Description Usage Arguments Details Value Warning References See Also Examples
Computes a table of posterior estimates and informativeness values
for the marginal posterior distributions
of different parameters in the NNHM
induced by the actual heterogeneity priors specified in tau.prior
.
Also provides the same estimates for the
posterior benchmarks proposed in Ott et al. (2021).
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df 
data frame with one column "y" containing the (transformed) effect estimates for the individual studies and one column "sigma" containing the standard errors of these estimates. 
tau.prior 
list of prior specifications, which are either functions returning the probability densities of the actual priors of interest for the heterogeneity parameter tau or character strings specifying priors implemented in the 
show.re 
logical. If 
estimate 
type of posterior point estimate. Either 
ci.method 
method for computation of 95% credible intervals (CrIs). Either 
H.dist.method 
method for computation of Hellinger distances between marginal posterior densities. Either 
scale.hn0 
scale parameter of the halfnormal benchmark prior (usually a small number to obtain an anticonservative benchmark which has most of its probability mass close to 0). Defaults to 0.002. 
mu.mean 
mean of the normal prior for the effect mu. Defaults to 0. 
mu.sd 
standard deviation of the normal prior for the effect mu. Defaults to 4. 
The two posterior benchmarks used are introduced in Ott et al. (2021, Section 3.4), where they are denoted by po_{J}(Ψ) and po_{HN0}(Ψ). Here, Ψ \in \{ μ, τ, θ_1, ..., θ_k, θ_{new} \} denotes the parameter of interest in the NNHM, where θ_{i} is the random effect in the ith study and θ_{new} the predicted effect for a new study. For the overall mean parameter μ, we additionally consider the fixedeffects model benchmark po_{FE}(μ).
Note that Jeffreys reference posterior po_{J} is proper if there are at least two studies in the metaanalysis data set. It is based on the improper Jeffreys reference prior, which is minimally informative given the data. The computation of the informativeness values is described in Ott et al. (2021, Section 3.6).
The absolute value of the signed informativeness quantifies how close the actual posterior and the reference posterior po_{J} are. If the signed informativeness is negative, then the actual prior is anticonservative with respect to Jeffreys reference prior J (that is puts more weight on smaller values for τ than J). If the signed informativeness is positive, then the actual prior is conservative with respect to Jeffreys reference prior J (that is puts more weight on larger values for τ than J).
If integralbased computation (H.dist.method = "integral"
) of Hellinger distances is selected (the default), numerical integration is applied to obtain the Hellinger distance between the two marginal posterior densities (by using the function H
).
If momentbased computation (H.dist.method = "moment"
) is selected, the marginal densities are first approximated by normal densities with the same means and standard deviations and then the Hellinger distance between these normal densities can be obtained by an analytical formula (implemented in the function H_normal
).
The default values for mu.mean
and mu.sd
are suitable for effects mu on the log odds (ratio) scale.
A matrix with 6 columns and a number of columns depending on the number
of actual heterogeneity priors specified and the parameters of interests in the NNHM
(if show.re = FALSE
, then there are 3 parameters of interest (μ, τ, θ_{new}) and the matrix has 3*(n+2)+1 rows, where
where n=length(tau.prior
) is the number of actual heterogeneity priors specified;
if show.re = TRUE
, then the matrix has (k+3)*(n+2)+1 rows, where
k is the number of studies in the metaanalysis data set
(so that there are k+3 parameters of interest).)
The row names specify the parameter in the NNHM for which the marginal posterior is considered,
followed by the heterogeneity prior used to compute that posterior.
HN0, J and FE denote the three benchmark priors introduced in Ott et al. (2021).
pri_act_i
denotes the ith prior in the tau.prior
list.
The 6 columns provide the following estimates:

posterior point estimate (median or mean) 

lower limit of the 95% credible interval 

upper limit of the 95% credible interval 

length of the 95% credible interval 

Hellinger distance between the posterior benchmark po_{HN0}(Ψ) and the marginal posterior induced by the heterogeneity prior listed on the left, for the parameter Ψ listed on the left 

Signed informativeness, i.e. sign(H(po_{HN0}, po_{act})  H(po_{HN0}, po_{J})) H(po_{act}, po_{J}), for the marginal posterior induced by the heterogeneity prior listed on the left, for the parameter Ψ listed on the left 
If the integralbased method is used to compute Hellinger distances (H.dist.method = "integral"
),
numerical problems may occur in some cases, which may lead to implausible outputs.
Therefore, we generally recommend to doublecheck the results of the integralbased method using the momentbased method (H.dist.method = "moment"
)  especially if the former results are implausibe. If large differences between the two methods are observed, we recommend to rely on the momentbased method unless a normal approximation of the involved densities is inappropriate.
Ott, M., Plummer, M., Roos, M. How vague is vague? How informative is informative? Reference analysis for Bayesian metaanalysis. Manuscript revised for Statistics in Medicine. 2021.
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