Stata Technical Bulletin
funnel requests a filled funnel graph be displayed showing the data, the meta-analytic estimate, and pseudo confidence-interval
limits about the meta-analytic estimate. The estimate and confidence interval in the graph are derived using fixed or
random-effects meta-analysis, as specified by option ref feet.
level (#) specifies the confidence level percent for the pseudo confidence intervals; the default is 95%.
idvar Varnamee) indicates the character variable used to label the studies.
save (filename[, replace]) saves the filled data in a separate Stata data file. The filename is assumed to have extension .dta
(an extension should not be provided by the user). If filename does not exist, it is created. If filename exists, an error will
occur unless replace is also specified. Only three variables are saved: a study id variable and two variables containing
the filled theta and seJheta values. The study id variable, named id in the saved file, is created by metatrim; but when
option idvar() is specified, it is based on that id variable. The filled theta and seJheta variables are named filled and
sef ill in the saved file.
graph-options are those allowed with graph, twoway, except ylabel(), symbol(), xlog, ytick and gap are not recognized by
graph. For funnel, the default graph-options include connect (111..), symbol (iiioS), and pen(35522) for displaying
the meta-analytic effect, the pseudo confidence interval limits (two lines), and the data points, respectively.
Specifying input variables
The individual effect estimates (and a measure of their variability) can be provided to metatrim in any of three ways:
1. The effect estimate and its corresponding standard error (the default method):
. metatrim theta seJheta ...
2. The effect estimate and its corresponding variance (note that option var must be specified):
. metatrim theta vanJletta, var ...
3. The risk (or odds) ratio and its confidence interval (note that option ci must be specified):
. metatrim exp(theta) ll ul, ci ...
where exp(theta) is the risk (or odds) ratio, ll is the lower limit and ul is the upper limit of the risk ratio’s confidence
interval.
When input method 3 is used, cl is an optional input variable that contains the confidence level of the confidence interval
defined by ll and ul:
. metatrim exp(theta) ll ul cl, ci ...
If cl is not provided, metatrim assumes that a 95% confidence level was reported for each study. cl allows the user to
combine studies with diverse or non-95% confidence levels by specifying the confidence level for each study not reported
at the 95% level. Note that option level() does not affect the default confidence level assumed for the individual studies.
Values of cl can be provided with or without a decimal point. For example, 90 and .90 are equivalent and may be mixed
(i.e., 90, .95, 80, .90, etc.). Missing values within cl are assumed to indicate a 95% confidence level.
Note that data in binary count format can be converted to the effect format used in metatrim by use of program metan
(Bradburn et al. 1998). metan automatically creates and adds variables for theta and seJheta to the raw dataset, naming them
_ES and -seES. These variables can be provided to metatrim using the default input method.
Explanation
Meta-analysis is a popular technique for numerically synthesizing information from published studies. One of the many
concerns that must be addressed when performing a meta-analysis is whether selective publication of studies could lead to bias
in estimating the overall meta-analytic effect and in the inferences derived from the analysis. If publication bias appears to exist,
then it is desirable to consider what the unbiased dataset might look like and then to reestimate the overall meta-analytic effect
after any apparently “missing” studies are included. Duval and Tweedie’s “nonparametric ‘trim and fill’ method” is designed to
meet these objectives and is implemented in this insert.
An early, visual approach used to assess the likelihood of publication bias and to provide a hint of what the unbiased data
might look like was the funnel graph (Light and Pillemer 1984). The funnel graph plotted the outcome measure (effect size) of
the component studies against the sample size (a measure of variability). The approach assumed that all studies in the analysis
were estimating the same effect. Therefore, the effect estimates should be distributed about the unknown true effect level and