878812
#> attr(,"error")
#> [1] 0.000365923
#> attr(,"msg")
#> [1] "Normal Completion"