M d li Utiliti T

M

o

d

eling Utilities over T

Vilija R. Joyce, MS

April 28, 2010 April 28, 2010
Obj ti ec ves

 T d ib h l h l h To describe how to analyze health-r

quality of life (HRQoL) data with 

multiple observations over time
O tli u ne

 Introduction to longitudinal modeling Introduction to longitudinal modeling

– Study design– Longitudinal models Longitudinal models

 Real-world example: Modeling the ch

health-related quality of life ( related quality of life (HRQoL) 

patients with advanced HIV (OPTIMA 

– OPTIMA– Exploratory analysis– Model
A k th A di ( hit b 

A

s

k the 

A

udience 

(

whit

e

boa

 Wh t t di h b i l d ith 

Wh

a

t s

t

udies 

have you 

been 

invo

lve

d with 

have measured change (in HRQoL or othe

outcomes)?
St d D i Study Design

 Checklist for designing health Checklist for designing health-related quality 

related quality 

(HRQoL) studies

1. Rationale for studying HRQoL2. Explicit research objectives3. Strategies to limit the exclusion of subjects4. Rationale for timing of assessments and off Rationale for timing of assessments and off-st

st

5. Rationale for instrument selection6. Minimizing bias and missing data7. A l ti l Analytic planFairclough DL. Design and Analysis of Quality of Life Studies in Clinical Trials. 1st ed. B

Chap ; man and Hall/CRC Press; 2002.
O tli u ne

 Introduction to longitudinal modeling Introduction to longitudinal modeling

– Study design– Longitudinal models Longitudinal models

 Real-world example: Modeling the cha

health-related quality of life ( related quality of life (HRQoL) 

patients with advanced HIV (OPTIMA 

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

Longitudinal Studies

1. M lti l f d t M

ulti

p

le waves o

f

d

a

t

a

2. Sensible metric for time3. Outcomes that change systematic

over time

– Precision of outcomes must be equ

over time

– Outcomes must be equally valid ov– Preserve outcome precision over ti

Preserve outcome precision over ti
R t dM M d 

Repea

t

e

d

Measures 

M

o

d

e

 A li bl di h Applicable to studies w

here...

– Subjects are experiencing the same 

condition

– Assessments corres

pond to an event o

intervention phase

– Assessments are limited (< 4) with tim

Assessments are limited (< 4) with tim

conceptualized as a categorical variab
R t d M M d l ( 

Repea

t

e

d

Measures 

M

o

d

e

ls 

(co

F i l h DL D i d A l i f Q lit f Lif St di i Cli i l T i l 1 t d B F

aircloug

h DL. Design and

Analysis of Quality of Life Studies 

in Clinical

Trials. 1st e

d. Bo

Chapman and Hall/CRC Press; 2002.
Repeated Measures Models 

Drawbacks

 A t tt k l h Assessmen

ts ma

y no

t

t

a

ke p

lace w

hen 

scheduled.
Repeated Measures Models 

Drawbacks (cont’d)

 Timing of observations for 1 site over 1 year in the OPTIMA trial
Hi t f G th C M 

Hi

s

tory o

f

Growth

Curve 

M

 1980s = development of statistical mod

1980s

= development of statistical mod

 Various names

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

 Describe changes in height and weight 

function of a

ge in children.
Wh N t U OLS? Why 

N

o

t

Use OLS?

 O di l (OLS) 

O

rdinary 

least squares (OLS) regre

assumes that observations are 

independent

 Biased standard errors Biased standard errors Growth curve models can handle 

correl d ate

d errors
D fi iti f G th C M 

D

efi

nition o

f a 

Growth

Curve 

M

 Change over time in a phenomenon of interest (e g qua

Change over time in

a phenomenon of interest (e.g. qua

life) at both the individual and aggregate levels.

