Fixed and random effects meta-analysis

hat calculates the leverages (the diagonal elements of the projection hat

matrix).

Saved results
When the permute() option is not specified, metareg saves the following

in e():
Scalars

e(N) number of observations

e(df_m) model degrees of freedom

e(df_Q) degrees of freedom for test of Q=0

e(df_r) residual degrees of freedom (if t tests used)

e(remll) REML log likelihood

e(chi2_c) chi^2 for comparison test

e(F) model F statistic

e(tau2) estimate of tau2

e(Q) Cochran's Q

e(I2) I-squared

e(q_KH) Knapp-Hartung variance modification factor

e(remll_c) REML log likelihood, comparison model

e(tau2_0) tau2, constant-only model

e(chi2) model chi^2

Macros

e(cmd) metareg

e(predict) program used to implement predict

e(wsse) name of wsse() variable

e(depvar) name of dependent variable

e(method) REML, Method of moments, or Empirical Bayes

e(properties) b V
Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of estimators
Functions

e(sample) marks estimation sample

Examples
. metareg logrr latitude, wsse(selogrr) eform
. metareg logrr latitude, wsse(selogrr) graph
. metareg smd abstract duration itt, wsse(sesmd) permute(10000)
. metareg smd abstract duration itt, wsse(sesmd) permute(1000,

univariable)

. xi: metareg logor i.group, wsse(selogor) permute(1000, joint(i.group))

Note
metareg is programmed as a Stata estimation command and so supports many

of the commands listed under estcom and postest (except when the

permute() option is used). One deliberate exception is lrtest, which is

not appropriate after metareg (because the REML log likelihood cannot be

used to compare models with different fixed effects, while the method of

moments is not based on a likelihood). For this reason, when the REML

method is used, the iteration log showing the log likelihood is

suppressed by default; specify the log option if you wish to see it.

References
DerSimonian, R., and N. Laird. 1986. Meta analysis in clinical trials.

Controlled Clinical Trials 7: 177-188.

Higgins, J. P. T, and S. G. Thompson. 2004. Controlling the risk of

spurious findings from meta-regression. Statistics in Medicine 23:

1663-1682.
Knapp, G., and J. Hartung. 2003. Improved tests for a random effects

meta-regression with a single covariate. Statistics in Medicine 22:

2693-2710.
Morris, C. N. 1983. Parametric empirical Bayes inference: Theory and

applications. Journal of the American Statistical Association 78:

47-55.
Sharp, S. 1998. sbe23: Meta-analysis regression. Stata Technical Bulletin

42: 16-22. Reprinted in Stata Technical Bulletin Reprints, vol. 7,

pp. 148-155. College Station, TX: Stata Press.

Author
Roger M. Harbord

Department of Social Medicine

University of Bristol, UK

[e-mail]

Acknowledgments
This is a substantial revision of the original version of metareg written

by Stephen Sharp (1998), who gave his permission to release this version

under the same name and to incorporate his code. Julian Higgins gave

advice on the permutation test. Aijing Shang tested early versions and

made helpful suggestions. Portions of the new code borrow ideas from

official Stata commands such as nbreg, and I thank StataCorp for making

such code visible to the user.
A dialog box, written by Thomas J. Steichen, is available for the

original version of the metareg command.

Also see
Article: Stata Journal, volume 8, number 4: sbe23_1,

Stata Technical Bulletin 42: sbe23

Manual: [R] meta,

[R] permute

Online: [R] vwls, [R] permute, meta (if installed), metan (if

installed), meta_dialog (if installed)

metafunnel
Funnel plots for meta-analysis
metafunnel { theta { se | var } | exp(theta) { ll ul [cl] }} [if exp]

[in range] [, by(by_var) [var | ci] noline forcenull reverse

eform egger graph_options ]

Description
metafunnel plots funnel plots. These graphical displays are used to

examine whether the results of a meta-analysis may have been affected by

publication or other types of bias.
The syntax is based on the same framework as for the meta, metabias,

metacum, and metatrim commands. The user provides the effect estimate

theta and either its standard error, se, or its variance, var.

