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<title>Supplementary material for the paper: </title>
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<div class=Section1>
<p class=MsoNormal style='line-height:200%'><b style='mso-bidi-font-weight:
normal'>Supplementary material for the paper: <o:p></o:p></b></p>
<p class=MsoNormal style='line-height:200%'><span class=GramE><span lang=EN-US
style='mso-ansi-language:EN-US'>Mixed comparison of stroke prevention
treatments in individuals with non-rheumatic <span class=SpellE>atrial</span>
fibrillation.</span></span><span lang=EN-US style='mso-ansi-language:EN-US'> <i>Archives
of Internal Medicine</i></span><b style='mso-bidi-font-weight:normal'><o:p></o:p></b></p>
<p class=MsoNormal style='line-height:200%'><b style='mso-bidi-font-weight:
normal'><o:p> </o:p></b></p>
<p class=MsoNormal style='line-height:200%'><b style='mso-bidi-font-weight:
normal'><o:p> </o:p></b></p>
<p class=MsoNormal style='line-height:200%'><b style='mso-bidi-font-weight:
normal'>EVIDENCE SYNTHESIS MODEL<o:p></o:p></b></p>
<p class=MsoNormal style='line-height:200%'>A random effects Poisson regression
model (<span class=SpellE>Spiegelhalter</span> et al. 2004) was applied using
the following model specification:</p>
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<p class=MsoNormal style='line-height:200%'>Where <span class=SpellE><i>r<sub>jk</sub></i></span>
is the number of events and <span class=SpellE><i>py<sub>jk</sub></i></span> is
the patient years of follow-up in trial <i>j</i> under treatment <i>k</i>.<span
style='mso-spacerun:yes'>�� </span><i><span style='font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:
symbol;mso-symbol-font-family:Symbol'>l</span></span><span class=SpellE><span
class=GramE><sub>jk</sub></span></span></i> is the mean of Poisson distribution
in trial <i>j</i> under treatment <i>k</i>, <i><span style='font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:
symbol;mso-symbol-font-family:Symbol'>m</span></span><span class=SpellE><sub>jb</sub></span></i>
is the log rate of an event (e.g. ischemic stroke, bleed, etc.) in trial <i>j</i>
on baseline treatment <i>b</i>, and <i><span style='font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:
symbol;mso-symbol-font-family:Symbol'>d</span></span><span class=SpellE><sub>jbk</sub></span></i>
is the trial-specific log<sub>e</sub>(rate ratio) of treatment <i>k</i>
relative to treatment <i>b</i>. <i><span style='mso-spacerun:yes'>�</span><span
class=SpellE><span class=GramE>d<sub>bk</sub></span></span></i> is the pooled
log<sub>e</sub>(rate ratio) for treatment <i>k</i> relative to treatment <i>b</i>
and <i>V</i> is the between-study variance parameter often referred to as the
heterogeneity parameter as it estimates how much variation exists between the
results of the different studies.<span style='mso-spacerun:yes'>� </span></p>
<p class=MsoNormal style='line-height:200%'><o:p> </o:p></p>
<p class=MsoNormal style='line-height:200%'>The model needs to take into
account the correlation structure induced by the multi-arm trials; for example,
multi-arm trials of A <i>vs</i>. B <i>vs</i>. C will induce a covariance
between the trial-specific log rate ratios, <i><span style='font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:
symbol;mso-symbol-font-family:Symbol'>d</span></span><span class=SpellE><sub>jAB</sub></span></i>
and <i><span style='font-family:Symbol;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-font-family:
Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>d</span></span><span
class=SpellE><sub>jAC</sub></span></i>.<span style='mso-spacerun:yes'>�
</span>This correlation structure can be formulated by the decomposition of
multivariate normal distribution as a series of conditional <span class=SpellE>univariate</span>
distributions (Caldwell et al. 2005).<span style='mso-spacerun:yes'>� </span>If
</p>
<p class=MsoNormal style='text-indent:36.0pt;line-height:200%'><sub><!--[if gte vml 1]><v:shape
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<p class=MsoNormal style='line-height:200%'><span class=GramE>then</span> the
conditional <span class=SpellE>univariate</span> distributions are:</p>
<p class=MsoNormal style='text-indent:36.0pt;line-height:200%'><sub><!--[if gte vml 1]><v:shape
id="_x0000_i1028" type="#_x0000_t75" style='width:266.25pt;height:56.25pt'
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DrawAspect="Content" ObjectID="_1203502930">
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</xml><![endif]--><span style='mso-tab-count:2'>������������������ </span></p>
<p class=MsoNormal style='line-height:200%'><o:p> </o:p></p>
<p class=MsoNormal style='line-height:200%'>The analyses were conducted in the
freely available Bayesian software, WinBUGS<!--[if supportFields]><span
style='mso-element:field-begin'></span> ADDIN EN.CITE
<EndNote><Cite><Author>Spiegelhalter</Author><Year>2003</Year><RecNum>2271</RecNum><MDL><REFERENCE_TYPE>1</REFERENCE_TYPE><REFNUM>2271</REFNUM><AUTHORS><styles></styles><AUTHOR>Spiegelhalter,D.</AUTHOR><AUTHOR>Thomas,A.</AUTHOR><AUTHOR>Best,N.</AUTHOR><AUTHOR>Lunn,D.</AUTHOR></AUTHORS><TITLE><styles></styles>WinBUGS
