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metabias1.2.4 (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] } [ifexp ] [inrange ] [, by(by_var){var |ci}graph({begg |egger }) gweightlevel(#)graph_options ]where { a | b |...} means choose one and only one of {a, b, ...}.

Description -----------

metabias6is the Stata 6 version of metabias originally published in the Stata Technical Bulletin as package sbe19 with updates through to sbe19.5.

metabias6performs 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.

metabias6carries 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, tometabias6as 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

thetaversusse_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., attheta +/- z * se_theta, wherezis the standard Normal variate for the confidence level specified by optionlevel(). 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.

metabias6will perform stratified versions of both the Begg and Mazumdar test and the Egger regression asymmetry test when optionby(by_var)is specified. Variableby_varindicates 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 byby_var.

varindicates thatvar_thetawas supplied on the command line instead ofse_theta. Optioncishould not be specified when optionvaris specified.

ciindicates thatexp(theta)and its confidence interval,(ll, ul), were supplied on the command line instead ofthetaandse_theta. Optionvarshould not be specified when optionciis 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.

gweightrequests 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_optionsare those allowed withgraph, twoway. Forgraph(begg), the default graph_options includeconnect(lll.),symbol(iiio), andpen(3552)for displaying the meta-analytic effect, the pseudo confidence interval limits (two lines), and the data points, respectively. Forgraph(egger), the default graph_options includeconnect(.ll),symbol(oid), andpen(233)for displaying the data points, regression line, and the confidence interval about the intercept, respectively. Settingt2title(.)blanks out the defaultt2titlein either graph.

Required input variables ------------------------

thetathe effect estimatese_thetathe corresponding standard erroror

thetathe effect estimatevar_thetathe corresponding varianceor

exp(theta)the risk (or odds) ratiollthe lower limit of the risk ratio's confidence intervalulthe upper limit of the risk ratio's confidence interval [cl] optional (see below)

Optional input variable -----------------------

clcontains the confidence level of the confidence interval defined byllandul. Ifclis not provided, the procedure assumes that each confidence interval is at the 95% confidence level.clallows the user to provide the confidence level, by study, when the confidence interval is not at the default level.clcan 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

metancan be used to facilitate conversion to effect format.metanautomatically addsexp(theta)andse_thetavariables to the dataset, calling them_ESand_seES. You must manually generatethetaas the natural log of_ES(for example,gen _lnES = ln(_ES)) then input the effect-format variables,_lnESand_seES, usingmetabias6's default input method.

Saved values ------------

The following items are saved in the global

S_# macros and are returned inr().

S_1 r(k)number of studiesS_2 r(score)Begg's scoreS_3 r(score_sd)s.d. of Begg's scoreS_4 r(Begg_p)Begg's p valueS_5 r(Begg_pcc)Begg's p, continuity correctedS_6 r(Egger_bc)Egger's bias coefficientS_7 r(Egger_p)Egger's p valueS_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 ----

metabias6calls programktau2, a modification of thektauprogram supplied with Stata.ktau2is included in the distribution files for this version ofmetabias6.

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)