Alternatively, the user may provide exp(theta), its confidence interval

(ll, ul), and, optionally, the confidence level. For more details, see

help meta.

Options
by(by_var) displays subgroups according to the value of by_var. The

legend displays the value labels for the levels of by_var if these

are present; otherwise, it displays the value of each level of

by_var.
var and ci indicate that instead of the standard error of theta, the user

supplied the variance of theta or confidence interval for exp(theta).

For more details, see help meta.

noline specifies that pseudo 95% confidence interval lines not be

included in the plot. The default is to include them.

forcenull forces the vertical line at the center of the funnel to be

plotted at the null treatment effect of zero (1 when the treatment

effect is exponentiated). The default is for the line to be plotted

at the value of the fixed-effect summary estimate.

reverse inverts the funnel plot so that larger studies are displayed at

the bottom of the plot with smaller studies at the top. This may

also be achieved by specifying noreverse as part of the

yscale(axis_description) graphics option.

eform exponentiates the treatment effect theta and displays the

horizontal axis (treatment effect) on a log scale. This is useful for

displaying ratio measures, such as odds ratios and risk ratios.
egger adds the fitted line corresponding to the regression test for

funnel-plot asymmetry proposed by Egger et al. (1997) and implemented

in metabias. This option may not be combined with the by() option.
graph_options can be most of the options allowed by the graph twoway

scatter command, such as marker_label_options. If option egger if

specified, the look of the fitted line can be changed using any of

the connect_options that start with cl*.

Remarks
Funnel plots are simple graphical displays of a measure of study size on

the vertical axis against intervention or treatment effect on the

horizontal axis. The name "funnel plot" is based on the fact that the

precision in the estimation of the underlying intervention or treatment

effect will increase as the size of component studies increases. Results

from small studies will therefore scatter more widely, with the spread

narrowing among larger studies. In the absence of bias, the plot will

resemble a symmetrical inverted funnel.

If there is bias, for example, because smaller studies showing no

statistically significant effects remain unpublished, then such

publication bias will lead to an asymmetrical appearance of the funnel

plot. It should be noted that although funnel plots have traditionally

been used to examine evidence for publication bias, funnel-plot asymmetry

may reflect other types of bias or even result from the true intervention

or treatment effect differing between small and large studies. They

should, thus, be seen as displaying the evidence for "small study

effects" in general rather than publication bias in particular. These

issues are discussed by Egger et al. (1997) and Sterne, Egger, and Davey

Smith (2001).
metafunnel uses the same syntax as other meta-analysis commands, such as

meta, metabias, metainf, and metatrim. The user provides an estimate of

the treatment or intervention effect, theta, together with its associated

standard error se (the default) or variance var, in which case the var

option should be specified. Alternatively, the user provides a risk ratio

or odds ratio (exp(theta), its confidence interval (ll, ul), and,

optionally, the confidence level.
The funnel plots are displayed in line with meta-analytic convention and

the recommendations of Sterne and Egger (2001). The effect of the

treatment or intervention in each study:
The horizontal axis is plotted against the study size, as measured by

the standard error of the treatment or intervention effect.

The vertical axis is reversed so that larger studies are displayed

towards the top of the graph (this behavior may be changed using

the reverse option).
Users who wish to plot the treatment effect on the vertical axis should

use the graph(begg) option of the metabias command. The funnel command,

which is part of the metan package, also provides an alternative way to

draw funnel plots.

The plots include pseudo-95% confidence interval lines, which are drawn

around the summary fixed-effect estimate of the intervention or treatment

effect. The lines may be omitted using the nolines option. The user may

also specify that the pseudo confidence limits are centered around a zero

intervention effect using the forcenull option.
When the eform option is used, the label of the horizontal axis

(treatment effect, theta) is changed accordingly, unless there is a

variable label for theta or the xtitle(axis_title) graphics option is

used.
By default, the subtitle "Funnel plot with pseudo 95% confidence limits"

is displayed (or simply "Funnel plot" if the nolines option is

specified). This may be changed using the graphics option

subtitle(tinfo).

