Either the patient level data or both mu_hat as well as S_hat must to be provided. If patient level data is provided mu_hat and S_hat are calculated within the function using a linear model. This function calculates the posterior distribution. Depending on the input for S_hat this step is either performed for every dose group independently via the RBesT function postmix() or the mvpostmix() function of the DoseFinding package is utilized. In the latter case conjugate posterior mixture of multivariate normals are calculated (DeGroot 1970, Bernardo and Smith 1994)
Usage
getPosterior(
prior_list,
data = NULL,
mu_hat = NULL,
S_hat = NULL,
calc_ess = FALSE,
probability_scale = attr(data, "probability_scale")
)Arguments
- prior_list
a prior list with information about the prior to be used for every dose group
- data
dataframe containing the information of dose and response. Also a simulateData object can be provided. Default NULL.
- mu_hat
vector of estimated mean values (per dose group). Default NULL.
- S_hat
covariance matrix specifying the (estimated) variability. The variance-covariance matrix should be provided and the dimension of the matrix needs to match the number of dose groups. Default NULL.
- calc_ess
boolean variable, indicating whether effective sample size should be calculated. Default FALSE.
- probability_scale
A boolean to specify if the trial has a continuous or a binary outcome. Setting to TRUE will transform calculations from the logit scale to the probability scale, which can be desirable for a binary outcome. Default
attr(data, "probability_scale").
Value
posterior_list, a posterior list object is returned with information about (mixture) posterior distribution per dose group (more detailed information about the conjugate posterior in case of covariance input for S_hat is provided in the attributes)
Details
Kindly note that one can sample from the posterior_list with lapply(posterior_list, RBesT::rmix, n = 10).
For binary endpoints, if separation occurs (for example, when one treatment arm has only responders or only non‑responders), we use penalized logistic regression with Firth’s correction to prevent convergence issues and obtain more stable estimates. See the references for additional details.
References
BERNARDO, Jl. M., and Smith, AFM (1994). Bayesian Theory. 81.
Heinze, G. & Schemper, M. (2002). A solution to the problem of separation in logistic regression. Statistics in Medicine, 21(16), 2409–2419.
Liu et al. (2022). Commentary: analyzing binary data using MCPMod when zero counts are expected. arXiv, 2202.08781, https://arxiv.org/abs/2202.08781
Examples
prior_list <- list(Ctrl = RBesT::mixnorm(comp1 = c(w = 1, m = 0, s = 5), sigma = 2),
DG_1 = RBesT::mixnorm(comp1 = c(w = 1, m = 1, s = 12), sigma = 2),
DG_2 = RBesT::mixnorm(comp1 = c(w = 1, m = 1.2, s = 11), sigma = 2) ,
DG_3 = RBesT::mixnorm(comp1 = c(w = 1, m = 1.3, s = 11), sigma = 2) ,
DG_4 = RBesT::mixnorm(comp1 = c(w = 1, m = 2, s = 13), sigma = 2))
mu_hat <- c(0, 1, 1.5, 2, 2.5)
S_hat <- diag(c(5, 4, 6, 7, 8)^2)
posterior_list <- getPosterior(
prior_list = prior_list,
mu_hat = mu_hat,
S_hat = S_hat)
summary(posterior_list)
#> mean sd 2.5% 50.0% 97.5%
#> Ctrl 0.000000 3.535534 -6.929519 0.000000 6.929519
#> DG_1 1.000000 3.794733 -6.437540 1.000000 8.437540
#> DG_2 1.431210 5.267373 -8.892652 1.431210 11.755072
#> DG_3 1.798235 5.905630 -9.776588 1.798235 13.373058
#> DG_4 2.362661 6.813267 -10.991096 2.362661 15.716418