pri_par_adjust: Heterogeneity prior adjustment based on the relative latent...
In pa4bayesmeta: Prior Accuracy for Bayesian Meta-Analysis

Description Usage Arguments Details Value References See Also Examples

View source: R/pri_par_adjust.R

Adjusts the scale parameter of the specified one-parameter priors for the between-study standard deviation such that the probability mass above the reference threshold equals the given tail probability. The reference threshold used depends on the target RLMC and the with-study standard errors in the data set. The supported priors are the half-normal (HN), the half-Cauchy (HC), the exponential (EXP) and the Lomax (LMX) distributions. The shape parameter of the LMX distribution is fixed at 1.

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pri_par_adjust(df, rlmc = 0.5, tail.prob = 0.5, 
               distributions = c("HN", "HC"), 
               type.sigma.ref = "geometric")

`df`	data frame with one column "sigma" containing the standard errors of the estimates for the individual studies
`rlmc`	target relative latent model complexity. Real number in [0,1]. Defaults to 0.5.
`tail.prob`	probability mass of the prior above the reference threshold (which depends on `rlmc` and `df$sigma`) Real number in [0,1]. Defaults to 0.5, which corresponds to aliging the median of the prior.
`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").
`type.sigma.ref`	either `"geometric"` or `"harmonic"`. Defaults to `"geometric"`. Specifies if the geometric mean or a weighted harmonic mean is used to compute the reference standard deviation. See details for more information.

This heterogeneity prior adjustment applies to Bayesian meta-analysis expressed by a normal-normal hierarchical model. The reference threshold U is given by

U = σ_{ref} √{rlmc/(1-rlmc)},

where σ_{ref} is the reference standard deviation of the data set, i.e. by default the geometric mean of df$sigma. Then, a prior tail-adjustment is applied for this reference threshold and the specified tail probability: The free parameter of the prior is determined such that

P[τ > U] = α,

where α = tail.prob.

Ott et al. (2021) suggest to use tail.prob = 0.5 as default, so that the median of the prior will be aligned with the reference threshold.

If type.sigma.ref = "geometric", the reference standard deviation is given by the geometric mean of the standard deviations of the individual studies (Sorbye & Rue 2014 (equation (7)).
If type.sigma.ref = "harmonic", the reference standard deviation σ_{ref} is the square root of a weighted harmonic mean of the variances of the individual studies, as described in Hoaglin (2016, page 490). See sigma_ref for the formula.

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

`p_HN`	parameter of half-normal prior
`p_HC`	parameter of half-Cauchy prior
`p_EXP`	parameter of exponential prior
`p_LMX`	scale parameter for Lomax prior with shape parameter=1

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.

Sorbye, S., Rue, H. (2014). Scaling intrinsic Gaussian Markov random field priors in spatial modelling. Spatial Statistics 8, 39–51. https://doi.org/10.1016/j.spasta.2013.06.004

Hoaglin, D. (2016). Misunderstandings about Q and "Cochran's Q test" in meta-analysis. Statistics in Medicine 35(4), 485–495. https://doi.org/10.1002/sim.6632

sigma_ref

# load the steriod-resistant rejection (SRR) data analyzed in Friede et al. (2017)
data(srr)
 
# for the SRR data, compute the following:                 
# 50%-RLMC-based adjustment of HN and HC priors used in Ott et al. (2021)
# with target RLMC 0.5
pri_par_adjust(df = srr, rlmc = 0.5)
# 50%-RLMC-based adjustment of EXP and LMX priors used in Ott et al. (2021)
# with target RLMC 0.8
pri_par_adjust(df = srr, distributions = c("EXP", "LMX"),
               rlmc = 0.8)
# 50%-RLMC-based adjustment of HN and HC priors with target RLMC 0.2
# using the harmonic mean to determine the reference threshold
pri_par_adjust(df = srr, rlmc = 0.2,
              type.sigma.ref = "harmonic")