pri_par_adjust_dynamic: Dynamic heterogeneity prior adjustment based on the relative...
In sl4bayesmeta: Sensitivity and learning for Bayesian meta-analysis

Description Usage Arguments Details Value References See Also Examples

Adjusts the scale parameter of the half-normal, exponential, half-Cauchy and Lomax prior 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 shape parameter of the Lomax distribution is fixed at 1.

1 2	pri_par_adjust_dynamic(df, rlmc=0.5, tail_prob=0.5, 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].
`tail_prob`	probability mass of the prior above the reference threshold (which depends on `rlmc` and `df$sigma`)
`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.

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. the geometric mean of df$sigma. Then, the static prior tail-adjustment is applied for this reference threshold and the specified tail probability. This prior adjustment applies to Bayesian meta-analysis expressed by a normal-normal hierarchical model.

Ott et al. (2020) suggest to use tail_prob=0.5 as default, so that the medians of the priors 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 four scale parameter values (one for each prior considered):

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

Ott, M., Hunanyan, S., Held, L., Roos, M. Sensitivity quantification in Bayesian meta-analysis. Manuscript revised for Research Synthesis Methods. 2020.

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

pri_par_adjust_static, sigma_ref

# Acute Graft rejection data analyzed in Friede et al. (2017), Sect. 3.2, 
# URL: https://doi.org/10.1002/bimj.201500236
df <- data.frame(y = c(-2.310, -1.258), # log-odds-ratio
                 sigma = c(0.599, 0.642), # SE(log-odds-ratio)
                 labels = c(1:2))
                  
pri_par_adjust_dynamic(df=df, rlmc=0.25)
pri_par_adjust_dynamic(df=df, rlmc=0.5)
pri_par_adjust_dynamic(df=df, rlmc=0.5, type_sigma_ref="harmonic")