Modern Approaches to Longitudinal Data Analysis

Modern Approaches to
Longitudinal Data Analysis
Brent J. Small, PhD
University
U
e s ty o
of Sout
South Florida,
o da, Tampa,
a pa, FL
Moffitt Cancer Center, Tampa, FL
Wefel JS, Vardy J, Ahles T, et al: International Cognition and Cancer Task Force recommendations to
harmonise studies of cognitive function in patients with cancer. The Lancet Oncology 12:703-708, 2011
These are Classic Issues
1. Identification of intraindividual change
2. Identification of interindividual differences in
intraindividual change
3. Interrelationships in behavioral change
4. Causes of intraindividual change
5 Causes of interindividual differences in
5.
intraindividual change
Baltes PB, Nesselroade JR: History and rationale of longitudinal research, in Nesselroade JR,
Baltes PB (eds): Longitudinal research in the study of behavior and development. New York, NY,
Academic Press, 1979, pp 1-39
Tailored to Cancer and Cognition
1. Does cognitive performance change among
persons with cancer?
2. Identification of interindividual differences in
intraindividual change
3 Interrelationships in behavioral change
3.
4. Causes of intraindividual change
5. Causes of interindividual differences in
intraindividual change
g
Baltes PB, Nesselroade JR: History and rationale of longitudinal research, in Nesselroade JR,
Baltes PB (eds): Longitudinal research in the study of behavior and development. New York, NY,
Academic Press, 1979, pp 1-39
Tailored to Cancer and Cognition
1. Does cognitive performance change among
persons with cancer?
2. Is there variability in rate of change in
cognition across persons?
3 Interrelationships in behavioral change
3.
4. Causes of intraindividual change
5. Causes of interindividual differences in
intraindividual change
g
Baltes PB, Nesselroade JR: History and rationale of longitudinal research, in Nesselroade JR,
Baltes PB (eds): Longitudinal research in the study of behavior and development. New York, NY,
Academic Press, 1979, pp 1-39
Tailored to Cancer and Cognition
1. Does cognitive performance change among
persons with cancer?
2. Is there variability in rate of change in
cognition across persons?
3 Are changes in different cognitive abilities
3.
related to one another?
4. Causes of intraindividual change
5. Causes of interindividual differences in
intraindividual change
Baltes PB, Nesselroade JR: History and rationale of longitudinal research, in Nesselroade JR,
Baltes PB (eds): Longitudinal research in the study of behavior and development. New York, NY,
Academic Press, 1979, pp 1-39
Tailored to Cancer and Cognition
1. Does cognitive performance change among
persons with cancer?
2. Is there variability in rate of change in
cognition across persons?
3 Are changes in different cognitive abilities
3.
related to one another?
4. Do certain events increase or decrease the
rate of change?
5. Causes of interindividual differences in
intraindividual change
Baltes PB, Nesselroade JR: History and rationale of longitudinal research, in Nesselroade JR,
Baltes PB (eds): Longitudinal research in the study of behavior and development. New York, NY,
Academic Press, 1979, pp 1-39
Tailored to Cancer and Cognition
1. Does cognitive performance change among
persons with cancer?
2. Is there variability in rate of change in
cognition across persons?
3 Are changes in different cognitive abilities
3.
related to one another?
4. Do certain events increase or decrease the
rate of change?
5. Are there factors that predict why some
people change more rapidly than others?
Baltes PB, Nesselroade JR: History and rationale of longitudinal research, in Nesselroade JR,
Baltes PB (eds): Longitudinal research in the study of behavior and development. New York, NY,
Academic Press, 1979, pp 1-39
Challenges of Longitudinal
Data
• Attrition
• Practice effects
• Unbalanced research designs
• Heterogeneity of change
1.0
Attention
Memory
Executive Functioning
Motor
Total Score
0.8
0.6
Z
Z-Score
0.4
0.2
0.0
-0.2
-0.4
06
-0.6
-0.8
0
2
4
6
8
10
12
14
Time of Measurement
Jacobs SR, Small BJ, Booth-Jones M, et al: Changes in cognitive functioning in the year after
hematopoietic stem cell transplantation. Cancer 110:1560-7, 2007
Jacobs SR, Small BJ, Booth-Jones M, et al: Changes in cognitive functioning in the year after
hematopoietic stem cell transplantation. Cancer 110:1560-7, 2007
What is Your Model of Change?
