metaLik {metaLik} | R Documentation |
First- and higher-order likelihood inference in meta-analysis and meta-regression models
Description
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.
Usage
metaLik(formula, data, subset, contrasts = NULL, offset, sigma2, weights=1/sigma2)
Arguments
formula |
an object of class |
data |
an optional data frame, list or environment (or object
coercible by |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
contrasts |
an optional list. See the contrasts.arg of |
offset |
this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be |
sigma2 |
a vector of within-study estimated variances. The length of the vector must be the same of the number of studies. |
weights |
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 |
Details
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.
Value
An object of class "metaLik"
with the following components:
y |
the y vector used. |
X |
the model matrix used. |
fitted.values |
the fitted values. |
sigma2 |
the within-study variances used. |
K |
the number of studies. |
mle |
the vector of the maximum likelihood parameter estimates. |
vcov |
the variance-covariance matrix of the parameter estimates. |
max.lik |
the maximum log-likelihood value. |
beta.mle |
the vector of fixed-effects parameters estimated according to maximum likelihood. |
tau2.mle |
the maximum likelihood estimate of |
DL |
the vector of fixed-effects parameters estimated according to DerSimonian and Laird's pproach. |
tau2.DL |
the method of moments estimate of the heterogeneity parameter |
vcov.DL |
the variance-covariance matrix of the DL parameter estimates. |
call |
the matched call. |
formula |
the |
terms |
the |
offset |
the offset used. |
contrasts |
(only where relevant) the |
xlevels |
(only where relevant) a record of the levels of the factors used in fitting. |
model |
the model frame used. |
Generic functions coefficients
, vcov
, logLik
, fitted
, residuals
can be used to extract fitted model quantities.
Author(s)
Annamaria Guolo and Cristiano Varin.
References
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.
See Also
Function summary.metaLik
for summaries.
Function test.metaLik
for hypothesis testing.
Examples
## 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)