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 help for ^metabias^            (STB-41: sbe19; STB-44: sbe19.1; STB-57: sbe19.2;
                                               STB-58: sbe19.3; STB-61: sbe19.4)
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Tests for publication bias in meta-analysis
-------------------------------------------

   ^metabias^ { theta { se_theta | var_theta } | exp(theta) ll ul [cl] }
            [ ^if^ exp ] [ ^in^ range ] [^, by(^by_var^)^ { ^v^ar | ^ci^ } 
              ^g^raph^(b^egg | ^e^gger^) gw^eight ^l^evel^(^#^)^ graph_options ]

      where { a | b |...} means choose one and only one of {a, b, ...}.


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

^metabias^ 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.  ^metabias^ 
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 ^metabias^ 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.

^metabias^ 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 ^metabias^'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
--------

 . ^metabias logrr selogrr, graph(begg)^
 . ^metabias logrr varlogrr if site==3, var graph(egger)^
 . ^metabias rr ll ul, ci by(site)^
 . ^metabias logor selogor if region==4, graph(egger) level(90)^


Note
----

^metabias^ calls program ^ktau2^, a modification of the ^ktau^ program
supplied with Stata.  ^ktau2^ is included in the distribution files
for this version of ^metabias^.


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)
