glm.random.a0: Model fitting for generalized linear models with random a0

Description Usage Arguments Details Value References See Also Examples

View source: R/main_func.R

Description

Model fitting using normalized power priors for generalized linear models with random a_0

Usage

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glm.random.a0(
  data.type,
  data.link,
  y,
  n = 1,
  x,
  historical,
  prior.a0.shape1 = 1,
  prior.a0.shape2 = 1,
  a0.coefficients,
  lower.limits = rep(-100, 50),
  upper.limits = rep(100, 50),
  slice.widths = rep(0.1, 50),
  nMC = 10000,
  nBI = 250
)

Arguments

data.type

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

data.link

Character string specifying the link function. The options are "Logistic", "Probit", "Log", "Identity-Positive", "Identity-Probability" and "Complementary Log-Log". Does not apply if data.type is "Normal".

y

Vector of responses.

n

(For binomial data only) vector of integers specifying the number of subjects who have a particular value of the covariate vector. If the data is binary and all covariates are discrete, collapsing Bernoulli data into a binomial structure can make the slice sampler much faster.

x

Matrix of covariates. The first column should be the treatment indicator with 1 indicating treatment group. The number of rows should equal the length of the response vector y.

historical

List of historical dataset(s). East historical dataset is stored in a list which contains two named elements: y0 and x0.

  • y0 is a vector of responses.

  • x0 is a matrix of covariates. x0 should NOT have the treatment indicator. Apart from missing the treatent/control indicator, x0 should have the same set of covariates in the same order as x.

For binomial data, an additional element n0 is required.

  • n0 is vector of integers specifying the number of subjects who have a particular value of the covariate vector.

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.

a0.coefficients

Vector of coefficients for a_0 returned by the function normalizing.constant. This is necessary for estimating the normalizing constant for the normalized power prior. Does not apply if data.type is "Normal".

lower.limits

Vector of lower limits for parameters to be used by the slice sampler. If data.type is "Normal", slice sampling is used for a_0, and the length of the vector should be equal to the number of historical datasets. For all other data types, slice sampling is used for β and a_0. The first P+1 elements apply to the sampling of β and the rest apply to the sampling of a_0. The length of the vector should be equal to the sum of the total number of parameters (i.e. P+1 where P is the number of covariates) and the number of historical datasets. The default is -100 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. If data.type is "Normal", slice sampling is used for a_0, and the length of the vector should be equal to the number of historical datasets. For all other data types, slice sampling is used for β and a_0. The first P+1 elements apply to the sampling of β and the rest apply to the sampling of a_0. The length of the vector should be equal to the sum of the total number of parameters (i.e. P+1 where P is the number of covariates) and the number of historical datasets. The default is 100 for all parameters (may not be appropriate for all situations).

slice.widths

Vector of initial slice widths used by the slice sampler. If data.type is "Normal", slice sampling is used for a_0, and the length of the vector should be equal to the number of historical datasets. For all other data types, slice sampling is used for β and a_0. The first P+1 elements apply to the sampling of β and the rest apply to the sampling of a_0. The length of the vector should be equal to the sum of the total number of parameters (i.e. P+1 where P is the number of covariates) and 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

The user should use the function normalizing.constant to obtain a0.coefficients (does not apply if data.type is "Normal").

If data.type is "Normal", the response y_i is assumed to follow N(x_i'β, τ^{-1}) where x_i is the vector of covariates for subject i. Historical datasets are assumed to have the same precision parameter as the current dataset for computational simplicity. The initial prior for τ is the Jeffery's prior, τ^{-1}. The initial prior for β is the uniform improper prior. Posterior samples for β and τ are obtained through Gibbs sampling. Posterior samples for a_0 are obtained through slice sampling.

For all other data types, posterior samples are obtained through slice sampling. The initial prior for β is the uniform improper prior. The default lower limits for the parameters are -100. The default upper limits for the parameters are 100. 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 β, τ and a_0 are returned. For all other data types, posterior samples of β and a_0 are returned.

References

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

See Also

normalizing.constant and power.glm.random.a0

Examples

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data.type <- "Bernoulli"
data.link <- "Logistic"

# Simulate current data
set.seed(1)
p <- 3
n_total <- 100
y <- rbinom(n_total,size=1,prob=0.6)
# The first column of x is the treatment indicator.
x <- cbind(rbinom(n_total,size=1,prob=0.5),
           matrix(rnorm(p*n_total),ncol=p,nrow=n_total))

# Simulate two historical datasets
# Note that x0 does not have the treatment indicator
historical <- list(list(y0=rbinom(n_total,size=1,prob=0.2),
                        x0=matrix(rnorm(p*n_total),ncol=p,nrow=n_total)),
                   list(y0=rbinom(n_total, size=1, prob=0.5),
                        x0=matrix(rnorm(p*n_total),ncol=p,nrow=n_total)))

# Please see function "normalizing.constant" for how to obtain a0.coefficients
# Here, suppose one-degree polynomial regression is chosen by the "normalizing.constant" 
# function. The coefficients are obtained for the intercept, a0_1 and a0_2. 
a0.coefficients <- c(1, 0.5, -1)

# Set parameters of the slice sampler
# The dimension is the number of columns of x plus 1 (intercept) 
# plus the number of historical datasets
lower.limits <- rep(-100, 7) 
upper.limits <- rep(100, 7)
slice.widths <- rep(0.1, 7)

nMC <- 500 # nMC should be larger in practice
nBI <- 100
result <- glm.random.a0(data.type=data.type, data.link=data.link, y=y, x=x,
                        historical=historical, a0.coefficients=a0.coefficients,
                        lower.limits=lower.limits, upper.limits=upper.limits,
                        slice.widths=slice.widths, nMC=nMC, nBI=nBI)

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