Modeling Health Modeling Health 

-Relat

Q ualit

yof Life over Ti

Vilija R Joyce MS Vilija 

R. Joyce, MS

November 14, 2012
Brief CEA Review

CostIntervention – CostUsualCare 

OutcomeIntervention – OutcomeUsualCa

 Quality-Adjusted Life Year (QALY

– Length of life weighted by quality 

Length of life weighted by quality 

– Utilities, preference-based health

qualit f lif ( lity of life 

(HRQ Lo

L

) 

 EQ-5D, Health Utilities Index (HU
Objectives

 To describe how to analyze health

qualit f lif ( lity of life (HRQ Lo ) d t ith ) data with

multiple observations over time
Outline

 Introduction to types of longitudin

studies and models studies and models 

 Real-world example: Modeling the 

change in health-related quality of 

(HRQoL) in patients with advance

) in patients with advance

– OPTIMA – Exploratory analysis – Models 
3 Important Features of 3 Important Features of

Longitudinal Studies

1. Multiple waves of data 2. S ibl t i f Sensible me

t

r

ic 

for ti me 

3. Outcomes that chang y e s

ystemat

over time

– Precision of outcomes must be Precision of outcomes must be eq

eq

over time 

– O utcomes must b e equa

ll y valid o

– Preserve outcome 

precision over 
Repeated Measures Mod

 Applicable to studies where...

– S bj i h S

ubjects are exper

ienc

ing t

he same 

condition 

– Assessments correspond to an event 

intervention phase intervention phase 

– Assessments are limited (< 4) with t

conceptualized as a categorical vari
Repeated Measures Models (c

Fairclough DL. rclough DL. Design and Analysis of Quality of Life Studies in Clinical Trials. 

2nd Fai Design and Analysis of Quality of Life Studies in Clinical Trials. 2 ed

ed

Chapman and Hall/CRC Press; 2010. 
Repeated Measures Model

Drawbacks

 Assessments may not take place when 

scheduled. 
Repeated Measures Model

Drawbacks (cont’d)

 Timing of observations for 1 site over 1 year in the OPTIMA trial
History of Growth Curve M

 1980s = development of statistical m Various names Various names 

– Individual growth curve models – Random coefficient models Random coefficient models – Hierarchical linear models – Multilevel models Multilevel models – Mixed models

 D ib h i h i h d i h Describe c

hanges 

in 

h

e

i

g

ht an

d we

i

g

h

function of age in children. 
Why Not Use OLS?
Why Not Use OLS? 

 Ordinary least squares (OLS) regr

assumes th t ti th

a

t o

bservations are 

inde

penden

t

 Biased standard errors  Growth curve models can handle 

correlated errors correlated errors 
Definition of a Growth Curve 

 Change over time in a phenomenon of interest (e.g. q

life) at both the individual and aggregate levels. 

 2 types of questions about change: 

Level 1: Within-person change (how individua

c

han

ge over t

ime

) 

Time-varying predictors (e.g. days sincrandomization) randomization) 

Level 2: Between-person differences in change 

changes vary across individuals) 

Time-invariant predictors (e.

g. random

group) 
=

Level 1 Submodel – Within-P

    ijiiij ij Y   time )(   10    

Yij = The outcome of interest (for subject i at tim

π0i = Intercept, or subject i’s true value of QoL at 

π1i = Slope, or subject i’s rate of change in true Q

ε = Residual or random measurement error ij Residual or random measurement error 
Level 2 Submodels – Between-P







 j iii

ij

ij Y   time )(



 10 Level 

i i INTVN 01000 

 0



 





j 

j

j

L l 

i i INTVN 11101 

 1 

 





Level 

ITVN = Intervention Intervention γ00 = Population intercep

γ01 = Deviation from popζ

0i = Residual 

γ10 = Population slope 

γ11 = Deviation from pop

ζ1i = Residual 
Integrated Growth Curve M

Y Le

ij 





0i 





1i 

(timeij 

)





 ij 





0i 

 00 01 

 INTVN 



 0i 









 INTVN 



 L

1i 10 11 1i 

Yij 



( 00 



 10TIMEij 



 01 

INTVNi 

Fixed Effects R

 11

(

INTVNi TIMEij 

)