user manual: Version 1.4</TITLE><PLACE_PUBLISHED><styles></styles>Cambridge</PLACE_PUBLISHED><PUBLISHER><styles></styles>MRC
Biostatistics
Unit</PUBLISHER><YEAR>2003</YEAR><KEYWORDS><styles></styles><KEYWORD>WinBUGS</KEYWORD><KEYWORD>Bayesian</KEYWORD><KEYWORD>MCMC</KEYWORD></KEYWORDS><LABEL>6911</LABEL></MDL></Cite></EndNote><span
style='mso-element:field-separator'></span><![endif]--><sup>20</sup><!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]-->.<span
style='mso-spacerun:yes'>� </span>Therefore, prior distributions needed to be
specified for <i><span style='font-family:Symbol;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-font-family:
Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>m</span></span><span
class=SpellE><sub>jb</sub></span></i>, <i>d</i> and <i>V</i>. All prior
distributions in this analysis were intended to be vague:</p>
<p class=MsoNormal style='line-height:200%'><span
style='mso-spacerun:yes'>�</span><span style='mso-tab-count:1'>���������� </span><sub><!--[if gte vml 1]><v:shape
id="_x0000_i1029" type="#_x0000_t75" style='width:375pt;height:21pt' o:ole="">
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<p class=MsoNormal style='line-height:200%'><o:p> </o:p></p>
<p class=MsoNormal style='line-height:200%'>The goodness-of-fit of the model to
the data was measured by calculating the residual deviance </p>
<p class=MsoNormal style='line-height:200%'><sub><!--[if gte vml 1]><v:shape
id="_x0000_i1030" type="#_x0000_t75" style='width:1in;height:17.25pt' o:ole="">
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<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1030"
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style='width:176.25pt;height:18.75pt' o:ole="">
<v:imagedata src="supplement_files/image013.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=235 height=25
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<p class=MsoNormal style='line-height:200%'><o:p> </o:p></p>
<p class=MsoNormal style='line-height:200%'><span class=GramE>Where <span
class=SpellE><i style='mso-bidi-font-style:normal'>loglik<sub>model</sub></i></span><i
style='mso-bidi-font-style:normal'> </i>and <span class=SpellE><i
style='mso-bidi-font-style:normal'>loglik<sub>saturated</sub></i></span> are
the deviances for the fitted model and the saturated model respectively.</span>
The deviance measures the fit of the model to the data points using the
likelihood function.<span style='mso-spacerun:yes'>� </span>For Poisson data,
the residual deviance is given by:</p>
<p class=MsoNormal style='text-indent:36.0pt;line-height:200%'><sub><!--[if gte vml 1]><v:shape
id="_x0000_i1032" type="#_x0000_t75" style='width:254.25pt;height:39.75pt'
o:ole="">
<v:imagedata src="supplement_files/image015.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=339 height=53
src="supplement_files/image030.gif" v:shapes="_x0000_i1032"><![endif]></sub><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032"
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<p class=MsoNormal style='line-height:200%'>Where <sub><!--[if gte vml 1]><v:shape
id="_x0000_i1033" type="#_x0000_t75" style='width:15pt;height:18.75pt' o:ole="">
<v:imagedata src="supplement_files/image017.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=20 height=25
src="supplement_files/image031.gif" v:shapes="_x0000_i1033"><![endif]></sub><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033"
DrawAspect="Content" ObjectID="_1203502935">
</o:OLEObject>
</xml><![endif]--><span style='mso-spacerun:yes'>�</span>is the observed number
of events (i.e. ischemic stroke or bleed) and <sub><!--[if gte vml 1]><v:shape
id="_x0000_i1034" type="#_x0000_t75" style='width:15pt;height:18.75pt' o:ole="">
<v:imagedata src="supplement_files/image019.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=20 height=25
src="supplement_files/image032.gif" v:shapes="_x0000_i1034"><![endif]></sub><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034"
DrawAspect="Content" ObjectID="_1203502936">
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</xml><![endif]--><span style='mso-spacerun:yes'>�</span>is the expected number
of events estimated from the current model for <i style='mso-bidi-font-style:
normal'>j</i> =1 to <i style='mso-bidi-font-style:normal'>J</i> trials and <i
style='mso-bidi-font-style:normal'>k</i> represents the treatments compared in
trial <i style='mso-bidi-font-style:normal'>j</i>.<span
style='mso-spacerun:yes'>� </span>Under the null hypothesis that the model
provides an adequate fit to the data, it is expected that<sub><!--[if gte vml 1]><v:shape
id="_x0000_i1035" type="#_x0000_t75" style='width:21.75pt;height:18.75pt'
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<v:imagedata src="supplement_files/image021.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=29 height=25
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<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035"
