metabias 1.2.4 (STB's 41, 44, 57, 58, 61: sbe19-sbe19.5)
Tests for publication bias in meta-analysis -------------------------------------------
metabias6 { theta { se_theta | var_theta } | exp(theta) ll ul [cl] } [ if exp ] [ in range ] [, by(by_var) { var | ci } graph({ begg | egger }) gweight level(#) graph_options ]
where { a | b |...} means choose one and only one of {a, b, ...}.
Description -----------
metabias6 is the Stata 6 version of metabias originally published in the Stata Technical Bulletin as package sbe19 with updates through to sbe19.5.
metabias6 performs the Begg and Mazumdar adjusted rank correlation test for publication bias and performs the Egger et al. regression asymmetry test for publication bias. As options, it provides a funnel graph of the data or the regression asymmetry plot.
The Begg adjusted rank correlation test is a direct statistical analogue of the visual funnel graph. Note that both the test and the funnel graph have low power for detecting publication bias. The Begg and Mazumdar procedure tests for publication bias by determining if there is a significant correlation between the effect estimates and their variances. metabias6 carries out this test by, first, standardizing the effect estimates to stabilize the variances and, second, performing an adjusted rank correlation test based on Kendall's tau.
The Egger et al. regression asymmetry test and the regression asymmetry plot tend to suggest the presence of publication bias more frequently than the Begg approach. The Egger test detects funnel plot asymmetry by determining whether the intercept deviates significantly from zero in a regression of the standardized effect estimates against their precision.
Egger et al. claim that the test predicts the discordance (if any) of meta-analytic results and single large trials, but no formal analysis of coverage (i.e., nominal significance level) or power has been performed.
The user provides the effect estimate, theta, to metabias6 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 (i.e., its standard error, se_theta, or its variance, var_theta). Alternatively, the user may provide the exponentiated form, exp(theta), (i.e., a risk ratio or odds ratio) and its confidence interval, (ll, ul).
The funnel graph plots theta versus se_theta. Guide lines to assist in visualizing the funnel are plotted at the variance-weighted (fixed effects) meta-analytic effect estimate and at pseudo confidence interval limits about that effect estimate (i.e., at theta +/- z * se_theta, where z is the standard Normal variate for the confidence level specified by option level(). Asymmetry on the right of the graph (where studies with high standard error are plotted) may give evidence of publication bias.
The regression asymmetry graph plots the standardized effect estimates, theta / se_theta, versus precision, 1 / se_theta, along with the regression line and the confidence interval about the intercept. Failure of this confidence interval to include zero indicates asymmetry in the funnel plot and may give evidence of publication bias. Guide lines at x = 0 and y = 0 are plotted to assist in visually determining if zero is in the confidence interval.
metabias6 will perform stratified versions of both the Begg and Mazumdar test and the Egger regression asymmetry test when option by(by_var) is specified. Variable by_var indicates the categorical variable that defines the strata. The procedure reports results for each strata and for the stratified tests. The graphs, if selected, plot only the combined unstratified data.
Options -------
by(by_var) requests that the stratified tests be carried out with strata defined by by_var.
var indicates that var_theta was supplied on the command line instead of se_theta. 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 se_theta. Option var should not be specified when option ci is specified.
graph(begg) requests the Begg funnel graph showing the data, the fixed-effects (variance-weighted) meta-analytic effect, and the pseudo confidence interval limits about the meta-analytic effect.
graph(egger) requests the Egger regression asymmetry plot showing the standardized effect estimates versus precision, the regression line, and the confidence interval about the intercept.
gweight requests that the graphic symbols representing the data in the plot be sized proportional to the inverse variance.
level() sets the confidence level % for the pseudo confidence intervals; the default is 95%.
graph_options are those allowed with graph, twoway. For graph(begg), the default graph_options include connect(lll.), symbol(iiio), and pen(3552) for displaying the meta-analytic effect, the pseudo confidence interval limits (two lines), and the data points, respectively. For graph(egger), the default graph_options include connect(.ll), symbol(oid), and pen(233) for displaying the data points, regression line, and the confidence interval about the intercept, respectively. Setting t2title(.) blanks out the default t2title in either graph.
Required input variables ------------------------
theta the effect estimate se_theta the corresponding standard error
or
theta the effect estimate var_theta the corresponding variance
or
exp(theta) the risk (or odds) ratio ll the lower limit of the risk ratio's confidence interval ul the upper limit of the risk ratio's confidence interval [cl] optional (see below)
Optional input variable -----------------------
cl contains the confidence level of the confidence interval defined by ll and ul. If cl is not provided, the procedure assumes that each confidence interval is at the 95% confidence level. cl allows the user to provide the confidence level, by study, when the confidence interval is not at the default level. cl can be specified with or without a decimal point. For example, 90 and .90 are equivalent and may be mixed (i.e., 90, .95, 80, .90 etc.).
Note ----
If your data are in raw count format, program metan can be used to facilitate conversion to effect format. metan automatically adds exp(theta) and se_theta variables to the dataset, calling them _ES and _seES. You must manually generate theta as the natural log of _ES (for example, gen _lnES = ln(_ES)) then input the effect-format variables, _lnES and _seES, using metabias6's default input method.
Saved values ------------
The following items are saved in the global S_# macros and are returned in r().
S_1 r(k) number of studies S_2 r(score) Begg's score S_3 r(score_sd) s.d. of Begg's score S_4 r(Begg_p) Begg's p value S_5 r(Begg_pcc) Begg's p, continuity corrected S_6 r(Egger_bc) Egger's bias coefficient S_7 r(Egger_p) Egger's p value S_8 r(effect) overall effect (log scale)
Examples --------
. metabias6 logrr selogrr, graph(begg) . metabias6 logrr varlogrr if site==3, var graph(egger) . metabias6 rr ll ul, ci by(site) . metabias6 logor selogor if region==4, graph(egger) level(90)
Note ----
metabias6 calls program ktau2, a modification of the ktau program supplied with Stata. ktau2 is included in the distribution files for this version of metabias6.
References ----------
Begg, C. B., Mazumdar, M., 1994. Operating characteristics of a rank correlation test for publication bias. Biometrics 50: 1088-1101.
Egger, M., Smith, G. D., Schneider, M., Minder, C., 1997. Bias in meta-analysis detected by a simple, graphical test. British Medical Journal 315: 629-634.
Author ------
Thomas J. Steichen, RJRT, steicht@rjrt.com
Also see --------
STB: STB-41 sbe19; STB-44 sbe19.1 Manual: [R] spearman On-line: help for meta, metan, and ktau (if installed)