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

These functions implement maximum likeliihood (ML) and restricted maximum likelihood (REML) estimators for random-effects dose-response meta-analysis. They are meant to be used internally and not directly run by the users.

1 2 3 | ```
dosresmeta.ml(Xlist, Zlist, ylist, Slist, nalist, q, nall, control, ...)
dosresmeta.reml(Xlist, Zlist, ylist, Slist, nalist, q, nall, control, ...)
``` |

`Xlist` |
a m-dimensional list of study-specific design matrices for the fixed-effects part of the model. |

`Zlist` |
a m-dimensional list of study-specific design matrices for the random-effects part of the model. |

`ylist` |
a m-dimensional list of study-specific of vectors of estimated outcomes. |

`Slist` |
a m-dimensional list of within-study (co)variance matrices of estimated outcomes. |

`nalist` |
a m-dimensional list of k-dimensional study-specific logical vectors, identifying missing outcomes. |

`q` |
numeric scalars: number of predictors, number of observations (excluding missing). |

`nall` |
numeric scalars: number of predictors, number of observations (excluding missing). |

`control` |
list of parameters for controlling the fitting process, usually internally set to default values by |

`...` |
further arguments passed to or from other methods. Currently not used. |

The estimation involves *p* fixed-effects coefficients and the *p(p+1)/2* random-effects parameters defining the between-study (co)variance matrix.
The hybrid estimation procedure is based first on few runs of iterative generalized least square algorithm and then quasi-Newton iterations,
using specific likelihood functions, until convergence. The estimation algorithm adopts a profiled (or concentrated) approach, that is expressed
only in terms of the random-effects parameters. Cholesky and and QR decompositions are used for computational stability and efficiency, and for assuring the
positive-definiteness of the estimated between-study (co)variance matrix. See the help page for the likelihood functions for further details.

These functions return an intermediate list object, whose components are then processed by `dosresmeta.fit`

. Other components are added later
through `dosresmeta`

to finalize an object of class "`dosresmeta`

".

Alessio Crippa, alessio.crippa@ki.se

Gasparrini, A., Armstrong, B., Kenward, M. G. (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine, 31(29), 3821-3839.

`dosresmeta`

, `dosresmeta-package`

, `dosresmeta.ml`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
data("alcohol_cvd")
## Random-effect dose-response model assuming linearity, ML estimator
lin.ml <- dosresmeta(formula = logrr ~ dose, type = type, id = id,
se = se, cases = cases, n = n, data = alcohol_cvd,
, method = "ml")
summary(lin.ml)
## Random-effect dose-response model assuming linearity, REML estimator
lin.reml <- dosresmeta(formula = logrr ~ dose, type = type, id = id,
se = se, cases = cases, n = n, data = alcohol_cvd,
, method = "reml")
summary(lin.reml)
``` |

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