post_RA_fits {ra4bayesmeta}R Documentation

Posterior reference analysis based on bayesmeta fits

Description

Computes a table of Hellinger distances between marginal posterior distributions for different parameters in the NNHM between the actual model fits in fits.actual and the benchmark fits in fits.bm. All fits should be based on the same data set.

Usage

post_RA_fits(fits.actual, fits.bm)

Arguments

fits.actual

a list of model fits of class bayesmeta, computed with the bayesmeta function in the package bayesmeta.

fits.bm

a list of model fits of class bayesmeta, computed with the bayesmeta function in the package bayesmeta. To be used as benchmarks.

Details

Suggestions for posterior benchmarks are provided in Ott et al. (2020, Sections 2.5 and 2.6) and they can be computed using the function fit_models_RA.

Value

A matrix of Hellinger distance estimates between marginal posteriors with n.bm columns and n.act*(k+3) rows, where n.bm=length(fits.bm) is the number of benchmark fits specified, n.act=length(fits.actual) the number of actual fits specified and k the number of studies in the meta-analysis data set (so that there are k+3 parameters Ψ \in \{ μ, τ, θ_1, ..., θ_k, θ_{new} \} of potential interest in the NNHM).

The columns of the matrix give the following Hellinger distance estimates between two marginal posteriors (for the parameter of interest Ψ varying with rows) induced by the following two heterogeneity priors (from left to right):

H(po_bm_1, po_act)

first benchmark prior bm_1 inducing the fit fits.bm[[1]] and actual prior

H(po_bm_2, po_act)

second benchmark prior bm_2 inducing the fit fits.bm[[2]] and actual prior

...

...

H(po_bm_n.bm, po_act)

last benchmark prior bm_n.bm inducing the fit fits.bm[[n.bm]] and actual prior

The actual heterogenity prior and the parameter of interest Ψ vary with the rows in the following order:

mu, pri_act_1

Ψ=μ and first actual prior in tau.prior

mu, pri_act_2

Ψ=μ and second actual prior in tau.prior

...

...

mu, pri_act_n

Ψ=μ and nth actual prior in tau.prior

tau, pri_act_1

Ψ=τ and first actual prior in tau.prior

...

...

tau, pri_act_n

Ψ=τ and nth actual prior

theta_1, pri_act_1

Ψ=θ_1 and first actual prior

...

...

theta_k, pri_act_n

Ψ=θ_k and nth actual prior

theta_new, pri_act_1

Ψ=θ_{new} and first actual prior

...

...

theta_new, pri_act_n

Ψ=θ_{new} and nth actual prior

References

Ott, M., Plummer, M., Roos, M. How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Manuscript submitted to Statistics in Medicine. 2020.

See Also

bayesmeta in the package bayesmeta, fit_models_RA, post_RA, pri_RA_fits

Examples

# for aurigular acupuncture (AA) data set
data(aa)
# compute the model fits
# actual standard half-normal and half-Cauchy heterogeneity priors
fits <- fit_models_RA(df=aa, tau.prior=
                             list(function(t)dhalfnormal(t, scale=1),
                                  function(t)dhalfcauchy(t, scale=1)))[[1]]
# benchmark fits under SGC(m_inf), Jeffreys' and SIGC(M_inf) priors
fits.bm.post <- fits[c(1,5,4)]
fits.actual <- fits[c(6,7)]
post_RA_fits(fits.actual=fits.actual, fits.bm=fits.bm.post)

[Package ra4bayesmeta version 0.1-2 Index]