 0i 
e be ev be

Advantages of Growth Curve M

 Advantages 

– D d l d h i di Data modeled at the individ l l 

idual leve

– Flexible time variable – Easy handling of missing data – Easily incorporate data nesting/clus
–

Outline 

 Introduction to types of longitudin

studies and models studies and models 

 Real-world example: Modeling th

ch i l h hange in health-related li f 

d quality of 

(HRQoL) in patients with advance

– OPTIMA

Exploratory analysis Exploratory analysis 

– Models 
–

OPTIMA

 Effective antiretroviral therapy (ART) improves survival in HIV-inf The optimal management strategy for advanced HIV patients infect

drug resistant HIV was unclear. 

 CSP #512, Options in Management with Antiretrovirals  2x2 open randomized study 

– 3 month therapy interruption vs no interruption 3 month therapy interruption vs. no interruption – Treatment intensification (5+ antiretroviral drugs) vs. standard treatment (4 or few

 UK, Canada, and US  June 2001 June 2001 - December December 2007 368 patients randomized 
e o s se ous dve se eve

Outcomes

 Primary and secondary outcomes 

– Time to first AIDS 

-d fi e

n

ing event 

– Tim

e t

o fir

st serious adve

rse event 

 No significant differences in outc

among the management strategy 
-

Outcomes (cont’d) 

 Other sociodemographic and clinical data (e.g. a

serious adverse events) 

 Health -Related Quality of Life ( Related Quality of Life (HRQoL) 

– Baseline, 6, 12, 24, every 12 weeks thereafter – Health Utilities Index Mark 3 (HUI3) – EQ-5D 

– Visual analog scale 

– Medical Outcomes Study HIV Health Survey Medical Outcomes Study HIV Health Survey – Standard gamble (SG) (US patients only) – Time trade-off (TTO) (US patients only) – 5,141 HRQoL assessments over 6 2 f f ll 6.25 years of follow

3.2 years) 
HRQoL Outcome: Health Utilities 

Outcome: Health Utilities 

Mark 3 (HUI3)

 Preference/utility-based instrument  17 questions 8 attributes each with 5 17 questions, 8 attributes, each with 5 

levels 

 972,000 possible heal ht states. Weights are estimated with valuation 

from a sample of adults in Hamilton, 

Canada

 Utilities range from -0.36 to 1
Research Questions 

 What is the longitudinal effect of treat

intensification on intensification on HRQoL in patients w

in patients w

advanced HIV? 

 What is the effect of ongoing serious a

events 

(a time-de

pendent 

predictor

) on 

HRQoL? 
Outline 

 Introduction to types of longitudin

studies and models studies and models 

 Real-world example: Modeling th

change in health-related quality of (HRQoL) in patients with advance

) in patients with advance

– OPTIMA – Exploratory analysis – Models 
Missing Data 

 Why is missing data a problem?
oss o stat st ca

Missing Data 

 Why is missing data a problem? 

– Loss of statistical power– Bias of estimates 

 At baseline 4% of HUI3 assessments 

At baseline, 4% of HUI3 assessments 

OPTIMA trial were missing. 

 Plots to describe Plots to describe missingness missingness 

– Average QoL scores by time of drop-o– Average Q Lo scores b ti yme t d oeath – Average QoL scores by % missing ov
Mean HUI3 by Visit Week Patients Gro

Mean HUI3 by Visit Week, Patients Gro

When They Were Lost to Follow-U
Missing Data

 Other patterns/mechanisms? 

– Do baseline characteristics predict drop Do baseline characteristics predict drop -ou

 Proportional hazards model (PROC PHREG

– Are “skippers skippers ” - patients with intermittent 

patients with intermittent 

assessments – different from those with feassessments? 

 Regressions (PROC REG) 

– Are certain clinical events associated with 

QoL assessments? 

 Generalized linear mixed model (PROC GLI
Missing Data

 What next? 

– Serious adverse events predicted missing Serious adverse events predicted missing H

data in the OPTIMA trial. 

