All You Need to Know About Longitudinal Data Analysis:

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Institute for Health Research and Policy

University of Illinois at Chicago

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Institute for Health Research and Policy

University of Illinois at Chicago

Some Things You Need to Know About Longitudinal Data Analysis:

Richard T. Campbell

Division of Epidemiology and Biostatistics

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/master07_image001.gif content-transfer-encoding: base64 content-type: image/gif R0lGODlhAwB7AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgAC AHgAgAAAAAAAAAINjI+py+0Po5y02otzKwA7 ------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/master07_image002.gif content-transfer-encoding: base64 content-type: image/gif R0lGODlhWQAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABX ABUAgQAAAAAAAMwzAMyZAAKohA+hiu0PhYS0ojHsWZxpLYXip2HmSXVqQD7iG7bPSZvOissHzE86 UAtmELicrNf7CYWb4kqHTMqWTGexFUW2qFXrk5SVlrhCr9ESFlvIZbPqk1ZT2EH3GxSHfeg1ewee 97LHd+LHARjoM0aIYeiBGEjCaOLIApYosMVoYAgVOUXY5OYZp8TXMPqT9wPE9uDFahAWa0CWckYL oJVby/RhyeuiGHwx9FAAADs= ------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0002.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Major Themes of This Talk

¢= There are two major revolutions in data analysis in the past 40 years or so

lThe general linear model revolution (1965)

lThe computing (MLE) revolution (~1985)

¢= Despite the plethora of models, methods, terminology and software, most longitudinal analysis falls in a few basic categories.

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UIC IHRP

Institute for = Health
Research and Policy

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UIC IHRP

Institute for = Health
Research and Policy

Two Generic Issues in Longitu= dinal Data Analysis

¢Conceptual:

lHow do we conceptualize the outcome? <= /span>

lHow to we represent the role of time? =

¢Statistical:

lHow do we deal with the fact that we have repeate= d measures on the same persons or entities, thereby= violating the classical statistical assumptions?&= #13;

lHow do we deal with the messiness of longitudinal= data; attrition and variation in timing of measures?

¢These two issues are not unrelated<= /div>

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UIC IHRP

Institute for = Health
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What Questions Can We Ask?

¢End point analysis.

¢Trajectory/growth analysis.

¢Survival analysis.

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UIC IHRP

Institute for = Health
Research and Policy

The GLM revolution

¢Thinking of longitudinal data for some continuous outcome, we generally consider = “factors” (experimental conditions, <= /span>categorical variables such as race and gender) and covariates, both continuous and categorical.

¢Traditional ANOVA uses this terminology which is expressed in software like SPSS.

¢For most of us, this is the way we were trained and it’s a natural way of thinking.=

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UIC IHRP

Institute for = Health
Research and Policy

A simple example of a GLM

Anova Table

Sex

Condition

Sex x Condition

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UIC IHRP

Institute for = Health
Research and Policy

Regression (GLM) formulation

But isn’t that a whole lot more <= span style=3D'font-size:133%'>complicated?

Yes, but it’s a whole lot more flexible

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charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Its all Regression

¢All ANOVA type-models can be <= span style=3D'position:absolute;top:35.5%;left:21.34%;width:72.28%;height:6.5%= '>written as a regression equation. ¢To a degree= , this matters only to statisticians, but most modern software, such as HLM, assumes users are comfortable with this and= require them to specify models in regression terms.

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0006.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

In fact, its more general than that

¢= Most of us were trained to deal with normally distributed, continuous outcomes.

¢= But the regression model extends to all kinds of other outcomes including:

lSimple dichotomies (logistic)

lOrdered categories (ordered logistic)

lNominal categories (multinomial)

lWaiting times (survival)

lCounts (Poisson and generalizations thereof).

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0040.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

The key point is this:

¢No matter = what is on the left side of the equation – continuous, logistic, whatever --, the right hand side looks <= span style=3D'position:absolute;top:48.75%;left:21.34%;width:71.16%;height:6.5= %'>exactly the same with very few exceptions

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0007.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Setup For a Generic Example of a longitudinal study

¢Three Experimental Conditions

lControl, Minimal Exercise, Intense Exercise

¢Concern with interaction with sex

¢Covariates such as age

¢Measures at three points in time

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UIC IHRP

Institute for = Health
Research and Policy

Design Layout for the data

Begin with equal N’= ;s in cells, but N depleted by attrition.