 2 types of questions about change: 2 types of questions about change:

Level 1: Within-person change (how individuals 

change over time)

Time

-varying predictors (e g days since varying predictors (e.g. days since

randomization)

Level 2: Between-person differences in change (h

changes vary across individuals) changes vary across individuals)Time-invariant predictors (e.g. randomizgroup)
L l1 eve Sb dl u mo el – Within-Pe

[ ] [ ] ij i i ij ij Y = π +π (time ) + ε 0 1

Yij = The outcome of interest (for subject i at time j 

[ ] [ ] j j j

π0i = Intercept, or subject i’s true value of QoL at baπ1i = Slope, or subject i’s rate of change in true QoL

εij = Residual or random measurement error
L l2S b d l Leve

l

2

S

u

bmo

d

e

ls 

– B t e

tweenP

[

]

[

] ij

i

i ij ij

Y

=

π

+

π

(time

)

+

ε

0

1

Level 1 m

i i 0 00 01INTVN

ζ 0

π

=

γ

+

γ

+

i i 1 10 11INTVN

ζ 1 π

=

γ

+

γ

+

Level 2 

ITVN = Interventionγ00 = Population intercept

γ01 = Deviation from popula

ζ0i = Residualγ10 = Population slope

γ11 = Deviation from popula

ζ1i = Residualζ1i
I t t d G th C M 

I

n

tegra

t

e

d

Growth

Curve 

M

Y

[

(

)

]

[

] ij

i

i ij ij

Y

=

π

+

π

(time

)

+

ε

0

1

i i 0 00 01INTVN

ζ 0

π

=

γ

+

γ

+

Leve

i i 0 00 01INTVN

ζ 0

π

γ

+

γ

+

i i 1 10 11INTVN

ζ 1 π

=

γ

+

γ

+ Leve

[ ][ 

ij ij i i TIMEij i 

Y

=

γ

+

γ TIME

+

γ INTVN

+

γ INTVN

×

+

ζ

+

00 10 01 11

0 

(

(

)

Fixed Effects Ran
Ad t f G th C M 

Advan

tages o

f

Growth

Curve 

M

 Advantages

– Data modeled at the individual level– Flexible time variable– Easy handling of missing data Easy handling of missing data– Easily incorporate data nesting/cluste
O tli u ne

 Introduction to longitudinal modeling Introduction to longitudinal modeling

– Study design– Longitudinal models Longitudinal models

 Real-world example: Modeling the cha

health-related quality of life ( related quality of life (HRQoL) patients with advanced HIV (OPTIMA 

– OPTIMA– Exploratory analysis– Model
OPTIMA

 Effective antiretroviral therapy (ART) improves survival in HIV-inf

pati t en s.

 The optimal management strategy for advanced HIV patients infecte

drug resistant HIV is unclear. 

 CSP #512 Options in Management with CSP #512, Options in Management with Antiretrovirals Antiretrovirals 2x2 open randomized study UK, Canada, and US June 2001 December 2007

Antiretroviral th

intensificatio

June 2001 - December 2007

 368 patients randomized Control

(≤ 4 drugs)

Exp

(≥ 

12 weekantiretroviral therapyi i

Control Neither 

Experiment 1 

interruption
R h Q ti Researc

h

Questions

 Wh t i th l it di l ff t f t t 

Wh

a

t

is the 

longitudina

l effec

t o

f

trea

tm

interruption and ART intensification the

on HRQ L i lti HRQ

o

L

in a multi

-d i t t HIV dru

g res

i

s

tan

t HIV

infected patient population?

 Does HRQoL improve for patients rand

to the interruption group during the interruption period?
O t u comes

 Pi d d r mary and secondary outcomes

– Time to first AIDS-defining event or – Time to first serious adverse event

 Other sociodemographic and clinic

Other sociodemographic and clinic

(e.g. age, sex, transmission risk gro

et ) c.
O t ( t’d) O

u

tcomes 

(cont’d)

 Health

-Related Quality of Life ( Related Quality of Life

(HRQoL

– Baseline, 6, 12, 24, every 12 weeks thereaf– Health Utilities Index Mark 3 

( ) HUI3

)

