# Funnel plot to examine publication bias

### Description

Function to examine publication bias. For both fixed- and random-effects models,
estimates from no-pooling effects model are used as study-specific estimates. For
random-effects models, the corresponding fixed-effects models are implemented at
background to obtain pooled estimate. For example, if users call `bmeta`

to
run random-effects meta-analysis with normal prior, fixed-effects meta-analysis
with normal prior are implemented at background to obtain pooled estimate for
graphing. In the absence of publication and heterogeneity, the scatter resembles
a symmetrical funnel and the triangle area formed by connecting the centred summary
estimate with its 2.5% and 97.5% quantiles on either side includes about 95% of
the studies if the fixed-effects model assumption holds (i.e. all the studies
estimate the same effect).

### Usage

1 |

### Arguments

`x` |
a |

`xlab` |
title of x-axis. If unspecified, the function sets an appropriate lable by default. |

`ylab` |
title of x-axis. If unspecified, the function sets an appropriate lable by default. |

`title` |
title of the plot if specified |

`xlim` |
horozontal limits of the plot region. If unspecified, the function sets the horizontal plot limits to (-6,6). |

### Author(s)

Tao Ding Gianluca Baio

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
### Read and format the data (binary)
data = read.csv(url("http://www.statistica.it/gianluca/bmeta/Data-bin.csv"))
### List data for binary outcome
data.list <- list(y0=data$y0,y1=data$y1,n0=data$n0,n1=data$n1)
### Select random-effects meta-analysis with t-distribution prior for binary
### data
x <- bmeta(data.list, outcome="bin", model="std.dt", type="ran")
### using output from bmeta to produce funnel plot
funnel.plot(x)
### using output from bmeta and specify title of the plot
funnel.plot(x,title="funnel plot")
### using output from bmeta and specify the limit of x-axis and title
funnel.plot(x,title="funnel plot",xlim=c(-2,1))
``` |