two.grp.random.a0: Model fitting for two groups (treatment and control group, no...

Description Usage Arguments Details Value References See Also Examples

View source: R/main_func.R

Description

Model fitting using normalized power priors for two groups (treatment and control group, no covariates) with random a_0

Usage

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two.grp.random.a0(
  data.type,
  y.c,
  n.c,
  v.c,
  historical,
  prior.mu.c.shape1 = 1,
  prior.mu.c.shape2 = 1,
  prior.a0.shape1 = 1,
  prior.a0.shape2 = 1,
  lower.limits = rep(0, 10),
  upper.limits = rep(1, 10),
  slice.widths = rep(0.1, 10),
  nMC = 10000,
  nBI = 250
)

Arguments

data.type

Character string specifying the type of response. The options are "Normal", "Bernoulli", "Poisson" and "Exponential".

y.c

Sum of responses for the control group.

n.c

Sample size of the control group.

v.c

(For normal data only) sample variance of responses for the control group.

historical

Matrix of historical dataset(s). If data.type is "Normal", historical is a matrix with three columns:

  • The first column contains the sum of responses for the control group.

  • The second column contains the sample size of the control group.

  • The third column contains the sample variance of responses for the control group.

For all other data types, historical is a matrix with two columns:

  • The first column contains the sum of responses for the control group.

  • The second column contains the sample size of the control group.

Each row represents a historical dataset.

prior.mu.c.shape1

First hyperparameter of the initial prior for μ_c. The default is 1. Does not apply if data.type is "Normal".

prior.mu.c.shape2

Second hyperparameter of the initial prior for μ_c. The default is 1. Does not apply if data.type is "Normal".

prior.a0.shape1

First shape parameter of the beta prior for a_0. The default is 1.

prior.a0.shape2

Second shape parameter of the beta prior for a_0. The default is 1.

lower.limits

Vector of lower limits for parameters to be used by the slice sampler. The length of the vector should be equal to the number of historical datasets. The default is 0 for all parameters (may not be appropriate for all situations).

upper.limits

Vector of upper limits for parameters to be used by the slice sampler. The length of the vector should be equal to the number of historical datasets. The default is 1 for all parameters (may not be appropriate for all situations).

slice.widths

Vector of initial slice widths used by the slice sampler. The length of the vector should be equal to the number of historical datasets. The default is 0.1 for all parameter (may not be appropriate for all situations).

nMC

Number of iterations (excluding burn-in samples) for the slice sampler or Gibbs sampler. The default is 10,000.

nBI

Number of burn-in samples for the slice sampler or Gibbs sampler. The default is 250.

Details

If data.type is "Bernoulli", "Poisson" or "Exponential", a single response from the treatment group is assumed to follow Bern(μ_t), Pois(μ_t) or Exp(rate=μ_t), respectively, where μ_t is the mean of responses for the treatment group. If data.type is "Normal", a single response from the treatment group is assumed to follow N(μ_t, τ^{-1}) where τ is the precision parameter. The distributional assumptions for the control group data are analogous.

If data.type is "Bernoulli", the initial prior for μ_t is beta(prior.mu.t.shape1, prior.mu.t.shape2). If data.type is "Poisson", the initial prior for μ_t is Gamma(prior.mu.t.shape1, rate=prior.mu.t.shape2). If data.type is "Exponential", the initial prior for μ_t is Gamma(prior.mu.t.shape1, rate=prior.mu.t.shape2). The initial priors used for the control group data are analogous.

If data.type is "Normal", historical datasets are assumed to have the same precision parameter τ as the current dataset for computational simplicity. The initial prior for τ is the Jeffery's prior, τ^{-1}. The initial prior for the μ_c is the uniform improper prior. Posterior samples of μ_c and τ are obtained through Gibbs sampling.

Posterior samples of a_0 are obtained through slice sampling. The default lower limits for the parameters are 0. The default upper limits for the parameters are 1. The default slice widths for the parameters are 0.1. The defaults may not be appropriate for all situations, and the user can specify the appropriate limits and slice width for each parameter.

Value

If data.type is "Normal", posterior samples of μ_c, τ and a_0 are returned. For all other data types, posterior samples of μ and a_0 are returned. If there are K historical datasets, then a_0 = (a_{01},\cdots,a_{0K}).

References

Neal, Radford M. Slice sampling. Ann. Statist. 31 (2003), no. 3, 705–767.

See Also

power.two.grp.random.a0

Examples

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data.type <- "Bernoulli"
y.c <- 70
n.c <- 100

# Simulate three historical datasets
historical <- matrix(0, ncol=2, nrow=3)
historical[1,] <- c(70, 100)
historical[2,] <- c(60, 100)
historical[3,] <- c(50, 100)

# Set parameters of the slice sampler
lower.limits <- rep(0, 3) # The dimension is the number of historical datasets
upper.limits <- rep(1, 3)
slice.widths <- rep(0.1, 3)

result <- two.grp.random.a0(data.type=data.type, y.c=y.c, n.c=n.c, historical=historical,
                            lower.limits=lower.limits, upper.limits=upper.limits,
                            slice.widths=slice.widths, nMC=10000, nBI=250)

BayesPPD documentation built on Sept. 8, 2021, 5:06 p.m.