Stata Technical Bulletin
STB-57
sbe39 Nonparametric trim and fill analysis of publication bias in meta-analysis
Thomas J. Steichen, RJRT, [email protected]
Abstract: This insert describes metatrim, a command implementing the Duval and Tweedie nonparametric “trim and fill”
method of accounting for publication bias in meta-analysis. Selective publication of studies, which may lead to bias in
estimating the overall meta-analytic effect and in the inferences derived, is of concern when performing a meta-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 an approach designed to meet these objectives.
Keywords: meta-analysis, publication bias, nonparametric, data augmentation.
Syntax
metatrim {hheaa { seJheta ∣ var-theta } ∣ exp(theta) llul [d]} [if exp] [in range]
[, {var I ci} reffect print estimât({run ∣ linear ∣ quadratic}) eform graph
funnel level (#) idvar (vaaaame') save filename [, replace]) graph-options ]
where {α ∣ b ∣ ...} means choose one and only one of {α, b,...}.
Description
metatrim performs the Duval and Tweedie (2000) nonparametric “trim and fill” method of accounting for publication bias
in meta-analysis. The method, a rank-based data-imputation technique, formalizes the use of funnel plots, estimates the number
and outcomes of missing studies, and adjusts the meta-analysis to incorporate the imputed missing data. The authors claim that
the method is effective and consistent with other adjustment techniques. As an option, metatrim provides a funnel plot of the
filled data.
The user provides the effect estimate, theta, to metatrim as a log risk-ratio, log odds-ratio, or other direct measure of
effect. Along with theta, the user supplies a measure of theta’s variability (that is, its standard error, seJheta, or its variance,
var Jheta). Alternatively, the user may provide the exponentiated form, exp(theta), (that is, a risk ratio or odds ratio) and its
confidence interval, (ll, ul).
The funnel plot graphs theta versus seJheta for the filled data. Imputed observations are indicated by a square around the
data symbol. Guide lines to assist in visualizing the center and width of the funnel are plotted at the meta-analytic effect estimate
and at pseudo-confidence-interval limits about that effect estimate (that is, at theta ± z × seJheta, where z is the standard normal
variate for the confidence level specified by option level()).
Options
var indicates that varJheta was supplied on the command line instead of seJheta. Option ci should not be specified when
option var is specified.
ci indicates that exp(theta) and its confidence interval, (ll, ul), were supplied on the command line instead of theta and seJheta.
Option var should not be specified when option ci is specified.
ref feet specifies an analysis based on random-effects meta-analytic estimates. The default is to base calculations on fixed-effects
meta-analytic estimates.
print requests that the weights used in the filled meta-analysis be listed for each study, together with the individual study
estimates and confidence intervals. The studies are labeled by name if the idvar() option is specified, or by number
otherwise.
estimât ({run ∣ linear ∣ quadratic}) specifies the estimator used to determine the number of points to be trimmed in
each iteration. The user is cautioned that the run estimator, R0, is nonrobust to an isolated negative point, and that the
quadratic estimator, Q0, may not be defined when the number of points in the data set is small. The linear estimator,
Lis, is stable in most situations and is the default.
eform requests that the results in the final meta-analysis, and in the print option, be reported in exponentiated form. This is
useful when the data represent odds ratios or relative risks.
graph requests that point estimates and confidence intervals be plotted. The estimate and confidence interval in the graph are
derived using fixed- or random-effects meta-analysis, as specified by option reffect.