help for metan, labbe

Fixed and random effects meta-analysis

metan
varlist
[if exp]
[in range]
[weight]
[,
measure_and_model_options
options_for_continuous_data
output_options
forest_plot_options
]

where measure_and_model_options may be

or
rr
rd
fixed
random
fixedi
peto
cornfield
chi2
breslow
nointeger
cc(#)
wgt(weightvar)
second(model or estimates and description)
first(estimates and description)

and where options_for_continuous_data may be

cohen
hedges
glass
nostandard
fixed
random

and where output_options may be

by(byvar)
nosubgroup
sgweight
log
eform
efficacy
ilevel(#)
olevel(#)
sortby(varlist)
label(namevar yearvar)
nokeep
notable
nograph
nosecsub

and where forest_plot_options may be

legend(string)
xlabel(#,...)
xtick(#,...)
boxsca(#)
nobox
nooverall
nowt
nostats
group1(string)
group2(string)
effect(string)
force

...with further forest_plot_options in the version 9 update

lcols(varlist)
rcols(varlist)
astext(#)
double
nohet
summaryonly
rfdist
rflevel(#)
null(#)
nulloff
favours(string # string)
firststats(string)
secondstats(string)
boxopt()
diamopt()
pointopt()
ciopt()
olineopt()
classic
nowarning
graph_options

labbe
varlist
[if exp]
[in range]
[weight]
[,
nowt
percent
or(#)
rr(#)
rd(#)
null
logit
wgt(weightvar)
symbol(symbolstyle)
nolegend
id(idvar)
textsize(#)
clockvar(clockvar)
gap(#)
graph_options

Description

These routines provide facilities to conduct meta-analyses of data from
more than one study and to graph the results. Either binary (event) or
continuous data from two groups may be combined using the metan
command. Additionally, intervention effect estimates with corresponding
standard errors or confidence intervals may be meta-analysed. Several
meta-analytic methods are available, and the results may be displayed
graphically in a Forest plot. A test of whether
the summary effect measure is equal to the null is given,
as well as a test for heterogeneity, i.e., whether the true effect in all
studies is the same. Heterogeneity is also quantified using the I-squared
measure (Higgins et al 2003).

metan (the main meta-analysis routine) requires either two, three, four
or six variables to be declared. When four variables are specified
these correspond to the number of events and non-events in the experimental group
followed by those of the control group, and
analysis of binary data is performed on the 2x2 table.
With six variables, the data are assumed
continuous and to be the sample size, mean and standard deviation of
the experimental group followed by those of the control group.
If three variables are specified these are assumed to be the effect estimate and
its lower and upper confidence interval, and it is suggested that these are
log transformed for odds ratios or risk ratios and the eform option used.
If two variables are specified these are assumed to be the effect estimate and standard
error; again, it is recommended that odds ratios or risk ratios are log transformed.

labbe draws a L'Abbe plot for event data (proportion of successes in the
two groups). This is an alternative to the graph produced by metan8.

Note that the metan command now requires
Stata version 9 and has been updated
with several new options. Changes are mainly to graphics options which
are collected in the section Further options in the v9 update for metan: Forest plot,
or otherwise marked v9 update. The previous version is still available under
the name -metan7-

Remarks on funnel (discontinued)

The metafunnel command has more options for
funnel plots and version 8 graphics; as such funnel has been removed.
See metafunnel (if installed)

Options for metan

Specifying the measure and model

These options apply to binary data.

rr pools risk ratios (the default).

or pools odds ratios.

rd pools risk differences.

fixed specifies a fixed effect model using the method of
Mantel and Haenszel (the default).

fixedi specifies a fixed effect model using the inverse variance method.

peto specifies that Peto's method is used to pool odds ratios.

random specifies a random effects model using the method of
DerSimonian & Laird, with the estimate of heterogeneity being taken from the
from the Mantel-Haenszel model.

randomi specifies a random effects model using the method of
DerSimonian & Laird, with the estimate of heterogeneity being taken from the
inverse-variance fixed-effect model.

cornfield computes confidence intervals for odds ratios by method of
Cornfield, rather than the (default) Woolf method.

chi2 displays chi-squared statistic (instead of z) for the test
of significance of the pooled effect size. This is available only for
odds ratios pooled using Peto or Mantel-Haenszel methods.

breslow produces Breslow-Day test for homogeneity of ORs.