– EQ-5D – Visual analog scale– Medi l d l h dica

l Outcomes Study HIV Hea

l

t

h Surv

– Standard gamble (SG) (US patients only)– Time trade Time trade

-off (TTO) (US patients only) off (TTO) (US patients only)

– 5,141 HRQoL assessments over 6.25 years 

follow-up (median 3.2 years)
HRQoL Outcome: Health Utilities I

Outcome: Health Utilities I

Mark 3 (HUI3)

 P f / tilit Preference/utility-b di t t based instrument 8 attributes, each with 5–6 levels 972,000 possible health states. Weights are estimated with valuatio

Weights are estimated with valuatio

from a sample of adults in Hamilton

Ontario Canada Ontario, Canada

 Utilities range from -0.36 to 1
O tli u ne

 Introduction to longitudinal modeling Introduction to longitudinal modeling

– Study design– Longitudinal models Longitudinal models

 Real-world example: Modeling the ch

health-related quality of life ( related quality of life (HRQoL

patients with advanced HIV (OPTIM

– OPTIMA– Exploratory analysis– Model
A k th A di A

s

k the 

A

udience

 Wh i i i d bl ? Why 

is m

iss

ing 

data a problem

?
Mi i D t Missing Data

 Why is missing data a problem? Why is missing data a problem?

– Loss of statistical power– Bias of estimates Bias of estimates

 At baseline, 4% of HUI3 assessments 

OPTIMA trial were missing. OPTIMA trial were missing.

 Plots to describe missingness

– Ave ge ra QoL sco es by e o d op res by time of drop-ou– Average QoL scores by time to death– Average QoL scores by g % missing over 
Mean HUI3 by Visit Week, Patients Grou

Mean HUI3 by Visit Week, Patients Grou

When They Were Lost to Follow-U
Mi i D t Missing Data

 Other patterns/mechanisms? Other patterns/mechanisms?

– Do baseline characteristics predict drop-out?

 Proportional hazards model (PROC PHREG) Proportional hazards model (PROC PHREG)

– Are “skippers” - patients with intermittent Q

assessments – different from those with few 

assessments?

 Regressions (PROC REG)

– Are certain clinical events associated with “m

Are certain clinical events associated with “m

QoL assessments?

 Generalized linear mixed model ( 

PROC GLIM
Mi i D t Missing Data

 What next? What next?

– Serious adverse events predicted missing HR

data in the OPTIMA trial. data in the OPTIMA trial.

– BUT, serious adverse events were distribute

equally among the randomization groups.

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

i bl ?gnorable?

 Consider imputation as part of your sensitivity  Fairclough 2002, Ch. 7, Multiple Imputation 2002, Ch. 7, Multiple Imputation
Person-P i d D t (L Period Data (Long-F 

or

 Each subject has multiple records one per ass

Each subject has multiple records, one per ass

ID HUI3 MONTHS

FROM

MALE

Person-Period (Long)

ID HUI3_ 

MONTH 0

HUI3_MONTH 1

HUI3MON

Person-Level (Wide)

RAND

1 .80 0 11 .85 1 11 .97 2 1

MONTH_0 MONTH_1 MON

1 .80 .85 .97 2 .65 .77 .75 3 .99 . . 

1 .97 2 12 .65 0 02 .77 1 02 .75 2 0

 Reshape from wide to long? 

– UCLA Academic Technology Service

3 .99 0 1
Level 1: Within-Person Change over 

[ ] [ ] ij i i ij ij

Y

=

π

+

π

(time

)