Examples
. metafunnel meandiff semeandiff
. metafunnel logor selogor, eform xtitle("Odds ratio (log scale)")
. metafunnel sttd stderr, by(dose) subtitle(Funnel plot with subgroups)

forcenull

. metafunnel logor varlogor, var reverse nolines xtitle(log odds ratio)


Acknowledgments
metafunnel was written by Jonathan Sterne and Roger Harbord, University

of Bristol. Portions of the code were originally written by Tom

Steichen, who also gave helpful comments on an early version of the

command and provided the dialog. Nick Cox provided extensive programming

advice.

References
Egger, M., G. Davey Smith, M. Schneider, and C. Minder. 1997. Bias in

meta-analysis detected by a simple, graphical test. British Medical

Journal 315: 629-634.
Sterne, J. A. C., M. Egger, and G. Davey Smith. 2001. Investigating and

dealing with publication and other biases in meta-analysis. British

Medical Journal 323: 101-105.
Sterne, J. A. C. and M. Egger. 2001. Funnel plots for detecting bias in

meta-analysis: guidelines on choice of axis. Journal of Clinical

Epidemiology 54: 1046-1055.

Also see
Online: help for meta, metabias, metainf, metatrim, metan, funnel (if

installed)

confunnel
Realce en el gráfico en embudo de los contornos de significación estadística
Syntax
confunnel varname1 varname2 [if] [in] [, options]

options description

-------------------------------------------------------------------------

contours(numlist) specify significance levels of the

contours to be plotted; default is

1%, 5%, and 10% significance levels

contcolor(colorstyle) specify color of the contour lines

if shadedcontours is not specified

extraplot(plots) specify additional plots to overlay

the funnel plot

functionlowopts(options) pass options to the twoway function

commands used to draw the contours

functionuppopts(options) pass options to the twoway function

commands used to draw the contours

legendlabels(labels) specify labels in the legend for

added items

legendopts(options) specify options that affect the plot

legend

metric(se|invse|var|invvar) the scale of the y axis; either se,

invse, var, or invvar

onesided(lower|upper) lower- or upper-tailed, one-sided

significance contours

scatteropts(options) specifies any of the options

documented in scatter

shadedcontours specify shaded, instead of black,

contour lines

[no]shadedregions specify or suppress shaded regions

between the contours

solidcontours specify solid, instead of dashed,

contour lines

studylab(string) the legend label for the scatter

points

twowayopts(twoway_options) pass options to the twoway plot

twoway_options pass options to the twoway plot

-------------------------------------------------------------------------

Description
confunnel plots contour-enhanced funnel plots for assessing small-study

reporting bias in meta-analysis.

Vontours illustrating the statistical significance of the study-effect

estimates are plotted from either a one- or two-tailed test.

confunnel requires two input variables; varname1 a variable of effect

estimates such as log odds ratios and varname2 a variable of the standard

errors of the effect estimates.
The y axis can be specified using different scales, namely, standard

error, inverse standard error, variance, and inverse variance.

Options_contours'>Options
contours(numlist) specifies the significance levels of the contours to be

plotted; the default is contours(1 5 10). There are only distinct

line patterns for 8 significance levels. See numlist.
contcolor(colorstyle) specifies the color of the contour lines if

noshadedcontours is specified. See [G] colorstyle.

extraplot(plots) specifies one or multiple additional plots to be

overlaid on the funnel plot.

functionlowopts(options) and functionuppopts(options) pass options to the

twoway function commands used to draw the significance contours; for

example, the line widths can be changed. See [G] graph twoway

function.