cc(#) defines a fixed continuity correction to add in the case where
a study contains a zero cell. By default, metan8
adds 0.5 to each cell of a trial where a zero is encountered when
using Inverse-Variance, Der-Simonian & Laird or Mantel-Haenszel
weighting to enable finite variance estimators to be derived.
However, the cc() option allows the use of other constants
(including none). See also the nointeger option.

nointeger allows the cell counts to be non-integers. This may be useful
when a variable continuity correction is sought for studies containing
zero cells, but also may be used in other circumstances, such as where a
cluster-randomised trial is to be incorporated and the "effective sample
size" is less than the total number of observations.

wgt(weightvar) specifies alternative weighting
for any data type. The effect size is to be computed by assigning
a weight of weightvar to the studies. When RRs or ORs are declared,
their logarithms are weighted. You should only use this option if you are
satisfied that the weights are meaningful.

second(model or estimates and description) (v9 update)
A second analysis may be performed using another method, using fixed,
random or peto. Alternatively, the user may define their own
estimate and 95% CI based on calculations performed externally to metan,
along with a description of their method, in the format
es lci uci description. The results of this analysis are then displayed
in the table and forest plot. Note that if by is used then sub-estimates
from the second method are not displayed with user defined estimates, for
obvious reasons.

first(estimates and description) (v9 update)
Use of this command completely changes the way metan operates, as results
are no longer based on any standard methods. The user defines their own
estimate, 95% CI and description as in the above, and must supply their own
weightings using wgt(weightvar) to control display of box sizes. Note
that data must be supplied in the 2 or 3 variable syntax
(theta se_theta or es lci uci) and
by may not be used used for obvious reasons.

Continuous data

cohen pools standardised mean differences by the method of Cohen
(the default).

hedges pools standardised mean differences by the method of Hedges.

glass pools standardised mean differences by the method of Glass.

nostandard pools unstandardised mean differences.

fixed specifies a fixed effect model using the inverse variance method
(the default).

random specifies a random effects model using the DerSimonian & Laird
method.

nointeger denotes that the number of observations in each arm does not
need to be an integer. By default, the first and fourth variables specified
(containing N_intervention and N_control respectively) may occasionally be
non-integer (see entry for nointeger under binary data).

Output

by() specifies that the meta-analysis is to be stratified
according to the variable declared.

sgweight specifies that the display is to present the percentage
weights within each subgroup separately. By default metan presents
weights as a percentage of the overall total.

log reports the results on the log scale
(valid for OR and RR analyses from raw data counts only).

nosubgroup indicates that no within-group results are to be
presented. By default metan pools trials both within and across
all studies.

eform exponentiates all effect sizes and confidence intervals
(valid only when the input variables are log odds ratios or log
hazard ratios with standard error or confidence intervals).

efficacy expresses results as the vaccine efficacy (the proportion
of cases that would have been prevented in the placebo group that
would have been prevented had they received the vaccination).
Only available with odds ratios (OR) or risk ratios (RR).

ilevel(#) specifies the coverage (eg 90,95,99 percent) for the
individual trial confidence intervals. Default: $S_level.
ilevel() and olevel() need not be the same. See set level.

olevel(#) specifies the coverage (eg 90,95,99 percent) for the
overall (pooled) trial confidence intervals. Default: $S_level.
ilevel() and olevel() need not be the same. See set level.

sortby(varlist) sorts by variable(s) in varlist

label([namevar=namevar], [yearvar=yearvar])
labels the data by its name, year or both. Either or both option/s
may be left blank. For the table display the overall length of the
label is restricted to 20 characters. The option lcols() will
override this if invoked.

nokeep prevents the retention of study parameters in permanent
variables (see saved results below).

notable prevents display of table of results.

nograph prevents display of graph.

nosecsub (v9 update) prevents the display of sub-estimates
using the second method if second()
is used. Note that this is invoked automatically with user-defined
estimates.

Forest plot

effect() may be used when the effect size and its standard error
are declared. This allows the graph to name the summary statistic used.

nooverall revents display of overall effect size on graph
(automatically enforces the nowt option).

nowt prevents display of study weight on the graph.

nostats prevents display of study statistics on graph.

counts (v9 update) displays data counts (n/N) for each group when using
binary data, or the sample size, mean and SD for each group if mean
differences are used (the latter is a new feature).

group1(string), group2(string) may be
used with the counts option: the text should contain the
names of the two groups.

xlabel() (v9 update) defines x-axis labels. This has been modified
so that any number of points may defined. Also, there are no
longer any checks made as to whether these points are sensible, so the
user may define anything if the force option is used. Points must
be comma separated.

xtick() adds tick marks to the x-axis. Points must
be comma separated.