+

ε

0 1 Leve

Figure 1. Empirical growth plots for select OPTIMA patients. Smooth 

nonparameti t j t i i d tric trajectories superimpose

d. 
Level 2: Differences in Chan

g 

e Across 

i i 0 00 01INTVN

ζ 0

π

=

γ

+

γ

+

i i 1 10 11

INTVN

ζ 1 π

=

γ

+

γ

+

Leve

1i 10 11

ζ 1i γ

γ

Control Intervention 

1

QOL 

.5

0

Weeks post randomization

B 6 12 24 36 48 B 6 12 24 36 48
O tli u ne

 Introduction to longitudinal modelin

Introduction to longitudinal modeling

– Study design– Longitudinal models Longitudinal models

 Real-world example: Modeling the c

in health in health-related quality of life ( related quality of life (HRQ

patients with advanced HIV (OPTIM

– OPTIMA– Exploratory analysis– Model
F R h Q ti t M 

From 

Researc

h

Question 

to 

M

 Wh t i th l it di l ff t f t t t Wh

a

t

is the 

longitudina

l effec

t o

f

trea

tmen

t

interruption and ART intensification therapie

HRQoL in a multi HRQoL in

a multi

-drug resistant HIV drug resistant HIV

-1 infec

1 infec

patient population?

 Does HRQoL improve for patients randomize

Dependent variable? HUI3

Does HRQoL improve for patients randomize

interruption group during the interruption per

Independent variables? Time

Treatment Interruption

T t t I t ifi ti

Both Interruption aFirst quarter of the 

Trea

tmen

t

I

n

tensification
OPTIMA M d l OPTIMA

M

o

d

e

l

[ ] [ 

ij ij i i TIMEij i 

Y

=

γ

+

γ TIME

+

γ INTVN

+

γ INTVN

×

+

ζ

+

ζ

00 10 01 11

0 

[(

(

)] [ 

ij ij i i TIMEij i 

Y

γ

+

γ TIME

+

γ INTVN

+

γ INTVN

×

+

ζ

+

ζ

00 10 01 11

0 

(

(

)

Dependent variable? HUI3Independent variables? Time

Treatment Interruption

Both Interruption and First quarter of the tr

INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

TIME INTERRUPT INTENSIFY BOTH QUARTE

HUI

β

β

β

β

β

β

β

β

β

⎢⎢⎡

+

×

+

×

+

×

+

+

+

+

+

= ( 1) ( 1) ( 

( ( ) ( ) ( ) ( ) ( 

3

0 1 2 3 4 5

Treatment Intensification

ij 

BASELINEHUI

HUI INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

ββ

β

β

⎢

⎢⎣

+

=

+

×

+

×

+

×

( 3)

3 ( 1) ( 1) ( 

9

6 7 8

0.5 = -0.5 

0.5 
OPTIMA M d l OPTIMA Model – O h S ifi 

Other Specifica

1. I i h b li l Ignoring the baseline value2. Exp g ressing all values as a diffe

from baseline

3. Including the baseline value as 

Including the baseline value as covariate
OPTIMA Model 

– SAS co

ij 

BASELINEHUI

INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

TIME INTERRUPT INTENSIFY BOTH QUART

HUI

β

β

β

β

β

β

β

β

β

β

⎢⎢⎢⎣⎡

+

+

×

+

×

+

×

+

+

+

+

+

=

( 3)

( 1) ( 1) ( 

( ( ) ( ) ( ) ( ) ( 

3 6 7 8

0 1 2 3 4 5

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

/* default estimation method or restrict max 

where baseline=0; /*2. Using follow-up data only; baseline data 

d l h i3 /*3 D d t i bl QOL i t t HUI3*/

β BASELINEHUI 

⎢⎣

+ ( 3) 9

mo

d

e

l

h

ui3 = /*3. Depen

den

t var

i

able, QOL

ins

trumen

t HUI3*/

t /*4. Time in years*/sti_c /*5. Interruption group indicator, centered*/mega_c /*6. Intensification group indicator, centeredboth_c /*7. Interruption + intensification group inditime q1 time q1

/ 8. * First quarter of follow First quarter of follow-up indicator up indicator /*

/

sti_c*time_q1 /*9. Interaction term, 5 and 8*/ mega_c*time_q1 /*10. Interaction term, 6 and 8*/ both_c*time_q1 /*11. Interaction term, 7 and 8*/ dbase_hui3 /*12. Baseline value, deviation from the mean / solution ddfm=kr; /*13. Significance tests for all fixed effects 