legendlabels(labels) specifies labels in the legend for extra elements

added to the funnel plot. The option will take the form:

legendlabels(`"8 "new label""').
legendopts(options) passes options to the plot legend. See [G]

legend_option.

metric(se|invse|var|invvar) specifies the metric of the y axis of the

plot. se, invse, var, and invvar stand for standard error, inverse

standard error, variance, and inverse variance, respectively; the

default is se.

onesided(lower|upper) can be lower or upper, for lower-tailed or

upper-tailed levels of statistical significance, respectively. If

unspecified, two-sided significance levels are used to plot the

contours.

scatteropts(options) specifies any of the options documented in [G] graph

twoway scatter.

shadedcontours specifies shaded contour lines; specify with the

noshadedregions option.

[no]shadedregions specifies or suppresses shaded regions between the

contours. This option provides plots that are more similar to those

in the original paper by Peters et al. (2008) and the Cochrane

Handbook. A plot with shadedregions is now the default.

solidcontours specifies solid contour lines; specify with the

shadedcontours and noshadedregions option.

studylab(string) specifies the label for the scatter points in the

legend. If not specified the default is "Studies".

twowayopts(options) specifies options passed to the twoway plotting

function; see [G] twoway_options.

twoway_options see [G] twoway_options. As of confunnel version 1.0.5

twoway options can be specified at the end of the options and do not

have to be within twowayopts.

Remarks
The confunnel command is based on an idea by Peters et al. (2008) to

superimpose contours of statistical significance on a funnel plot in a

meta-analysis. The command was explained in Palmer et al. (2008).

Superimposing contours on funnel plots has also been suggested by

Spiegelhalter (2005) in a slightly different context.
confunnel can be used in conjunction with the results of the metan,

metatrim, and metabias commands. See meta in Stata version 10 for

information about user-written commands for meta-analysis.

Examples
The following examples use the example dataset accompanying metan.
. confunnel logOR selogOR

(click to run)

. confunnel logOR selogOR, noshadedregions

(click to run)

. confunnel logOR selogOR, solidcontours shadedcontours noshadedregions

(click to run)

. confunnel logOR selogOR, metric(invse)

(click to run)

. confunnel logOR selogOR, onesided(upper) noshadedregions

(click to run)

References
Palmer, T. M., J. L. Peters, A. J. Sutton, and S. G. Moreno. 2008.

Contour enhanced funnel plots for meta-analysis. Stata Journal 8:

242-254.
Peters, J. L., A. J. Sutton, D. R. Jones, K. R. Abrams, and L. Rushton.

2008. Contour-enhanced meta-analysis funnel plots help distinguish

publication bias from other causes of asymmetry. Journal of Clinical

Epidemiology. 61: 991-996.

Spiegelhalter, D. J. 2005. Funnel plots for comparing institutional

performance. Statistics in Medicine 24: 1185-1202.

Sterne, J. A. C., and M. Egger. 2001. Funnel plots for detecting bias in

meta-analysis: Guidelines on choice of axis. Journal of Clinical

Epidemiology 54: 1046-1055.
Sterne, J. A. C., and R. M. Harbord. 2004. Funnel plots in meta-analysis.

Stata Journal 4: 127-141.

Sterne, J. A. C., M. Egger, and D. Moher. 2008. Chapter 10: Addressing

reporting biases; Cochrane Handbook for Systematic Reviews of

Interventions Version 5.0.1.

Author
Tom Palmer, MRC Centre for Causal Analyses in Translational Epidemiology,

Department of Social Medicine, University of Bristol, UK.

[e-mail].

Jaime Peters wrote the first version of this command.

Thanks to Santiago G. Moreno for testing the command.
Please report any errors you may find.

