ess | R Documentation |
This function computes the effective sample size (ESS) of a posterior predictive distribution.
ess(object, ...)
## S3 method for class 'bayesmeta'
ess(object, uisd, method=c("elir", "vr", "pr", "mtm.pt"), ...)
object |
a |
uisd |
the unit infomation standard deviation
(a single numerical value, or a |
method |
a character string specifying the method to be used for
ESS computation. By default, the expected local-information-ratio
ESS ( |
... |
additional arguments |
The information conveyed by a prior distribution may often be
quantified in terms of an effective sample size
(ESS). Meta-analyses are commonly utilized to summarize
“historical” information in order to inform a future study,
leading to a meta-analytic-predictive (MAP) prior (Schmidli et
al., 2014). In the context of the normal-normal hierarchical model
(NNHM), the MAP prior results as the (posterior) predictive
distribution for a “new” study mean
\theta_{k+1}
. This function computes the ESS for the
posterior predictive distribution based on a bayesmeta
object.
Within the NNHM, the notion of an effective sample size requires the
specification of a unit information standard deviation (UISD)
(Roever et al., 2020); see also the ‘uisd()
’
function's help page. The UISD \sigma_\mathrm{u}
here
determines the Fisher information for one information unit,
effectively assuming that a study's sample size n_i
and
standard error \sigma_i
are related simply as
\sigma_i=\frac{\sigma_\mathrm{u}}{\sqrt{n_i}},
i.e., the squared standard error is inversely proportional to the
sample size. For the (possibly hypothetical) case of a sample size of
n_i=1
, the standard error then is equal to the UISD
\sigma_\mathrm{u}
.
Specifying the UISD as a constant is often an approximation,
sometimes it is also possible to specify the UISD as a function of the
parameter (\mu
). For example, in case the outcome in
the meta-analyses are log-odds, then the UISD varies with the (log-)
odds and is given by 2\,\mathrm{cosh}(\mu/2)
(see also the example below).
The ESS may be computed or approximated in several ways. Possible choices here are:
"elir"
: the expected local-information-ratio (ELIR) method (the default),
"vr"
: the variance ratio (VR) method,
"pr"
: the precision ratio (PR) method,
"mtm.pt"
: the Morita-Thall-Mueller / Pennello-Thompson (MTM.PM) method.
For more details on these see also Neuenschwander et al. (2020).
The effective sample size (ESS).
Christian Roever christian.roever@med.uni-goettingen.de
B. Neuenschwander, S. Weber, H. Schmidli, A. O'Hagan. Predictively consistent prior effective sample sizes. Biometrics, 76(2):578-587, 2020. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/biom.13252")}.
H. Schmidli, S. Gsteiger, S. Roychoudhury, A. O'Hagan, D. Spiegelhalter, B. Neuenschwander. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics, 70(4):1023-1032, 2014. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/biom.12242")}.
C. Roever, R. Bender, S. Dias, C.H. Schmid, H. Schmidli, S. Sturtz, S. Weber, T. Friede. On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis. Research Synthesis Methods, 12(4):448-474, 2021. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jrsm.1475")}.
bayesmeta
, uisd
.
# load data set:
data("BaetenEtAl2013")
print(BaetenEtAl2013)
## Not run:
# compute effect sizes (logarithmic odds) from the count data:
as <- escalc(xi=events, ni=total, slab=study,
measure="PLO", data=BaetenEtAl2013)
# estimate the unit information standard deviation (UISD):
uisd(as, individual=TRUE)
uisd(as) # = 2.35
# perform meta-analysis
# (using uniform priors for effect and heterogeneity):
bm <- bayesmeta(as)
# show forest plot:
forestplot(bm, zero=NA, xlab="log-odds")
# compute ESS_ELIR (based on fixed UISD):
ess(bm, uisd=2.35) # = 45.7 patients
# compute ESS_ELIR based on UISD as a function of the log-odds:
uisdLogOdds <- function(logodds)
{
return(2 * cosh(logodds / 2))
}
# Note: in the present example, probabilities are
# at approximately 0.25, corresponding to odds of 1:3.
uisdLogOdds(log(1/3))
# The UISD value of 2.31 roughly matches the above empirical figure.
ess(bm, uisd=uisdLogOdds) # = 43.4 patients
## End(Not run)
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