DrawAspect="Content" ObjectID="_1203502937">
</o:OLEObject>
</xml><![endif]-->would have a mean equal to the number of unconstrained data
points.<span style='mso-spacerun:yes'>� </span></p>
<p class=MsoNormal style='line-height:150%'><o:p> </o:p></p>
<p class=MsoNormal style='line-height:150%'><o:p> </o:p></p>
<p class=MsoNormal style='margin-bottom:6.0pt;line-height:200%'><b>References:<o:p></o:p></b></p>
<p class=MsoNormal style='margin-bottom:6.0pt;line-height:200%'><st1:place
w:st="on"><st1:City w:st="on"><span class=GramE><span style='mso-fareast-language:
EN-GB'>Caldwell</span></span></st1:City></st1:place><span class=GramE><span
style='mso-fareast-language:EN-GB'> DM, <span class=SpellE>Ades</span> AE,
Higgins JPT.</span></span><span style='mso-fareast-language:EN-GB'>
Simultaneous comparison of multiple treatments: combining direct and indirect
evidence. <i>BMJ</i> 2005<span class=GramE>;331:897</span>-900.<o:p></o:p></span></p>
<p class=MsoNormal style='margin-bottom:6.0pt;line-height:200%'><span
class=SpellE><span style='mso-fareast-language:EN-GB'>Spiegelhalter</span></span><span
style='mso-fareast-language:EN-GB'> DJ, <span class=SpellE>Abrams</span> KR,
Myles JP. Bayesian Approaches to Clinical Trials and Health-care Evaluation
(Statistics in Practice). <st1:place w:st="on">Chichester</st1:place>: John
Wiley and Sons Ltd; 2004.</span><b><br clear=all style='mso-special-character:
line-break;page-break-before:always'>
<o:p></o:p></b></p>
<p class=MsoNormal style='margin-bottom:6.0pt;line-height:200%'><b><o:p> </o:p></b></p>
<p class=MsoNormal style='margin-bottom:6.0pt;line-height:200%'><span
class=SpellE><b>WinBUGS</b></span><b> code for mixed treatment comparisons<o:p></o:p></b></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>model</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'><o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>{<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>for(</span></span><span class=SpellE><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>i</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'> in 1:ns)<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>w[</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>i,1] <-0<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>delta[</span></span><span
class=SpellE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>i,t</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>[i,1]]<-0<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=SpellE><span class=GramE><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>mu</span></span></span><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>[</span></span><span class=SpellE><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>i</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>] ~ <span class=SpellE>dunif</span>(-10,10)<span
style='mso-spacerun:yes'>��������������������������������������������������
</span><span style='mso-tab-count:3'>���������������������������������������� </span><i>#
vague priors for trial baselines</i><o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>for</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'> (k in 1:na[<span class=SpellE>i</span>])<span
style='mso-spacerun:yes'>� </span><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>r[<span class=SpellE>i,t</span>[<span
class=SpellE>i,k</span>]] ~ <span class=SpellE>dpois</span>(lambda[<span
class=SpellE>i,t</span>[<span class=SpellE>i,k</span>]])<span
style='mso-spacerun:yes'>����������������������� </span><span style='mso-tab-count:
3'>����������������������������������������������� </span><i># Poisson
distribution</i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>log(lambda[<span class=SpellE>i,t</span>[<span
class=SpellE>i,k</span>]])<-log(<span class=SpellE>py</span>[<span
class=SpellE>i,t</span>[<span class=SpellE>i,k</span>]]/1000)+<span
class=SpellE>mu</span>[<span class=SpellE>i</span>]+delta[<span class=SpellE>i,t</span>[<span
class=SpellE>i,k</span>]] <span style='mso-tab-count:1'>��� </span><i>#
evidence synthesis model</i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'><span style='mso-spacerun:yes'>�� </span><span style='mso-tab-count:
1'>������������ </span><span class=GramE>for</span> (k in 2:na[<span
class=SpellE>i</span>]) <o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{<o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>delta[<span class=SpellE>i,t</span>[<span
class=SpellE>i,k</span>]] ~ <span class=SpellE>dnorm</span>(<span class=SpellE>md</span>[<span
class=SpellE>i,t</span>[<span class=SpellE>i,k</span>]],<span class=SpellE>taud</span>[<span
class=SpellE>i,t</span>[<span class=SpellE>i,k</span>]]) <span
style='mso-tab-count:1'>��������������� </span><i># trial-specific log rate
ratio (LRR) </i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span class=SpellE><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>md</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>[<span class=SpellE>i,t</span>[<span class=SpellE>i,k</span>]]
<-<span style='mso-spacerun:yes'>� </span>d[t[<span class=SpellE>i,k</span>]]