– BUT, serious adverse events were distribu

equally among the randomization groups.

– Missing data left “as is”. – Other QoL studies, where missing data are 

ignorable? 

 Consider imputation as part of your sensitivi Fairclough 2010, Ch. 9, Multiple Imputation 
Excerpt from person Excerpt from person-period OPTIMA period OPTIMA HRQo

 Each subject has multiple records, one per assessment 
Level 1: Within-Person Chan

ge ove

Y 

 



 1 ij 

0i i ij ij (time 

)   Le
Level 2: Differences in Change Acros

Level 2: Differences in Change Acros



0i 

 00 01 

 INTVN 



 0i 

LL

 1i 

 10 11 

 INTVN 



 1i 
Outline 

 I t d ti t t f l it di 

Introduction to types of longitudin

studies and models 

 Real-world example: Modeling th

change in health-related quality of (HRQoL)in patients with advance

– OPTIMA – Exploratory analysis – Models 
Research Questions

 What is the longitudinal effect of treat

intensification on intensification on HRQoL in patients w

in patients w

advanced HIV? 

 What is the effect of ongoing serious a

events 

(a time-de

pendent 

predictor

) on 

HRQoL? 
       

Model for longitudinal treatmenModel for longitudinal treatmen

 What is the longitudinal effect of treatment intensif

HRQoL in patients wi ht advanced HIV?

Yij  (   10 TIMEij   01 INTVN i   11 (INTVNi TIMEij )  0i 

ij 00 10 ij 01 i ij 0 

HUI3 ij   00 ( TIMEij  10 

 

   i i TIMEij  01 INTENSIFY  11 ( INTENSIFY  ) 

proc mixed data = qol;model hui3 = 	time years intensify

time_years*intensify/ solution ddfm=kr;

random int time_years / subject=id type=un;

 

/*1. Evokes mixed procedure, identifies dat

/* default estimation method or restrict 

/*2. Dependent variable, QOL instrument HUI

/*3. Time in years*/
 

/*4. Intensification group indicator*/
 

/*5. Interaction term, time in years*intens

/*6. Significance tests for all fixed effec

/* Roger method of degrees of freedom*/
 

/*7. Specifies the intercept and time as ra

/*8. Specifies observations as nested withi

/*9. Specifies an unstructured variance/cov

/* for the random effects*/
 

run;
 
Results

The Mixed Procedure
 Covariance Parameter Estimates Covariance Parameter Estimates Cov Parm Subject Estimate Error Value Pr Z UN(1 1) id UN(1,1) id 0 07349 0 006017 12 21 0001 /* V i ti t f 

0.07349 0.006017 12.21

 <.

0001 /* Variance estimate for 

UN(2,1) id -0.00416 0.001222 -3.41 0.0007 /* Covariance estimate fUN(2,2) id 0.002837 0.000427 6.64 <.0001 /* Variance estimate for Residual 0.02942 0.000653 45.08 <.0001 /* Level 1 residual*/ 

Fit Statistics 

-2 Res Log Likelihood -1753.4 AIC (smaller is better) -1745.4 

AICC (smaller is better) -1745.3 

BIC (smaller is better) -1729.7 
Results (cont Results (cont d) ’

HUI 3  (   TIME   INTENSIFY   (INTENSIFY TIME )  

ij  ( 00   10TIMEij  01INTENSIFYi   11 INTENSIFYi TIMEij )  

Solution for Fixed Effects
 

Standard
 

Effect Estimate 

Error 

DF t Value Pr > 

Intercept 0.5967 0.02056 358 29.02 <.0

p 

time_years -0.01005 0.005510 191 

-1.82 

0.0

intensify 0.03245 0.02970 359 1.09 0.2time_years*intensify -0.00348 0.007979 188 -0.44 0.6

Conclusions: - no sustained differences in HUI3 HRQoL scores between the 2 g p rou s and over time
Research Questions 

 What is the longitudinal effect of treat

intensification on intensification on HRQoL in patients w

in patients w

advanced HIV? 

