pri_par_adjust_dynamic {sl4bayesmeta} | R Documentation |
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.
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 |
type_sigma_ref |
either |
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")