force forces the x-axis scale to be in the range specified
by xlabel().

boxsca() (v9 update) controls box scaling.
This has been modified slightly so that the default is 100 (as in a
percentage) and may be increased or decreased as such (e.g., 80 or 120 for
20% smaller or larger respectively)

nobox prevents a "weighted box" being drawn for each study
and markers for point estimates only are shown.

texts() (v9 update) specifies font size for text display on graph.
This has been modified slightly so that the default is 100 (as in a
percentage) and may be increased or decreased as such (e.g., 80 or 120 for
20% smaller or larger respectively)

Further options for the forest plot in the v9 update

lcols(varlist), rcols(varlist)
define columns of additional data to
the left or right of the graph. The first two columns on the right are
automatically set to effect size and weight, unless suppressed using
the options nostats and nowt. If counts is used this
will be set as the third column. textsize() can be used to fine-tune
the size of the text in order to acheive a satisfactory appearance.
The columns are labelled with the variable label, or the variable name
if this is not defined. The first variable specified in lcols() is assumed to be
the study identifier and this is used in the table output.

astext(#)
specifies the percentage of the graph to be taken up by text.
The default is 50 and the percentage must be in the range 10-90.

double
allows variables specified in lcols and rcols to run over two
lines in the plot. This may be of use if long strings are to be used.

nohet
prevents display of heterogeneity statistics in the graph.

summaryonly
shows only summary estimates in the graph (may be of use for multiple
subgroup analyses)

rfdist
displays the confidence interval of the approximate predictive
distribution of a future trial, based on the extent of heterogeneity.
This incorporates uncertainty in the location and spread of the random
effects distribution using the formula t(df) x sqrt(se2 + tau2)
where t is the t-distribution with k-2 degrees of freedom, se2 is the
squared standard error and tau2 the heterogeneity statistic.
The CI is then displayed with lines extending from the diamond. Note that
with <3 studies the distribution is inestimable and effectively infinite, thus
displayed with dotted lines, and where heterogeneity is zero there is still
a slight extension as the t-statistic is always greater than the corresponding
normal deviate. For further information see Higgins JPT, Thompson SG (2006)

rflevel(#) specifies the coverage (eg 90,95,99 percent) for the
confidence interval of the predictive distribution. Default: $S_level.
See set level.

null(#)
displays the null line at a user-defined value rather than 0 or 1.

nulloff
removes the null hypothesis line from the graph

favours(string # string)
applies a label saying something about the treatment effect to either
side of the graph (strings are separated by the # symbol). This replaces
the feature available in b1title in the previous version of metan.

firststats(string), secondstats(string)
labels overall user-defined estimates when these have been specified.
Labels are displayed in the position usually given to the heterogeneity
statistics.

boxopt(), diamopt(), pointopt(), ciopt(), olineopt()
specify options for the graph routines within the program, allowing the
user to alter the appearance of the graph. Any options associated with a
particular graph command may be used, except some that would cause incorrect
graph appearance. For example, diamonds are plotted using the twoway pcspike
command, so options for line styles are available (see line options);
however, altering the x-y
orientation with the option horizontal or vertical is not
allowed. So, diamopt(lcolor(green) lwidth(thick)) feeds into a command
such as pcspike(y1 x1 y2 x2, lcolor(green) lwidth(thick))

boxopt() controls the boxes and uses options for a weighted marker
(e.g., shape, colour; but not size). See marker options

diamopt() controls the diamonds and uses options for pcspike (not horizontal/vertical).
See line options

pointopt() controls the point estimate using marker options.
See marker options and marker label options

ciopt() controls the confidence intervals for studies using options
for pcspike (not horizontal/vertical). See line options

olineopt() controls the overall effect line with options for an additional
line (not position). See line options

classic specifies that solid black boxes without point estimate markers are used as
in the previous version of metan.

nowarning switches off the default display of a note warning that studies are
weighted from random effects anaylses.

graph_options
specifies overall graph options that would appear at the end of a twoway
graph command. This allows the addition of titles, subtitles, captions etc.,
control of margins, plot regions, graph size, aspect ratio and the use of schemes.
As titles may be added in this way previous options b2title etc. are no
longer necessary. See graph options

Options for labbe

nowt declares that the plotted data points are to be the same size.

percent displays the event rates as percentages rather than proportions.

null draws a line corresponding to a null effect (ie p1=p2).

or(#) draws a line corresponding to a fixed odds ratio of
#.

rd(#) draws a line corresponding to a fixed risk difference of
#.