 What is the effect of ongoing serious a

events 

( a time-de

p p ) endent 

predictor

) on

HRQoL? 
adve se eve ts

M do el f or eff ect of ongo ing ser

adverse events (S AE)

 What is the effect of ongoing serious adverse event

HRQoL?

HUI3  (   TIME  )  0i   1

ij 00 10 ij 

proc mixed data = qol; /*1. Evokes mixed procedure, identifies datas

/* default estimation method or restrict ma

model hui3 = /*2. Dependent variable, QOL instrument HUI3*time years /*3. Time in years*/
 sae_ongoing /*4. Indicator ongoing serious adverse event time_years*sae_ongoing /*5. Interaction term, time in years*SAE*/
 / solution ddfm=kr; /*6. Significance tests for all fixed effects 

/* Roger method of degrees of freedom*/
 

random int time_years / /*7. Specifies the intercept and time as rand

subject=id /*8. Specifies observations as nested within type=un; /*9. Specifies an unstructured variance/covar

/* for the random effects*/
 

run;
 

SAE ij SAEij TIMEij  20  (  30 
Results

HUI ij  ( 00   10TIMEij  20 SAEij  ( 30 SAEij TIMEij )   0i  1HUI3  (   TIME   SAE  ( SAE TIME )    

Solution for Fixed Effects
 

Standard
 

Effect Estimate 

Error 

DF t Value Pr > 

Intercept 0.6130 0.01483 363 41.32 <.0

p 

time_years -0.00922 0.003879 192 

-2.38 

0.0

sae_ongoing -0.03967 0.02604 4575 

-1.52 

0.1

time_year*sae_ongoin -0.03445 0.01116 

4429 

-3.09 0.0

Conclusions: - Effect of ongoing SAE status varies over time - Rate of change in HUI3 scores over time differs by ongoing SAE status 

-.009/year (no ongoing SAEs) 009/year (no ongoing SAEs) 

vs. 

-.04/year (ongoing SAEs; -0.00922+ -0.03445) 
A few final notes 

 Centering 

– Si lifi i Simplifies 

interpretat

ion 

– 2x2 trial? 

 Treatment A, Treatment B, Both  0 5 ti t d i d t th 0.5 = patien

t ran

dom

ized 

to the group 

 -0.5 = patient not randomized to the gr Ex. Randomized to both? A=.5; B=.5; 
A few final notes (cont’

 M d l fit M

o

d

el fit 

– Deviance statistic (-2 Res Log Likelihood)

 Mod l b i d i id i l d d

e

ls must 

be est

imate

d us

i

ng ident

ical 

data 

 Models must be nested within one another 

– Akaike Information Criteria (AIC)/Bayesian Inf

Information Criteria (AIC)/Bayesian Inf

Criteria (BIC) 

 Models must be fit to the identical set of data; not-nes Smaller information criterion is better  Raftery (1995) on BIC 

– 0-2 “weak” 

– 2-6 “positive” – 6-10 “strong” – >10 “very strong” 
Summary

 Introduction to growth curve mod Application of growth curve mode

longitudinal quality of life data frolongitudinal quality of life data fro

OPTIMA.
Suggested References 

 Fairclough DL. Design and Analysis of Quality of Life Studies in 

Trials. 

2nd ed. Boca Raton, FL: Chapman and Hall/CRC Press; 2

 Singer JD, Willett JB. Applied Longitudinal Analysis. Modeling 

Event Occurrence. 

1st ed. New York, NY: Oxford University Pre

–

http:// www.ats.uc

la.e

d

u

/stat/examp

les

/

ald a/

 UCLA Academic Technology Service Statistical Com

putin

g 

– http://www.ats.ucla.edu/stat/ 
Questions? 

 Budget Impact Analysis– 11/28/12 

- Register: Register: 

http://www.hsrd.research.va.gov/cyberseminarsupcoming-series.cfm?seriessort=hcea 

Vilija R. Joyce, MS

Health Economics Resource Center (HERC)

VA Palo Alto Healthcare System

795 Willow Road (152) 795 Willow Road (152)

Menlo Park, CA USA

(650) 493-5000 ext. 2-23852

vilija.joyce@va.gov