metaLik: First- and higher-order likelihood inference in meta-analysis...

In metaLik: 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 "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’.
data	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.
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 model.matrix.default.
offset	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.
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 sigma2 is supplied, the value of weights is discarded.

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 τ^2.
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 τ^2.
vcov.DL	the variance-covariance matrix of the DL parameter estimates.
call	the matched call.
formula	the formula used.
terms	the terms object used.
offset	the offset used.
contrasts	(only where relevant) the contrasts specified.
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)

Example output

Likelihood inference in random-effects meta-analysis models

Call:
metaLik(formula = y ~ 1, data = education, sigma2 = sigma2)

Estimated heterogeneity parameter tau2 = 0.03829

Fixed-effects:
             estimate  std.err.  signed logLRT  p-value  Skovgaard  p-value
(Intercept)    0.3004    0.0832         2.8989   0.0037     2.6778   0.0074

Log-likelihood: 8.3768 

Likelihood inference in random-effects meta-analysis models

Call:
metaLik(formula = y ~ 1, data = albumin, sigma2 = sigma2)

Estimated heterogeneity parameter tau2 = 7.071e-05

Fixed-effects:
             estimate  std.err.  signed logLRT  p-value  Skovgaard  p-value
(Intercept)   60.9949    0.5457        27.9857        0    25.4928        0

Log-likelihood: -2.163 

Likelihood inference in random-effects meta-analysis models

Call:
metaLik(formula = y ~ latitude, data = vaccine, sigma2 = sigma2)

Estimated heterogeneity parameter tau2 = 0.1676

Fixed-effects:
             estimate  std.err.  signed logLRT  p-value  Skovgaard  p-value
(Intercept)   -0.3050    0.2241        -1.3378    0.181    -1.2245   0.2208
latitude      -0.0154    0.0064        -2.1203    0.034    -1.8164   0.0693

Log-likelihood: 1.1212 

Likelihood inference in random-effects meta-analysis models

Call:
metaLik(formula = heart_disease ~ chol_reduction, data = cholesterol, 
    weights = 1/sigma2)

Estimated heterogeneity parameter tau2 = 7.071e-05

Fixed-effects:
                estimate  std.err.  signed logLRT  p-value  Skovgaard  p-value
(Intercept)       0.1210    0.0974         1.2498   0.2114     1.3597   0.1739
chol_reduction   -0.4757    0.1384        -3.0323   0.0024    -2.4606   0.0139

Log-likelihood: 15.1519 

metaLik documentation built on May 1, 2019, 8:44 p.m.