bayes_sim_unbalanced: Unbalanced Bayesian Simulation in Conjugate Linear Model...

In bayesassurance: Bayesian Assurance Computation

Unbalanced Bayesian Simulation in Conjugate Linear Model Framework

Description

Approximates the Bayesian assurance of attaining u'β > C for unbalanced study designs through Monte Carlo sampling. See Argument descriptions for more detail.

Usage

bayes_sim_unbalanced(
  n1,
  n2,
  repeats = 1,
  u,
  C,
  Xn = NULL,
  Vn = NULL,
  Vbeta_d,
  Vbeta_a_inv,
  sigsq,
  mu_beta_d,
  mu_beta_a,
  alt,
  alpha,
  mc_iter,
  surface_plot = TRUE
)

Arguments

n1	first sample size (vector or scalar).
n2	second sample size (vector or scalar).
repeats	an positive integer specifying number of times to repeat c(n1, n2). Applicable for studies that consider multiple measures within each group. Default setting is repeats = 1 if not applicable.
u	a scalar or vector to evaluate u'β > C, where β is an unknown parameter that is to be estimated. Default setting is u = 1.
C	constant value to be compared to when evaluating u'β > C
Xn	design matrix that characterizes where the data is to be generated from. This is specifically designed under the normal linear regression model yn = Xnβ + ε, ε ~ N(0, σ^2 Vn). When set to NULL, Xn is generated in-function using bayesassurance::gen_Xn(). Note that setting Xn = NULL also enables user to pass in a vector of sample sizes to undergo evaluation.
Vn	a correlation matrix for the marginal distribution of the sample data yn. Takes on an identity matrix when set to NULL.
Vbeta_d	correlation matrix that helps describe the prior information on β in the design stage
Vbeta_a_inv	inverse-correlation matrix that helps describe the prior information on β in the analysis stage
sigsq	a known and fixed constant preceding all correlation matrices Vn, Vbeta_d and Vbeta_a_inv.
mu_beta_d	design stage mean
mu_beta_a	analysis stage mean
alt	specifies alternative test case, where alt = "greater" tests if u'β > C, alt = "less" tests if u'β < C, and alt = "two.sided" performs a two-sided test. By default, alt = "greater".
alpha	significance level
mc_iter	number of MC samples evaluated under the analysis objective
surface_plot	when set to TRUE and n1 and n2 are vectors, a contour map showcasing various assurance values corresponding to different combinations of n1 and n2 is produced.

Value

a list of objects corresponding to the assurance approximations

• assurance_table: table of sample size and corresponding assurance values

• contourplot: contour map of assurance values

• mc_samples: number of Monte Carlo samples that were generated and evaluated

Examples

## Example 1
## Sample size vectors are passed in for n1 and n2 to evaluate
## assurance. 
n1 <- seq(20, 75, 5)
n2 <- seq(50, 160, 10)

assur_out <- bayes_sim_unbalanced(n1 = n1, n2 = n2, repeats = 1, u = c(1, -1),
C = 0, Xn = NULL, Vbeta_d = matrix(c(50, 0, 0, 10),nrow = 2, ncol = 2),
Vbeta_a_inv = matrix(rep(0, 4), nrow = 2, ncol = 2),
Vn = NULL, sigsq = 100,  mu_beta_d = c(1.17, 1.25),
mu_beta_a = c(0, 0), alt = "two.sided", alpha = 0.05, mc_iter = 1000,
surface_plot = FALSE)

assur_out$assurance_table


## Example 2
## We can produce a contour plot that evaluates unique combinations of n1
## and n2 simply by setting `surfaceplot = TRUE`.

n1 <- seq(20, 75, 5)
n2 <- seq(50, 160, 10)
assur_out <- bayes_sim_unbalanced(n1 = n1, n2 = n2, repeats = 1, 
u = c(1, -1), C = 0, Xn = NULL, Vbeta_d = matrix(c(50, 0, 0, 10),
nrow = 2, ncol = 2), Vbeta_a_inv = matrix(rep(0, 4), nrow = 2, ncol = 2),
Vn = NULL, sigsq = 100,  mu_beta_d = c(1.17, 1.25),
mu_beta_a = c(0, 0), alt = "two.sided", alpha = 0.05, mc_iter = 1000,
surface_plot = TRUE)

assur_out$assurance_table
assur_out$contourplot

bayesassurance documentation built on June 17, 2022, 5:05 p.m.