rr(#) draws a line corresponding to a fixed risk ratio
of #. See also the rrn() option.

rrn(#) draws a line corresponding to a fixed risk ratio
(for the non-event) of #.
The rr() and rrn() options may require explanation.
Whereas the OR and RD are invariant to the definition of which of
the binary outcomes is the "event" and which is the "non-event",
the RR is not. That is, while the command metan a b c d , or
gives the same result as metan b a d c , or (with direction
changed), an RR analysis does not. The L'Abbe plot allows the display
of either or both to be superimposed risk difference.

logit is for use with the or() option; it displays the
probabilities on the logit scale ie log(p/1-p). On the logit scale the
odds ratio is a linear effect, and so this makes it easier to assess the
"fit" of the line.

wgt(weightvar) specifies alternative weighting by the specified variable
(default is sample size).

symbol(symbolstyle) allows the symbol to be changed (see help symbolstyle) the
default being hollow circles (or points if weights are not used).

nolegend suppresses a legend being displayed (the default if more than one
line corresponding to effect measures are specified).

id(idvar) displays marker labels with the specified ID variable idvar.
clockvar() and gap() may be used to fine-tune the display, which may become
unreadable if studies are clustered together in the graph.

textsize(#) increases or decreases the text size of the id label by specifying
# to be more or less than unity. The default is usually satisfactory, but may need to be adjusted.

clockvar(clockvar) specifies the position of idvar around the
study point, as if it were a clock face (values must be integers- see clockposstyle).
This may be used to organise labels where studies are clustered together. By default, labels are positioned
to the left (9 o'clock) if above the null and to the right (3 o'clock) if below. Missing values
in clockvar will be assigned the default position, so this need not be specified for all observations.

gap(#) increases or decreases the gap between the study marker and the id label by specifying
# to be more or less than unity. The default is usually satisfactory, but may need to be adjusted.

graph_options are options for Stata 8 graphs (see help on graph).

Remarks on metan

For two or three variables, a variance-weighted analysis is performed in
a similar fashion to the meta command; the two variable syntax
is theta and SE(theta). The 3 variable syntax is theta,
lower ci (theta), upper ci (theta). Note that in this situation
"theta" is taken to be the logarithm of the effect size if the odds
ratio or risk ratio is used. This differs from the equivalent in the meta command.
This program does not assume the three variables need log transformation:
if odds ratios or risk ratios are combined, it is up to the user to
log-transform them first. The eform option may be used to change
back to the original scale if needed. By default the confidence
intervals are assumed symmetric, and the studies are pooled by taking
the variance to be equal to (CI width)/2z.

Note that for graphs on the log scale (that is, ORs or RRs), values
outside the range [10e-8,10e8] are not displayed, and similarly graphs of
other measures (log ORs, RDs, SMDs) are restricted to the range [-10e8,10e8].
A confidence interval which extends beyond this, or the specified scale
if force is used, will have an arrow added at the end of the range.

Further notes on v9 update: If by is used with a string variable the
stratification variable is not sorted alpha-numerically and the original
order that the groups appear in the data is preserved. This may be of use if
a particular display order is required; if not, sortby may be used.
The option counts is now available for continuous data and displays
sample size, mean and SD in each group. The estimate for heterogeneity between
groups from a stratified analysis using the Mantel-Haenszel method, and
arguably the Peto method, is invalid. Therefore this is not displayed in the
output for either of these methods.

Remarks on labbe

By default the size of the plotting symbol is proportional to the sample
size of the study. If weights are specified the plotting size will be
proportional to the weight variable. Note that labbe has now been updated to version 8 graphics.
All options work the same as in the previous version, and some minor graphics options have been added.

Stored

By default, metan adds the following new variables to the data set:

_ES Effect size (ES)
_seES Standard error of ES
or, when OR or RR are specfied:
_selogES the standard error of its logarithm
_LCI Lower confidence limit for ES
_UCI Upper confidence limit for ES
_WT Study percentage weight
_SS Study sample size

Examples

All examples use a simulated example dataset (Ross Harris 2006)

. use http://fmwww.bc.edu/repec/bocode/m/metan_example_data

Risk difference from raw cell counts, random effects model, "label" specification with counts displayed

. metan tdeath tnodeath cdeath cnodeath,

rd random label(namevar=id, yearid=year) counts

(click to run)

Sort by year, use data columns syntax. Text size increased, specify percentage of graph as text and
two lines per study; suppress stats, weight, heterogeneity stats and table.