/* Roger method of degrees of freedom*/

random int t / /*14. Specifies the intercept and time as randsubject=newsubj_id /*15. Specifies observations as nested within 

type=un; /*16. Specifies an unstructured variance/covar

/* for the random effects*/
OPTIMA Model – SAS code 

( 

co

ij 

BASELINEHUI

INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

TIME INTERRUPT INTENSIFY BOTH QUART

HUI

β

β

β

β

β

β

β

β

β

β

⎢⎢⎢⎣⎡

+

+

×

+

×

+

×

+

+

+

+

+

=

( 3)

( 1) ( 1) ( 

( ( ) ( ) ( ) ( ) ( 

3 6 7 8

0 1 2 3 4 5

estimate "Difference between sti & no sti trend before 3 months" sti_c 1 sti_c*tiestimate "Difference between mega & no mega trend before 3 months" mega_c 1 mega_estimate "Difference between both & no both trend before 3 months" both_c 1 both_run;

β BASELINEHUI 

⎢⎣

+ ( 3) 9

run;
Results

The Mixed Procedure

Covariance Parameter Estimates

Cov Parm Subject EstimateUN(1,1) newsubj_id 0.02048 /* Variance estimate for intercept*/

UN(2,1) newsubj_id -0.00037 /* Covariance estimate for intercept 

UN(2,2) newsubj_id 0.002368 /* Variance estimate for slope*/

Residual 0.02956 / Residual 0.02956 /* Level 1 residual Level 1 residual /*

Fit Statistics

-2 Res Log Likelihood -1854.4

AIC (smaller is better) -1846.4AICC (smaller is better) -1846.4BIC (smaller is better) -1831.1
Results ( ) cont’d)

ij 

BASELINEHUI

INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

TIME INTERRUPT INTENSIFY BOTH QUART

HUI 

β

β β β

β β β β β β

⎢⎢⎢⎣⎡++ × + × + × + + + + + = ( 3) ( 1) ( 1) ( 

( ( ) ( ) ( ) ( ) ( 

3 96 7 8 0 1 2 3 4 5

Solution for Fixed Effects

Standard

Effect Estimate Error DF t Value Pr > |t| Effect Estimate Error DF t Value Pr > |t|Intercept 0.6288 0.009959 407 63.13 <.0001 /* 

t -0.01710 0.004214 199 -4.06 <.0001 /* sti_c -0.02380 0.01921 354 -1.24 0.2162 /* 

mega_c -0.01248 0.01848 358 -0.68 0.5000 /* 

both_c -0.02958 0.03832 354 -0.77 0.4406 /* time_q1 -0.01426 0.009555 3991 -1.49 0.1357 /* sti_c*time_q1 -0.02640 0.01870 3983 -1.41 0.1580 /* 

mega c*time q1 0 003552 0 01805 3975 0 20 0 8440 /* mega c*time q1 0.003552 0.01805 3975 0.20 0.8440 /* both_c*time_q1 0.04693 0.03739 3983 1.25 0.2096 /* 

dbase_hui3 0.6801 0.02849 321 23.87 <.0001 /* 
Results ( ) cont’d)

ij 

BASELINEHUI

INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

TIME INTERRUPT INTENSIFY BOTH QUART

HUI 

β

β β β

β β β β β β

⎢⎢⎢⎣⎡++ × + × + × + + + + + = ( 3) ( 1) ( 1) ( 

( ( ) ( ) ( ) ( ) ( 

3 96 7 8 0 1 2 3 4 5

Estimates

Standard

Label Estimate Error DF Difference between sti & no sti trend before 3 months -0.05019 0.02280 648 Difference between mega & no mega trend before 3 months -0.00893 0.02193 655 Difference between both & no both trend before 3 months 0.01734 0.04553 651 
Results (cont’d)

ij 

BASELINEHUI

INTERRUPT QUARTER INTENSIFY QUARTER BOTH Q

TIME INTERRUPT INTENSIFY BOTH QUART

HUI

β

β

β

β

β

β

β

β

β

β

⎢⎢⎢⎣⎡

+

+

×

+

×

+

×

+

+

+

+

+

=

( 3)

