bmn {BayesDissolution}

Bayesian Multivariate Normal Model for Dissolution Profile Modeling

Description

This function implements the Bayesian multivariate normal model described in Pourmohamad et al (2022).

Usage

bmn(dis_data, B = 10000)

Arguments

dis_data

A data frame containing the dissolution data. The first column of the data frame should denote the group labels identifying whether a given dissolution belongs to the "reference" or "test" formulation group. For a given dissolution run, the remaining columns of the data frame contains the individual run's dissolution measurements sorted in time. Alternatively, the user may provide a data object of class dis_data containing the dissolution data. See the make_dis_data() function for the particular structure of the data object.

B

A positive integer specifying the number of posterior samples to draw. By default B is set to 10000.

Value

The function returns a list of B posterior samples for the following parameters:

• delta: A vector of posterior samples of delta as defined in Novick et. al 2015

• f2: A vector of posterior values of f2

• muR: A matrix of posterior samples for the reference group mean. Each row of the matrix corresponds to an observed time point, and each column of the matrix corresponds to a posterior sample.

• muT: A matrix of posterior samples for the test group mean. Each row of the matrix corresponds to an observed time point, and each column of the matrix corresponds to a posterior sample.

Note

You should always check MCMC diagnostics on the posterior samples before drawing conclusions.

References

Novick, S., Shen, Y., Yang, H., Peterson, J., LeBlond, D., and Altan, S. (2015). Dissolution Curve Comparisons Through the F2 Parameter, a Bayesian Extension of the f2 Statistic. Journal of Biopharmaceutical Statistics, 25(2):351-371.

Pourmohamad, T., Oliva Aviles, C.M., and Richardson, R. Gaussian Process Modeling for Dissolution Curve Comparisons. Journal of the Royal Statistical Society, Series C, 71(2):331-351.

Examples

### dis_data comes loaded with the package
### We set B = 1000 to obtain 1000 posterior samples
B <- 1000
post <- bmn(dis_data, B = B)

### We can check how well the posterior samples of the means are mixing by
### plotting the individual chains by time point
burnin <- B * 0.1     # A 10% burn-in
post$mu_R <- post$muR[,-(1:burnin)]
post$mu_T <- post$muT[,-(1:burnin)]

N <- B - burnin      # Number of posterior samples after burn-in
chains <- data.frame(samples = rep(c(1:N, 1:N), each = ncol(dis_data) - 1),
                     group = rep(c("muR", "muT"), each = (ncol(dis_data) - 1) * N),
                     timepoint = paste("Time Point", rep(1:(ncol(dis_data) - 1), 2 * N)),
                     values = c(c(post$mu_R), c(post$mu_T)))

g <- ggplot2::ggplot(chains, ggplot2::aes(samples, values)) +
                     ggplot2::geom_line() +
                     ggplot2::labs(x = "Iterations", y = "Posterior Sample Values") +
                     ggplot2::facet_wrap(group ~ timepoint) +
                     ggplot2::theme(text = ggplot2::element_text(size = 16))

### If we want to calculate the Pr(f2 > 50)
post$f2<- post$f2[-(1:burnin)]
prob <- sum(post$f2 > 50) / (B - burnin)

### Or if we want calculate a 95% credible interval for f2
alpha <- 0.05
f2_cred <- c(quantile(post$f2, alpha / 2),quantile(post$f2, 1 - alpha / 2))