. metan tdeath tnodeath cdeath cnodeath,

sortby(year) lcols(id year country) rcols (population)

textsize(110) astext(60) double nostats nowt nohet notable

(click to run)

Analyse continuous data (6 parameter syntax), stratify by type of study, with weights summing to 100 within sub group,
second analysis specified, display random effects distribution, show raw data counts, display
"favours treatment vs. favours control" labels

. metan tsample tmean tsd csample cmean csd,

by(type_study) sgweight fixed second(random) rfdist

counts label(namevar = id)

favours(Treatment reduces blood pressure # Treatment increases blood pressure)

(click to run)

Generate log odds ratio and standard error, analyse with 2 parameter syntax. Graph has exponential form,
scale is forced within set limits and ticks added, effect label specified.

. gen logor = ln( (tdeath*cnodeath)/(tnodeath*cdeath) )

. gen selogor = sqrt( (1/tdeath) + (1/tnodeath) + (1/cdeath) + (1/cnodeath) )

. metan logor selogor, eform xlabel(0.5, 1, 1.5, 2, 2.5)

force xtick(0.75, 1.25, 1.75, 2.25) effect(Odds ratio)

(click to run)

Display diagnostic test data with 3 parameter syntax. Weight is number of positive diagnoses, axis label set
and null specified at 50%. Overall effect estimate is not displayed, graph for visual examination only.

. metan percent lowerci upperci, wgt(n_positives)

xlabel(0,10,20,30,40,50,60,70,80,90,100) force

null(50) label(namevar=id) nooverall notable

title(Sensitivity, position(6))

(click to run)

User has analysed data with a non-standard technique and supplied effect estimates, weights and description of statistics.
The scheme "Economist" has been used.

. metan OR ORlci ORuci, wgt(bweight)

first(0.924 0.753 1.095 Bayesian)

firststats(param V=3.86, p=0.012)

label(namevar=id)

xlabel(0.25, 0.5, 1, 2, 4) force

null(1) aspect(1.2) scheme(economist)

(click to run)

Variable "counts" defined showing raw data. Options to change the box, effect estimate marker and confidence interval used,
and the counts variable has been attached to the estimate marker as a label.

. gen counts = ". " + string(tdeath) + "/" + string(tdeath+tnodeath)

+ ", " + string(cdeath) + "/" + string(cdeath+cnodeath)

. metan tdeath tnodeath cdeath cnodeath,

lcols(id year) notable

boxopt( mcolor(forest_green) msymbol(triangle) )

pointopt( msymbol(triangle) mcolor(gold) msize(tiny)

mlabel(counts) mlabsize(vsmall) mlabcolor(forest_green) mlabposition(1) )

ciopt( lcolor(sienna) lwidth(medium) )

(click to run)

L'Abbe plot with labelled axes and display of risk ratio and risk difference.

. labbe tdeath tnodeath cdeath cnodeath,

xlabel(0,0.25,0.5,0.75,1) ylabel(0,0.25,0.5,0.75,1)

rr(1.029) rd(0.014) null

(click to run)

Authors

Michael J Bradburn, Jonathan J Deeks, Douglas G Altman.
Centre for Statistics in Medicine, University of Oxford,
Wolfson College Annexe, Linton Road, Oxford, OX2 6UD, UK

Version 9 update

Ross J Harris (rossharris1978@yahoo.co.uk), Roger M Harbord, Jonathan A C Sterne.
Department of Social Medicine, University of Bristol,
Canynge Hall, Whiteladies Road, Bristol BS8 2PR, UK

Other updates and improvements to code and help file

Patrick Royston. MRC Clinical Trials Unit, 222 Euston Road,
London, NW1 2DA

Acknowledgements

Thanks to Vince Wiggins, Kit Baum and Jeff Pitblado of Statacorp
who offered advice and helped facilitate the version 9 update.
Thanks also to all the people who helped with beta-testing and
made comments and suggested improvements.

References

Higgins JPT, Thompson SG, Deeks JJ,
Altman DG. Measuring inconsistency in meta-analyses. BMJ
2003; 327:557-560. http://dx.doi.org/10.1136/bmj.327.7414.557

Higgins JPT, Thompson SG (2006) Presenting random effects meta-analyses:
where we are going wrong? (from presentation, work in preparation)

Also see

STB: STB-44 sbe24
On-line: help for metan7, metannt
meta (if installed), metacum (if installed),
metareg (if installed), metabias (if installed),
metatrim (if installed), metainf (if installed),
galbr (if installed), metafunnel (if installed)