Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 |

`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 |

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.

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.

Annamaria Guolo and Cristiano Varin.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
## 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)
``` |

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