bdpnormal {bayesDP}R Documentation

Bayesian Discount Prior: Gaussian mean values

Description

bdpnormal is used for estimating posterior samples from a Gaussian outcome where an informative prior is used. The prior weight is determined using a discount function. This code is modeled after the methodologies developed in Haddad et al. (2017).

Usage

bdpnormal(
  mu_t = NULL,
  sigma_t = NULL,
  N_t = NULL,
  mu0_t = NULL,
  sigma0_t = NULL,
  N0_t = NULL,
  mu_c = NULL,
  sigma_c = NULL,
  N_c = NULL,
  mu0_c = NULL,
  sigma0_c = NULL,
  N0_c = NULL,
  discount_function = "identity",
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  number_mcmc = 10000,
  method = "mc",
  compare = TRUE
)

Arguments

mu_t

scalar. Mean of the current treatment group.

sigma_t

scalar. Standard deviation of the current treatment group.

N_t

scalar. Number of observations of the current treatment group.

mu0_t

scalar. Mean of the historical treatment group.

sigma0_t

scalar. Standard deviation of the historical treatment group.

N0_t

scalar. Number of observations of the historical treatment group.

mu_c

scalar. Mean of the current control group.

sigma_c

scalar. Standard deviation of the current control group.

N_c

scalar. Number of observations of the current control group.

mu0_c

scalar. Mean of the historical control group.

sigma0_c

scalar. Standard deviation of the historical control group.

N0_c

scalar. Number of observations of the historical control group.

discount_function

character. Specify the discount function to use. Currently supports weibull, scaledweibull, and identity. The discount function scaledweibull scales the output of the Weibull CDF to have a max value of 1. The identity discount function uses the posterior probability directly as the discount weight. Default value is "identity".

alpha_max

scalar. Maximum weight the discount function can apply. Default is 1. For a two-arm trial, users may specify a vector of two values where the first value is used to weight the historical treatment group and the second value is used to weight the historical control group.

fix_alpha

logical. Fix alpha at alpha_max? Default value is FALSE.

weibull_scale

scalar. Scale parameter of the Weibull discount function used to compute alpha, the weight parameter of the historical data. Default value is 0.135. For a two-arm trial, users may specify a vector of two values where the first value is used to estimate the weight of the historical treatment group and the second value is used to estimate the weight of the historical control group. Not used when discount_function = "identity".

weibull_shape

scalar. Shape parameter of the Weibull discount function used to compute alpha, the weight parameter of the historical data. Default value is 3. For a two-arm trial, users may specify a vector of two values where the first value is used to estimate the weight of the historical treatment group and the second value is used to estimate the weight of the historical control group. Not used when discount_function = "identity".

number_mcmc

scalar. Number of Monte Carlo simulations. Default is 10000.

method

character. Analysis method with respect to estimation of the weight paramter alpha. Default method "mc" estimates alpha for each Monte Carlo iteration. Alternate value "fixed" estimates alpha once and holds it fixed throughout the analysis. See the the bdpnormal vignette
vignette("bdpnormal-vignette", package="bayesDP") for more details.

compare

logical. Should a comparison object be included in the fit? For a one-arm analysis, the comparison object is simply the posterior chain of the treatment group parameter. For a two-arm analysis, the comparison object is the posterior chain of the treatment effect that compares treatment and control. If compare=TRUE, the comparison object is accessible in the final slot, else the final slot is NULL. Default is TRUE.

Details

bdpnormal uses a two-stage approach for determining the strength of historical data in estimation of a mean outcome. In the first stage, a discount function is used that that defines the maximum strength of the historical data and discounts based on disagreement with the current data. Disagreement between current and historical data is determined by stochastically comparing the respective posterior distributions under noninformative priors. With Gaussian data, the comparison is the proability (p) that the current mean is less than the historical mean. The comparison metric p is then input into the discount function and the final strength of the historical data is returned (alpha).

In the second stage, posterior estimation is performed where the discount function parameter, alpha, is used incorporated in all posterior estimation procedures.

To carry out a single arm (OPC) analysis, data for the current treatment (mu_t, sigma_t, and N_t) and historical treatment (mu0_t, sigma0_t, and N0_t) must be input. The results are then based on the posterior distribution of the current data augmented by the historical data.

To carry our a two-arm (RCT) analysis, data for the current treatment and at least one of current or historical control data must be input. The results are then based on the posterior distribution of the difference between current treatment and control, augmented by available historical data.

For more details, see the bdpnormal vignette:
vignette("bdpnormal-vignette", package="bayesDP")

Value

bdpnormal returns an object of class "bdpnormal". The functions summary and print are used to obtain and print a summary of the results, including user inputs. The plot function displays visual outputs as well.

An object of class bdpnormal is a list containing at least the following components:

posterior_treatment

list. Entries contain values related to the treatment group:

posterior_control

list. Similar entries as posterior_treament. Only present if a control group is specified.

final

list. Contains the final comparison object, dependent on the analysis type:

args1

list. Entries contain user inputs. In addition, the following elements are ouput:

References

Haddad, T., Himes, A., Thompson, L., Irony, T., Nair, R. MDIC Computer Modeling and Simulation working group.(2017) Incorporation of stochastic engineering models as prior information in Bayesian medical device trials. Journal of Biopharmaceutical Statistics, 1-15.

See Also

summary, print, and plot for details of each of the supported methods.

Examples

# One-arm trial (OPC) example
fit <- bdpnormal(
  mu_t = 30, sigma_t = 10, N_t = 50,
  mu0_t = 32, sigma0_t = 10, N0_t = 50,
  method = "fixed"
)
summary(fit)
## Not run: 
plot(fit)

## End(Not run)

# Two-arm (RCT) example
fit2 <- bdpnormal(
  mu_t = 30, sigma_t = 10, N_t = 50,
  mu0_t = 32, sigma0_t = 10, N0_t = 50,
  mu_c = 25, sigma_c = 10, N_c = 50,
  mu0_c = 25, sigma0_c = 10, N0_c = 50,
  method = "fixed"
)
summary(fit2)
## Not run: 
plot(fit2)

## End(Not run)


[Package bayesDP version 1.3.4 Index]