pri_RA_5bm | R Documentation |

Computes a table of Hellinger distance estimates between the actual heterogeneity prior(s) specified and four benchmark heterogeneity priors proposed in the Supplementary Material of Ott et al. (2021).

```
pri_RA_5bm(df, tau.prior=list(function(x) dhalfnormal(x, scale=1)),
m_J=NA, M_J=NA, upper.J=3, digits.J=2,
m_inf=NA, M_inf=NA, rlmc0=0.0001, rlmc1=0.9999,
mu.mean=0, mu.sd=4)
```

`df` |
data frame with one column "y" containing the (transformed) effect estimates for the individual studies and one column "sigma" containing the standard errors of these estimates. |

`tau.prior` |
list of prior specifications, which are |

`m_J` |
parameter value |

`M_J` |
parameter value |

`upper.J` |
upper bound for the parameters |

`digits.J` |
specifies the desired precision of the parameter values |

`m_inf` |
parameter value |

`M_inf` |
parameter value |

`rlmc0` |
RLMC target value for the SGC( |

`rlmc1` |
RLMC target value for the SIGC( |

`mu.mean` |
mean of the normal prior for the effect mu. |

`mu.sd` |
standard deviation of the normal prior for the effect mu. |

The methodology for a prior reference analysis and the four proper heterogeneity benchmark priors used are
introduced in the Supplementary Material of Ott et al. (2021, Sections 2.5 and 2.6).
There, these four benchmark priors are denoted by
SGC(`m_J`

), SIGC(`M_J`

), SGC(`m_{inf}`

) and SIGC(`M_{inf}`

).

A list with two elements:
The first element named "table" is a matrix containing the Hellinger distance estimates and the
second element called "par" is a named vector giving the parameter values
of the benchmark priors.
The vector "par" has the following five components:
`m_inf`

, `M_J`

, `m_J`

, `M_inf`

and `C`

.

The matrix "table" contains the Hellinger distance estimates between actual and benchmark
heterogeneity priors
and has `4`

columns and `n`

rows,
where `n`

is the number of actual heterogeneity priors specified,
i.e. the length of the list `tau.prior`

.

The columns of the matrix give the following Hellinger distance estimates between two heterogeneity priors (from left to right):

`H(SGC(m_inf), pri_act)`

:benchmark prior SGC(m_inf) and actual prior

`H(SIGC(M_J), pri_act)`

:benchmark prior SIGC(M_J) and actual prior

`H(SGC(m_J), pri_act)`

:benchmark prior SGC(m_J) and actual prior

`H(SIGC(M_inf), pri_act)`

:benchmark prior SIGC(M_inf) and actual prior

Each row corresponds to one actual heterogeneity prior
specified in the list `tau.prior`

, in the same order
as in that list. Thus, the row names are:

`pri_act_1`

:first actual prior in

`tau.prior`

`pri_act_2`

:second actual prior in

`tau.prior`

- ...
`pri_act_n`

:nth (last) actual prior in

`tau.prior`

This function may take several minutes to run if the parameter `m_J`

and/or `M_J`

is not specified,
especially if the desired precision is `digits.J=2`

or even `digits.J=3`

.

Ott, M., Plummer, M., Roos, M. (2021). Supplementary Material:
How vague is vague? How informative is informative? Reference analysis for
Bayesian meta-analysis. *Statistics in Medicine*.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.9076")}

`post_RA_3bm`

,
`pri_RA_fits`

```
# for aurigular acupuncture (AA) data set with one
# actual half-normal and the "DuMouchel" heterogeneity prior
data(aa)
# warning: it takes ca. 7 min. to run this function
pri_RA_5bm(df=aa, tau.prior=list(function(t)dhalfnormal(t, scale=1),
"DuMouchel"))
# computation is much faster if m_J and M_J are specified
pri_RA_5bm(df=aa, tau.prior=list(function(t)dhalfnormal(t, scale=1),
"DuMouchel"),
m_J = 1.35, M_J = 1.3)
```

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