- d[t[i,1]]<span style='mso-spacerun:yes'>� </span>+ <span class=SpellE>sw</span>[<span
class=SpellE>i,k</span>]<span style='mso-spacerun:yes'>������������� </span><span
style='mso-tab-count:1'>���������� </span><i># mean of LRR distribution</i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span class=SpellE><span class=GramE><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>taud</span></span></span><span class=GramE><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>[</span></span><span
class=SpellE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>i,t</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>[<span class=SpellE>i,k</span>]]
<- </span><span class=SpellE><span style='font-size:10.0pt;mso-fareast-language:
EN-GB'>tau</span></span><span style='font-size:10.0pt;mso-fareast-language:
EN-GB'> * 2*(k-1)/k<span style='mso-tab-count:1'>����������� </span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'><span style='mso-tab-count:2'>������������������������������� </span><i>#
precision of LRR distribution</i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>w[<span class=SpellE>i,k</span>] <- </span><span
style='font-size:10.0pt;mso-fareast-language:EN-GB'>delta[<span class=SpellE>i,t</span>[<span
class=SpellE>i,k</span>]]<span style='mso-spacerun:yes'>� </span>- d[t[<span
class=SpellE>i,k</span>]] + d[t[i,1]]<span style='mso-tab-count:1'>�������� </span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'><span style='mso-tab-count:1'>��������������� </span><i># adjustment,
multi-arm <span class=SpellE>RCTs</span></i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:287.85pt;text-indent:-215.85pt;
mso-layout-grid-align:none;text-autospace:none'><span class=SpellE><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>sw</span></span></span><span class=GramE><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>[</span></span><span class=SpellE><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>i,k</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>] <-sum(w[i,1:k-1]) /(k-1)<span
style='mso-spacerun:yes'>������������������������ </span><span
style='mso-tab-count:1'>����������������� </span>#<i> cumulative adjustment for
multi-arm trials</i><o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<span style='mso-spacerun:yes'>�� </span><o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>d[</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>1]<-0<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>for</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'> (k in 2:nt)<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>d[</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>k] ~ <span class=SpellE>dunif</span>(-10,10)<span
style='mso-spacerun:yes'>������������������� </span><span style='mso-tab-count:
3'>����������������������������������������� </span><i># vague priors for basic
parameters</i><o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<span style='mso-spacerun:yes'>�� </span><o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=SpellE><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>sd~</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>dunif</span></span><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>(0,2)<span
style='mso-spacerun:yes'>������������������������������������������� </span><span
style='mso-tab-count:3'>������������������������������������������� </span><i>#
vague prior for random effects standard deviation </i><o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=SpellE><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>tau</span></span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'><-1/pow(sd,2)<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>for</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'> (<span class=SpellE>i</span>
in 1:ns) <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>mu1[</span></span><span
class=SpellE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>i</span></span><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>] <- <span class=SpellE>mu</span>[<span
class=SpellE>i</span>] * equals(t[i,1],1) <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=DE style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:DE'>}<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
lang=DE style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
DE'>for (k in 1:nt)<span style='mso-spacerun:yes'>� </span><o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=DE style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:DE'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=DE style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:DE'>log(T[k])<- sum(mu1[])/nb +d[k] <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>for</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'> (k in 1:nt) <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=SpellE><span class=GramE><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>rk</span></span></span><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>[</span></span><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>k]<- rank(T[],k)<span
