Implements first-order and higher-order likelihood methods for inference in meta-analysis and meta-regression models, as described in Guolo (2012). Higher-order asymptotics refer to the higher-order adjustment to the log-likelihood ratio statistic for inference on a scalar component of interest as proposed by Skovgaard (1996). See Guolo and Varin (2012) for illustrative examples about the usage of metaLik package.
metaLik(formula, data, subset, contrasts = NULL, offset, sigma2, weights=1/sigma2)an object of class "formula" (or one that
can be coerced to that class): a symbolic description of the
model to be fitted. The details of model specification are given
under ‘Details’.
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula), typically the environment from which metaLik is called.
an optional vector specifying a subset of observations to be used in the fitting process.
an optional list. See the contrasts.arg of model.matrix.default.
this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset.
a vector of within-study estimated variances. The length of the vector must be the same of the number of studies.
a vector of the inverse of within-study estimated variances. The length of the vector must be the same of the number of studies. If sigma2 is supplied, the value of weights is discarded.
An object of class "metaLik" with the following components:
the y vector used.
the model matrix used.
the fitted values.
the within-study variances used.
the number of studies.
the vector of the maximum likelihood parameter estimates.
the variance-covariance matrix of the parameter estimates.
the maximum log-likelihood value.
the vector of fixed-effects parameters estimated according to maximum likelihood.
the maximum likelihood estimate of \(\tau^2\).
the vector of fixed-effects parameters estimated according to DerSimonian and Laird's pproach.
the method of moments estimate of the heterogeneity parameter \(\tau^2\).
the variance-covariance matrix of the DL parameter estimates.
the matched call.
the formula used.
the terms object used.
the offset used.
(only where relevant) the contrasts specified.
(only where relevant) a record of the levels of the factors used in fitting.
the model frame used.
Models for metaLik.fit are specified simbolically. A typical model has the form y ~ x1 + … + xJ, where y is the continuous response term and xj is the j-th covariate available at the aggregated meta-analysis level for each study. The case of no covariates corresponds to the classical meta-analysis model specified as y~1.
Within-study variances are specified through sigma2: the rare case of equal within-study variances implies Skovgaard's adjustment reaching a third-order accuracy.
DerSimonian and Laird estimates (DerSimonian and Laird, 1986) are also supplied.
DerSimonian, R. and Laird, N. (1986). Meta-Analysis in Clinical Trials. Controlled Clinical Trials 7, 177--188.
Guolo, A. (2012). Higher-Order Likelihood Inference in Meta-Analysis and Meta-Regression. Statistics in Medicine 31, 313--327.
Guolo, A. and Varin, C. (2012). The R Package metaLik for Likelihood Inference in Meta-Analysis. Journal of Statistical Software 50 (7), 1--14. http://www.jstatsoft.org/v50/i07/.
Skovgaard, I. M. (1996). An Explicit Large-Deviation Approximation to One-Parameter Tests. Bernoulli 2, 145--165.
Function summary.metaLik for summaries.
Function test.metaLik for hypothesis testing.
# NOT RUN {
## meta-analysis
data(education)
m <- metaLik(y~1, data=education, sigma2=sigma2)
summary(m)
## meta-analysis
data(albumin)
m <- metaLik(y~1, data=albumin, sigma2=sigma2)
summary(m)
## meta-regression
data(vaccine)
m <- metaLik(y~latitude, data=vaccine, sigma2=sigma2)
summary(m)
## meta-regression
data(cholesterol)
m <- metaLik(heart_disease~chol_reduction, data=cholesterol, weights=1/sigma2)
summary(m)
# }
Run the code above in your browser using DataLab