pri_par_epsilon_grid: Grid computation for epsilon-local sensitivity
In pa4bayesmeta: Prior Accuracy for Bayesian Meta-Analysis

Description Usage Arguments Details Value References Examples

View source: R/pri_par_epsilon_grid.R

Starting with a base prior from a one-parameter family, this function determines the parameters of two priors from the same parametric family which have the given Hellinger distance to the base prior. The supported one-parameter distributions are half-normal (HN), half-Cauchy (HC), exponential (EXP) and Lomax (LMX) with shape parameter = 1.

pri_par_epsilon_grid(distributions = c("HN", "HC"),
                     AA0.HN = 1,  AA0.HC = 1, 
                     AA0.EXP = NULL, AA0.LMX = NULL, 
                     grid.epsilon = 0.00354)

`distributions`	vector of strings. Specifies the parametric prior distributions to use. The options are "HN" (half-normal), "HC" (half-Cauchy), "EXP" (exponential) and "LMX" (Lomax with shape parameter = 1). Defaults to c("HN", "HC").
`AA0.HN`	scale parameter of the base half-normal prior
`AA0.EXP`	scale parameter of the base exponential prior
`AA0.HC`	scale parameter of the base half-Cauchy prior
`AA0.LMX`	scale parameter of the base Lomax prior with shape parameter=1
`grid.epsilon`	value for epsilon, the Hellinger distance between the base prior and the "lower"/"upper" prior on the grid

This 1-dimensional epsilon grid is needed for computation of the epsilon-local sensitivity in the functions prior_accuracy, HN_accuracy and HC_accuracy. See Ott et al. (2021, Section 3.5) for a brief description of this methodology and the Supplementary Material of Ott et al. (2021, Section 4.5) and Roos et al. (2015) for more details. The default value for grid.epsilon corresponds to the Hellinger distance between two normal distribution with unit variance and a difference in means of 0.01. See Roos et al. (2015, Section 2.2) and Ott et al. (2021b, Section 3.5) for calibration and interpretation of Hellinger distance values.

A list of maximum eight scale parameter values (including only those parameters for the distributions specified in distributions, in the same order as in distributions):

`p_HN_l`	parameter of the "lower" half-normal prior on the grid
`p_HN_u`	parameter of the "upper" half-normal prior on the grid
`p_HC_l`	parameter of the "lower" half-Cauchy prior on the grid
`p_HC_u`	parameter of the "upper" half-Cauchy prior on the grid
`p_EXP_l`	parameter of the "lower" exponential prior on the grid
`p_EXP_u`	parameter of the "upper" exponential prior on the grid
`p_LMX_l`	scale parameter of the "lower" Lomax prior (with shape parameter=1) on the grid
`p_LMX_u`	scale parameter of the "upper" Lomax prior (with shape parameter=1) on the grid

Ott, M., Hunanyan, S., Held, L., Roos, M. Sensitivity-based identification of inaccurate heterogeneity priors in Bayesian meta-analysis. Submitted to Statistical Methods in Medical Research. 2021.

Ott, M., Hunanyan, S., Held, L., Roos, M. Supplementary Material: Sensitivity-based identification of inaccurate heterogeneity priors in Bayesian meta-analysis. Submitted to Statistical Methods in Medical Research. 2021.

Roos, M., Martins, T., Held, L., Rue, H. (2015). Sensitivity analysis for Bayesian hierarchical models. Bayesian Analysis 10(2), 321–349. https://projecteuclid.org/journals/bayesian-analysis/volume-10/issue-2/Sensitivity-Analysis-for-Bayesian-Hierarchical-Models/10.1214/14-BA909.full

Ott, M., Plummer, M. and Roos M. (2021b). How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Statistics in Medicine (accepted May 10, 2021). https://onlinelibrary.wiley.com/doi/full/10.1002/sim.9076

# epsilon grid for the HN(0.5) and HC(1) base priors and 
# epsilon = 0.00354 (default)
pri_par_epsilon_grid(AA0.HN = 0.5, AA0.HC = 1)

# epsilon grid for the EXP(1) and LMX(2) (with shape parameter = 1) 
# base priors and epsilon = 0.00354 (default)
pri_par_epsilon_grid(distributions = c("EXP", "LMX"),
                     AA0.EXP = 1, AA0.LMX = 2)
                     
# load the steriod-resistant rejection (SRR) data analyzed in Friede et al. (2017)
data(srr)

# epsilon grid for 50%-RLMC adjusted HN and HC base priors with 
# target RLMC = 0.5 and epsilon = 0.00354 (default) for SRR data
pri_par_epsilon_grid(AA0.HN = pri_par_adjust(df = srr)[[1]], 
                     AA0.HC = pri_par_adjust(df = srr)[[2]])