style='mso-tab-count:4'>������������������������������������������������ </span><i>#Ranking
treatments<o:p></o:p></i></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'><span style='mso-spacerun:yes'>������������� </span><span class=GramE>best[</span>k]<-equals(<span
class=SpellE>rk</span>[k],1)<span style='mso-tab-count:4'>�������������������������������������������������������� </span><i>#Proportion
each treatment the �best� (i.e. ranked 1)</i><o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
class=GramE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>for</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'> (c in 1:(nt-1))<span
style='mso-tab-count:6'>���������������������������������������������������������������������������������� </span><i>#<span
class=SpellE>Pairwise</span> rate ratio</i><o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>for</span></span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'> (k in (c+1):<span class=SpellE>nt</span>) <o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>{ <o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span class=SpellE><span class=GramE><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>rr</span></span></span><span class=GramE><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>[</span></span><span
class=SpellE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>c,k</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>] <-exp(d[k]-d[c])<o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:36.0pt;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='text-indent:36.0pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;mso-ansi-language:EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>}<o:p></o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='mso-ansi-language:EN-US'><o:p> </o:p></span></p>
<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'><i><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:
EN-US'>#Data<o:p></o:p></span></i></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span class=GramE><span lang=EN-US style='font-size:10.0pt;
mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>list(</span></span><span
class=SpellE><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;
mso-ansi-language:EN-US'>nt</span></span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt;mso-ansi-language:EN-US'>= 9,ns=19, <span
class=SpellE>nb</span>=8<span style='color:black'>)</span><o:p></o:p></span></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;color:black;mso-ansi-language:EN-US'><o:p> </o:p></span></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:7.0pt;mso-bidi-font-size:
12.0pt;color:black;mso-ansi-language:EN-US'>r[,1]<span
style='mso-spacerun:yes'>��� </span><span class=SpellE>py</span>[,1]<span
style='mso-spacerun:yes'>��� </span>r[,2]<span style='mso-spacerun:yes'>���
</span><span class=SpellE>py</span>[,2]<span style='mso-spacerun:yes'>���
</span>r[,2]<span style='mso-spacerun:yes'>��� </span><span class=SpellE>py</span>[,3]<span
style='mso-spacerun:yes'>��� </span>r[,4]<span style='mso-spacerun:yes'>���
</span><span class=SpellE>py</span>[,4]<span style='mso-spacerun:yes'>���
</span>r[,5]<span style='mso-spacerun:yes'>��� </span><span class=SpellE>py</span>[,5]<span
style='mso-spacerun:yes'>��� </span>r[,6]<span style='mso-spacerun:yes'>���
</span><span class=SpellE>py</span>[,6]<span style='mso-spacerun:yes'>���
</span>r[,7]<span style='mso-spacerun:yes'>��� </span><span class=SpellE>py</span>[,7]<span
style='mso-spacerun:yes'>��� </span>r[,8]<span style='mso-spacerun:yes'>���
</span><span class=SpellE>py</span>[,8]<span style='mso-spacerun:yes'>���
</span>r[,9]<span style='mso-spacerun:yes'>��� </span><span class=SpellE>py</span>[,9]<span
style='mso-spacerun:yes'>��� </span>t[,1]<span style='mso-spacerun:yes'>���
</span>t[,2]<span style='mso-spacerun:yes'>� </span><span
style='mso-spacerun:yes'>��</span>t[,3]<span style='mso-spacerun:yes'>���
</span>t[,4]<span style='mso-spacerun:yes'>��� </span><span class=SpellE>na</span>[]<o:p></o:p></span></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:7.0pt;mso-bidi-font-size:
8.0pt;mso-ansi-language:EN-US'>��..<o:p></o:p></span></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:7.0pt;mso-bidi-font-size:
8.0pt;mso-ansi-language:EN-US'>��..<span style='mso-tab-count:1'>��� </span><o:p></o:p></span></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:7.0pt;mso-bidi-font-size:
8.0pt;mso-ansi-language:EN-US'>END<o:p></o:p></span></p>
<p class=MsoNormal style='tab-stops:22.8pt 54.15pt;mso-layout-grid-align:none;
text-autospace:none'><span lang=EN-US style='font-size:7.0pt;mso-bidi-font-size:
8.0pt;mso-ansi-language:EN-US'><o:p> </o:p></span></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:-36.0pt'><o:p> </o:p></p>
<p class=MsoNormal style='margin-left:36.0pt;text-indent:-36.0pt'><o:p> </o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
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