Also see
Article: Stata Journal, volume 9, number 2: gr0033_1

Stata Journal, volume 8, number 2: gr0033

Online: metabias, metafunnel, metan (if installed)
metabias
Syntax
metabias varlist [if] [in], egger harbord peters begg [graph nofit or

rr level(#) graph_options]

As in the metan command, varlist should contain either four or two

variables. When four variables are given, these are assumed to be cell

counts for the 2 x 2 table in this order: cases and noncases for the

experimental group, then cases and noncases for the control group (d1 h1

d0 h0). When two variables are specified, these are assumed to be the

effect estimate and its standard error (theta se_theta). It is

recommended that ratio-based effect estimates are log transformed as in

metan.
by is allowed with metabias; see [D] by.

Description
metabias performs updated regression tests for funnel plot asymmetry in

meta-analysis. The Harbord test regresses Z/sqrt(V) against sqrt(V),

where Z is the efficient score and V is Fisher's information (the

variance of Z under the null hypothesis). The Peters test regresses the

intervention effect estimate on 1/n with weights dh/n, where n is the

total sample size, d is the number experiencing the event, and h is the

number not experiencing the event. These can be calculated for the log

odds-ratio or log risk-ratio, from 2 x 2 tables of binary outcomes.

The Egger test is also implemented and performs a linear regression of

the intervention effect estimates on their standard errors, weighting by

1/(variance of the intervention effect estimate). This test is

recommended for intervention effects measured as mean differences but can

suffer from false-positive test results when analyzing odds ratios

because of the mathematical association between the log odds-ratio and

its standard error. For completeness, the Begg test is also implemented,

although this is widely accepted to be redundant because it suffers the

same statistical problems as Egger's test but has lower power.

Options
egger, harbord, peters, and begg specify that the original Egger test,

Harbord's modified test, Peters' test, or the rank correlation test

proposed by Begg and Mazumdar (1994) be reported, respectively.

There is no default; one test must be chosen.

graph displays a Galbraith plot (the standard normal deviate of

intervention effect estimate against its precision) for the original

Egger test or a modified Galbraith plot of Z/sqrt(V) versus sqrt(V)

for Harbord's modified test. There is no corresponding plot for the

Peters or Begg tests.
nofit suppresses the fitted regression line and confidence interval

around the intercept in the Galbraith plot.

or (the default for binary data) uses odds ratios as the effect estimate

of interest.

rr specifies that risk ratios rather than odds ratios be used. This

option is not available for the Peters test.

level(#) specifies the confidence level, as a percentage, for confidence

intervals. The default is level(95) or as set by set level.

graph_options are any of the options documented in [G] graph twoway

scatter. In particular, the options for specifying marker labels are

useful.

Examples
. metabias d1 h1 d0 h0, or harbord

. metabias tdeath tnodeath cdeath cnodeath, or harbord graph

mlabel(trial)

. metabias eventint noeventint eventcon noeventcon, or peters

. metabias theta se_theta, egger

Authors
Roger Harbord, Department of Social Medicine, University of Bristol, UK

Ross Harris, Centre for Infections, Health Protection Agency, London, UK

Jonathan Sterne, Department of Social Medicine, University of Bristol, UK
Reference
Begg, C. B., and M. Mazumdar. 1994. Operating characteristics of a rank

correlation test for publication bias. Biometrics 50: 1088-1101.

History and note on dialog box
This version of metabias revises and extends the previous package by

Thomas Steichen, first released as sbe19 in STB 41 and updated through to

sbe19.5. We are grateful for Tom's permission to release this version

under the same name.

The dialog box added to sbe19.5 (and to the distribution dated 20040409

on SSC) is not compatible with this revised and extended version of the

package, which does not currently include a dialog box.

Also see
Article: Stata Journal, volume 9, number 2: sbe19_6

Stata Journal, volume 3, number 4: sbe19_5

Stata Technical Bulletin 61: sbe19.4

Stata Technical Bulletin 58: sbe19.3

Stata Technical Bulletin 57: sbe19.2

Stata Technical Bulletin 44: sbe19.1

Stata Technical Bulletin 41: sbe19
Online: metan (if installed), metafunnel (if installed), confunnel (if

installed)