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UIC IHRP

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Typical Attrition Patterns

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UIC IHRP

Institute for = Health
Research and Policy

Resul= ts for a Hypothetical Study

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UIC IHRP

Institute for = Health
Research and Policy

Classical Repeated Measures Anova Solution

¢Until relatively recently, most students would be taught to do this with ANOVA or perhaps MANOVA.

¢Assumes

l=3D N’s per cell (no attrition)

lNo variation in measurement intervals across subjects

l“Compound symmetry” error structure<= /div>

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UIC IHRP

Institute for = Health
Research and Policy

Error Structures

¢From a statistical point of view, the major challenge is that classical models assume = that errors (the e in the regression model) are independent

¢But for longitudinal data, this is untenable =

¢From an ANOVA point of view, the classical fix is to treat subjects as a factor in the design

¢But even there, one has to make assumptions which are unreasonable

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0035.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

The MLE/Computing Revolution

¢Began in mid-1980’s

= ¢Developed as a result of increased computing power ¢Use iterative search methods to estimate coefficients of a complex = model (as do all SEM programs)

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UIC IHRP

Institute for = Health
Research and Policy

What more modern methods permi= t

¢Unequal nu= mbers of observations per cell ¢Varying ti= mes of measurement – in fact each subject can be measured a= t a unique time point

= ¢A wide variety of error structures

= ¢Both time-fixed and time-varying covariates

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0013.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Layouts for Longitudinal Data

¢Time-fixed= and time-varying covariates. ¢Classic “wide” or “multivariate” format – what we are used to. ¢“Long” or “univariate” format and why modern programs want to = see data this way.

¢Moving back and forth.

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UIC IHRP

Institute for = Health
Research and Policy

Data in wide for= mat

One case per row

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------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0041.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Conceptual issues

¢We are interested in the effect of exercise on depression. S= hould we:

lModel variation in depression at some end point?

lModel trajectories of change in depression

lModel how long it takes for someone to recover from depression

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0009.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

End Point Analysis

¢Strictly speaking, not a longitudinal method, in effect, its cross-sectional. ¢We are modeling some outcome at the end of the study, using data on independent variables collected over the course of the study. ¢The end point is often arbitrary, particularly in observational studies

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0010.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Trajectory or Growth Curve Analysi= s

¢We can plot each person’s trajectory on some outcome variable over time.

¢We then want to explain the variability in the intercepts and slopes of these trajectories as a functio= n of one or more other variables.

¢We can think of the dependent variable as the rate of change with respect to time.

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0042.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Person-specific Plots of
Math Achievement = By Time

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UIC IHRP

Institute for = Health
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Person-specific Plots of
Math Achievement = By Time

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UIC IHRP

Institute for = Health
Research and Policy

Person Specific Fitted
Regression Lines

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content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Person-Specific and
Overall Regression=

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------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0011.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

But the Basic Question is Simple<= /span>

¢Does the a= verage rate of change (slope) vary as a function of experimental group? ¢Does the rate of change vary as a function of other time-fixed and time-varying covariates? ¢This method easy generalizes to non-continuous outcomes. = ;

¢Example

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0012.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

Survival Analysis

¢We are interested primarily in the timing of transitions, hence the term “event history analysis” in some literatures.

¢The dependent variable is not directly observed; it is the “hazard rate” defined, loosely, as the probability of a transition at time t given that it has not occurred to that point.

¢We regress this variable on the usual = stuff.

------=_NextPart_01C6F6A8.1E297590 content-location: file:///C:/2132A1EC/campbell_files/slide0046.htm content-transfer-encoding: quoted-printable content-type: text/html; charset="us-ascii" All You Need to Know About Longitudinal Data Analysis:

UIC IHRP

Institute for = Health
Research and Policy

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An example of survival data

End of observation period

Censored cases

Time

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document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D32, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0002.htm",1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("= slide0008.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("s= lide0004.htm",1,-1,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("sl= ide0039.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("sli= de0006.htm",1,-1,1),new hrefList("slide0040.htm",1,-1,1),new hrefList("slid= e0007.htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide= 0017.htm",1,-1,1),new hrefList("slide0018.htm",1,-1,1),new hrefList("slide0= 019.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slide00= 35.htm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("slide001= 3.htm",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0038= .htm",1,-1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0009.= htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("slide0042.h= tm",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new hrefList("slide0044.ht= m",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0011.htm= ",1,-1,1),new hrefList("slide0012.htm",1,-1,1),new hrefList("slide0046.htm"= ,1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('

' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. ******************************************