dfped (version 1.1)

sigmaEss: The variance of the effective sample size (ESS).

Description

Let \(\pi_{ESS}(\alpha)\) be the prior normal distribution \(\mathcal{N} (\mu_\alpha, \sigma^{2}_{\alpha,ESS})\). The variance \(\sigma^{2}_{\alpha,ESS}\) was fixed such that the information introduced by the prior would be equivalent to the information introduced by a fixed number of patients, which was calibrated to control the amount of information. This approach is based on the effective sample size (ESS): the higher the ESS, the more informative the prior. For an ESS \(m^{*}\), parameters \((\mu_\alpha, \sigma^{2}_{\alpha,ESS})\) were chosen such that $$min_{m} \delta(m, \mu_\alpha, \sigma^{2}_{\alpha,ESS})) = m^{*}$$

Usage

sigmaEss(mStar, sigma, Mmin, Mmax, meana, c, wm, Tmc)

Arguments

mStar

The number of patients anticipated for the trial.

sigma

The vector of sigma.

Mmin

The minimum number of patients for which the effective sample size (ESS) is computed.

Mmax

The maximum number of patients for which the effective sample size (ESS) is computed.

meana

Mean value of the prior distribution (known or chosen).

c

The maximum number of iteration for the algorithm to compute the ESS. See references for more details.

wm

The working model.

Tmc

The number of draw in the normal distribution in the ESS algorithm. See references for more details.

References

Petit, C., et al, (2016) Unified approach for extrapolation and bridging of adult information in early phase dose-finding paediatric studies, Statistical Methods in Medical Research, <doi:10.1177/0962280216671348>.

Morita S., Thall P.F., and Muller P. (2008) Determining the effective sample size of a parametric prior. Biometrics.

Morita S. (2011) Application of the continual reassessment method to a phase I dose-finding trial in japanese patients: East meets west. Stat. Med.

Examples

# NOT RUN {
    wm_mat <- c(0.10, 0.21, 0.33, 0.55, 0.76 )
    wm_allo <- c(0.13, 0.27, 0.48, 0.70, 0.88)
    wm_linear <- c(0.07, 0.13, 0.21, 0.33, 0.55)
    c <- 10000
    meana <- 0.88
    Tmc <- 100000
    Mmax <- 30
    Mmin <- 1
    sigma_vect <- seq(0.1, 2, by = 0.01)
    mStar <- 30
    sigmaEss(mStar, sigma_vect, Mmin, Mmax, meana, c, wm_mat, Tmc)
# }