Modeling Utilities over T

Vilija R Joyce MS Vilija

R. Joyce, MS

January 11, 2012
Objectives

 To describe how to analyze health

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

multiple observations over time
Outline

 Introduction to types of longitudin

studies and models studies and models

 Real-world examp g le: Modeling th

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 data2. S ibl t i f ti Sensible me

t

r

ic 

for time

3. Outcomes that chan

gy 

e s

ystemat

over time

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

eq

over time

– O b ll lid 

Outcomes must 

be equally valid o

– Preserve outcome 

precision over 
Repeated Measures Mod

 Applicable to studies where...

– S bj i 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. Design and Analysis of Quality of Life Studies in Clinical Trials.

2nd ed

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

2 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?

 Ordinary least squares (OLS) regr

assumes th t b 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

ch i) an

ge over t

ime

)

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

Level 2: Between-person differences in change 

changes vary across individuals)

Time-invariant predictors (e.

g. random

group)
Level 1 Submodel

– Within-P

[

]

[

] ij

i

i ij ij

Y

=

π

+

π

(time

)

+

ε

0

1

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

[ ]

[

]

ij

i

i

ij

ij

Y

=

π

+

π

(time

)

+

ε

0

1

Level 

i i 0 00 01INTVN

ζ 0

π

=

γ

+

γ

+

j

j

j

L l

i i 1 10 11INTVN

ζ 1 π

=

γ

+

γ

+

Level 

ITVN = Interventionγ00 = Population intercep

γ01 = Deviation from popζ

0i = Residual

γ10 = Population slope

γ11 = Deviation from pop

ζ1i = Residual
Integrated Growth Curve M

[ ]

[

] ij

i

i ij ij

Y

=

π

+

π

(time

)

+

ε

0

1

Le

i i 0 00 01INTVN

ζ 0

π

=

γ

+

γ

+

i i 1 10 11INTVN

ζ 1 π

=

γ

+

γ

+ L

i i 1 10 11INTVN

ζ 1 π

γ

+

γ

+

[

]

[

ij ij i i TIMEij i 

Y

=

γ

+

γ TIME

+

γ

INTVN

+

γ

INTVN

×

+

ζ

00 10 01 11

0 

(

(

)

Fixed Effects R
Advantages of Growth Curve M

 Advantages

– D d l d h i di id l l 

Data mo

d

e

l

e

d at t

he 

i

ndi

vidua

l

leve

– Fl

e be ev be xi

b

l

e tim

e

varia

b

l

e

– 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 h lh hange in health-rel d li f 

lated quality of 

(HRQoL) p inatients 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 is 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 2007 December 2007 368 patients randomized
Outcomes

 Primary and secondary outcomes

– Ti fi AIDS Time to first AIDS-d fi i 

defining event 

– Time o s se ous dve se eve to first serious adverse 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 HR

QoL assessments over 6 2 f f ll 6.25 years o

f

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 possibl h l h ible health 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

pp ) endent 

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?

– Loss o stat st ca powe 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 t d th by time to death– 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” - 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 GL
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

[ ][ ] ij i i ij ij

Y

=

π

+

π

(time

)

+

ε

0 1 Le
Level 2: Differences in Change Acros

Level 2: Differences in Change Acros

i i 0 00 01INTVN

ζ 0

π

=

γ

+

γ

+

INTVN

ζ L

i i 1 10 11INTVN

ζ 1 π

=

γ

+

γ

+

L
I t d ti t t f l it di 

Outline



I

n

tro

duction 

to 

types o

f

longitudin

studies and models

 Real-world example: Modeling th

ch i h lth hange 

in 

health-rel t d lit f 

l

a

t

e

d quality o

f 

(HR

QoL

) p in 

patients with advance

– OPTIMA– Expl li oratory ana

lys

i

s

– 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

pp ) endent 

predictor

) on 

HRQoL?
Model for longitudinal treatmen

 What is the longitudinal effect of treatment intensif

i i ih d d

Model for longitudinal treatmen

[

]

[

ij ij i i TIMEij i 

Y

=

γ

+

γ TIME

+

γ

INTVN

+

γ

INTVN

×

+

ζ

00 10 01 11

0 

(

(

)

HRQoL

in pat

ients w

i

t

h a

dvance

d HIV?

[ ][ 

ij ij i i TIMEij 

HUI

=

γ

+

γ TIME

+

γ INTENSIFY

+

γ INTENSIFY

×

+

ζ

00 10 01 11

3

(

(

)

[

]

[

ij ij i i ij

ζ i 

γ

γ

γ

γ 00 10 01 11

0 

(

(

)

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

/* default estimation method or restrict 

model hui3 = /*2. Dependent variable, QOL instrument HUItime years /*3. Time in years*/intensify /*4. Intensification group indicator*/time_years*intensify /*5. Interaction term, time in years*intens/ solution ddfm=kr; /*6. Significance tests for all fixed effec

/g g / * Ro

ger method of de

grees of freedom*

/

random int time_years / /*7. Specifies the intercept and time as rasubject=id /*8. Specifies observations as nested withitype=un; /*9. Specifies an unstructured variance/cov

/* for the random effects*/

run;
Results

The Mixed ProcedureCovariance Parameter Estimates Covariance Parameter EstimatesCov Parm Subject Estimate Error Value Pr ZUN(1 1) id 0 07349 0 006017 12 21 0001 /* V i ti t f UN(1,1) id 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 -1753.4AIC (smaller is better) -1745.4

AICC (smaller is better) -1745.3

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

HUI3 = [(γ + γ TIME + γ INTENSIFY + γ (INTENSIFY ×TIME )]+ [ζ 

Solution for Fixed Effects

[ ] [ 

ij ij i i TIMEij 

HUI = γ + γ TIME + γ INTENSIFY + γ INTENSIFY × + ζ 

00 10 01 11 

3 ( ( )

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

pp ) endent 

predictor

) on 

HRQoL?
M d l f ff t f i 

M

o

d

e

l

for effec

t o

f ongo

ing ser

adve

rse eve

nts (SAE

)

 What is the effect of ongoing serious adverse event

HRQoL?

adve se eve ts (S )

[ ][ 

HUI ij TIMEij SAEij SAEij TIMEij i 

=

γ

+

γ

+

γ

+

γ

×

+

ζ

+

ζ

00 10 20 30

0 1 3

(

(

)

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 

/g g / * Ro

ger method of de

grees 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;
Results

HUI3 = [(γ + γ TIME + γ SAE + (γ SAE ×TIME )]+ [ζ + ζ 

Solution for Fixed Effects

[ ] [ 

HUI ij TIMEij SAEij SAEij TIMEij i 

= γ + γ + γ + γ × + ζ + ζ 

00 10 20 30 0 1 3 ( ( )

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 0.1time_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 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

ize

d

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

e

l 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

n

g ident

ica

l

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-ne 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.

 Growth curve modeling is powerf

flexible!
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

– h // l d / / l / ld / http://www.ats.uc

la.e

du

/stat/examp

les

/

ald

a

/

 UCLA Academic Technology p g Service Statistical Com

putin

g

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

 Next presentation – February 1, 2012

– Budg p y( , , , 

et Impact Analysis (Patsi Sinnott, P.T., Ph.D., 

- Register: 

http://www.hsrd.research.va.gov/cyberseminars/cata

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Vilija R. Joyce, MS

Health Economics Resource Center (HERC)

VA Palo Alto Healthcare System

795 Willow Road (152)

Menlo Park, CA USA

(650) 493-5000 ext. 2-23852

vilija.joyce@va.gov