This method function computes (empirical) best linear unbiased predictions from fitted univariate or multivariate meta-analytical models represented in objects of class "mvmeta". Such predictions are optionally accompanied by standard errors, prediction intervals or the entire (co)variance matrix of the predicted outcomes.
# S3 method for mvmeta
blup(object, se=FALSE, pi=FALSE, vcov=FALSE, pi.level=0.95,
format=c("matrix","list"), aggregate=c("stat","y"), …)an object of class "mvmeta".
logical switch indicating if standard errors must be included.
logical switch indicating if prediction intervals must be included.
logical switch indicating if the (co)variance matrix must be included.
a numerical value between 0 and 1, specifying the confidence level for the computation of prediction intervals.
the format for the returned results. See Value.
when format="matrix" and se or ci are required, the results may be aggregated by statistic or by outcome. See Value.
further arguments passed to or from other methods.
The results may be aggregated in matrices (the default), or returned as lists, depending on the argument format. For multivariate models, the aggregation is ruled by the argument aggregate, and the results may be grouped by statistic or by outcome. If vcov=TRUE, lists are always returned.
The method function blup produces (empirical) best linear unbiased predictions from mvmeta objects. For random-effects models, predictions are given by the sum of the estimated mean outcomes from the fixed part of the model, plus study-specific deviations predicted as random effects given the between-study distribution.
Predicted outcomes from blup are a shrunk version of study-specific realizations, where study-specific estimates borrow strength from the assumption of an underlying multivariate distribution of outcomes in a (usually hypothetical) population of studies. In practice, the results from blup represent a weighted average between population mean outcomes (estimated by the fixed part of the model) and study-specific estimates. The weights depend from the relative size of the within and between-study covariance matrices reported as components S and Psi in mvmeta objects (see mvmetaObject).
Fixed-effects models do not assume study-specific random effects, and the results of blup for these models are identical to predict with interval="confidence".
How to handle predictions for studies removed from estimation due to invalid missing pattern is determined by the na.action argument used in mvmeta to produce object. If na.action=na.omit, studies excluded from estimation will not appear, whereas if na.action=na.exclude they will appear, with values set to NA for all the outcomes. This step is performed by napredict. See Note below.
In the presence of missing values in the study-specific estimated outcome y of the fitted model, correspondent values of point estimates and covariance terms are set to 0, while the variance terms are set to 1e+10. In this case, in practice, the study-specific estimates do not provide any information (their weight is virtually 0), and the prediction tends to the value returned by predict with interval="prediction", when applied to a new but identical set of predictors. See also Note below.
Sera F, Armstrong B, Blangiardo M, Gasparrini A (2019). An extended mixed-effects framework for meta-analysis.Statistics in Medicine. 2019;38(29):5429-5444. [Freely available here].
Gasparrini A, Armstrong B, Kenward MG (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine. 31(29):3821--3839. [Freely available here].
See predict for standard predictions. See mvmeta-package for an overview of the package and modelling framework.
# NOT RUN {
# RUN THE MODEL
model <- mvmeta(cbind(PD,AL)~1,S=berkey98[5:7],data=berkey98)
# ONLY BLUP
blup(model)
# BLUP AND SE
blup(model,se=TRUE)
# SAME AS ABOVE, AGGREGATED BY OUTCOME, WITH PREDICTION INTERVALS
blup(model,se=TRUE,pi=TRUE,aggregate="y")
# WITH VCOV, FORCED TO A LIST
blup(model,se=TRUE,pi=TRUE,vcov=TRUE,aggregate="y")
# }
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