( 1) ( 1) ( 

( ( ) ( ) ( ) ( ) ( 

3

9

6 7 8

0 1 2 3 4 5

Effect Estimate Error DF t Value Pr > |t|Intercept 0.6288 0.009959 407 63.13 <.0001 /*

β0 

t -0.01710 0.004214 199 -4.06 <.0001 

/* β1 

⎢⎢⎢⎣⎡

++ − + − + −

+ − + − + − − + − − + −

=

(0.6801)

( 0.02640)(0.5)(1) (0.003552)( 0.5)(1) (0.04693)( 0.25)(1)

(0.6288 ( 0.01710) ( 0.02380)(0.5) ( 0.01248)( 0.5) ( 0.02958)( 0.25) ( 0.01426

HUI3ij

Interruption groupN i t ti

/

β1

sti_c -0.02380 0.01921 354 -1.24 0.2162 /*

β2 

mega_c -0.01248 0.01848 358 -0.68 0.5000 /*

β3 

both_c -0.02958 0.03832 354 -0.77 0.4406 /*

β4 

time_q1 -0.01426 0.009555 3991 -1.49 0.1357 /*

β5 

sti c*time q1 -0.02640 0.01870 3983 -1.41 0.1580 /* β6 

Non interruption group

⎢⎢⎢⎣⎡

+

+ − − + − + −

+ − + − − + − − + − − + −

=

(0.6801)

( 0.02640)( 0.5)(1) (0.003552)( 0.5)(1) (0.04693)( 0.25)(1)

(0.6288 ( 0.01710) ( 0.02380)( 0.5) ( 0.01248)( 0.5) ( 0.02958)( 0.25) ( 0.0142

HUI3ij 

sti c time q1 0.02640 Difference in HUI3 score interruption vs no interruption gr

0.01870 3983 1.41 0.1580

/

β6 

mega_c*time_q1 0.003552 0.01805 3975 0.20 0.8440 /*

β7 

both_c*time_q1 0.04693 0.03739 3983 1.25 0.2096 /*

β8 

dbase_hui3 0.6801 0.02849 321 23.87 <.0001 /* 1.252567 - 1.302767 = -0.0502 β9 */

Difference in HUI3 score, interruption vs. no interruption gr

first quarter of follow-up?

Standard

Label Estimate Error DF Difference between sti & no sti trend before 3 months -0.05019 0.02280 648 Difference between mega & no mega trend before 3 months -0.00893 0.02193 655 Difference between both & no both trend before 3 months 0.01734 0.04553 651 
Summary

 I d i h d l

Introduction to growth curve model

 App g 

lication of growth curve model

actual longitudinal quality of life dafrom OPTIMA from OPTIMA.

 Growth curve modeling is powerfu

fl ibl ! flexible!
S t dR f Suggested References

 S o , Joyce V , e G. innott PL, Joyce VR, Barnett PG. Preference Measurement in Eco

Analysis. Guidebook. Menlo Park CA. VA Palo Alto, Health EconResource Center; 2007. 

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

Trials. 1st ed. Boca Raton, FL: Chapman and Hall/CRC Press; 2002

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

Event Occurrence. 1st ed. New York, NY: Oxford University Press

– http p ://www.ats.ucla.edu/stat/examples/alda/

 UCLA Academic Technology Service Statistical Computing

– http://www.ats.ucla.edu/stat/
Q ti ? uestions?

 VA employees: VA employees:

http://vaww.infoshare.va.gov/sites/HERC

 Next presentation – May 12, 2010

– Paul Barnett, Ph.D.

– “How can Cost Effectiveness Analysis be Made 

Relevant to US Health Care?”

Vilija R. Joyce, MS

Health Economics Resource Center (HERC)

VA Palo Alto Healthcare System

795 Willow Road (152)

Menlo Park, CA USA

(650) 493-500 ext. 23852

vilij j @ ilija.joyce@va.gov