• People change at the same rate
– Repeated measures ANOVA is sufficient
• People change at different rates
– Random effects models are necessar
necessary
• Many investigators use statistical analyses that
do not match up with their view of changes in
behavior
Outline
• Repeated Measures ANOVA (rANOVA)
– Classic method, but may not be optimal
• Random Effects Models of Change
– Dealing with
ith attrition and practice effects
– Growth Mixture Models
– Latent Difference Score
• Data Harmonization Approaches
– How can we use the data we have already collected?
rANOVA – Benefits
• Readily available and widely respected
• Of the 7 papers that examined differential
change between groups, all used rANOVA
Traditional Roadblocks
Mi i D
Missing
Data
t
• rANOVA can be fitted
with incomplete data
• Anova and lmer in R
suggest any
difference can be
overcome with extra
model assumptions
S h i it Assumption
Sphericity
A
ti
• Difficult to achieve
with unbalanced
designs
• This issue has largely
been settled through
the use of correction
factors (e.g., ԑ)
• Methods
– Studies on behavioral, systems and cognitive
neuroscience from Nature,
Nature Science,
Science Nature
Neuroscience, Neuron, and The Journal of
Neuroscience were examined.
– Use of appropriate methods for longitudinal
comparisons
p
was examined
• Group
• Time
• Group
Gro p X Time
Nieuwenhuis S, Forstmann BU, Wagenmakers E-J: Erroneous analyses of interactions in
neuroscience: a problem of significance. Nature Neuroscience 14:1105-1107, 2011
Results
Common Error
• Researchers
contrast significance
levels of the two
effects, rather than
combine them.
• The claim of
differential change
may not be
statisticallyy valid
• May increase Type I
error rate
rANOVA – Summary
• Readily available and easy to learn
• Reporting the group X time interaction is critical
for establishing differential change
• But does it allow us to answer the questions
that we are most interested in?
Random Effects Models (REM)
• Can flexibly model time effects
• It is less affected by randomly missing data
• Use is increasing in psychological and medical
literature, but can still pose difficulties
Modeling change over time: An overview
Building
models
at each of At
two
levels
ofpersons)
a
At level-1 (within
person)
level-2
(between
Model the individual change
Model inter-individual differences in
hierarchy
trajectory, which describes how each
person’ss status depends on time
person
change, which describe how features of the
change trajectories vary across people
residuals for person i,
one per occasion
i j
4
4
3
2
slope for person i
(“growth rate”)
1
1
CA+
2
1
CA-
0
0
0
intercept for person i
(“initial status”)
Prrocessing Speed
Prrocessing Speed
3
1
2
Time
Yij   0i   1i (Time)ij   ij
0
1
2
Age
 0 i   00   01 Group i   0 i
 1i   10   11 Group i   1i
© Singer & Willett, page 21
For intercepts
For slopes
Resources
Practice Effects and REM
• Repeated test exposure may bias estimates of
true longitudinal changes
– Generalized practice effects
– Material specific practice effects
• Solutions
– Alternate forms
– Sequential research designs
– Including practice as a predictor in REM
Changes in Cognition after HSCT
• Examined whether cognitive functioning
improved after HSCT
• Evaluated whether changes were influenced by
practice effects or participant attrition
Jacobs SR, Small BJ, Booth-Jones M, et al: Changes in cognitive functioning in the year after
hematopoietic stem cell transplantation. Cancer 110:1560-7, 2007
Research Design
Sequential design
was employed
Group
PreHSCT
6months
post
12months
post
A
X
X
X
X
X
B
C
X
Results
Memory
1.0
No Controls
Att iti
Attrition
Practice
Attrition & Practice
Z-Score
0.8
0.6
0.4
0.2
0.0
0
6
Time of Measurement (months)
12
Conclusions
• Cognitive performance generally improved
after HSCT
• Sequential research designs are effective at
addressing practice effects
• However
However, these designs are very costly
costly, in
terms of number of participants
Growth Mixture Modeling
Objectives
• REM allow us to specify within person change
processes.
• Can we identify subgroups of patients based
upon a pattern of fatigue scores following
t t
treatment?
t?
• Can these subgroups
g
be distinguished
g
by
y
certain demographic, clinical, and psychosocial
variables?
Growth Mixture Models
• Variant
V i t off random
d
effects
ff t modeling
d li
• A categorical latent variable is incorporated to
specify sub-populations
• Used traditionally when the sub-populations
are unknown
Traditional Latent Modeling
Subjects
Overall Latent Curve
Traditional Latent Modeling
Group A Subjects
Group B Subjects
Overall Latent Curve
Growth Mixture Modeling
Group A Subjects
Group B Subjects
Overall Latent Curve
Group A Latent Curve
Group B Latent Curve
Participant Characteristics
Age
55.3 + 9.9
% CT+RT
42.5
Measurement Point
n
Fatigue Score
Baseline
245
3.1 + 2.3
2 months
230
2 3 + 2.1
2.3
21
4 months
214
2.2 + 2.1
6 months
194
2.1 + 2.1
Measures
• Composite Score of 4 FSI items
–
–
–
–
Most fatigue
Least fatigue
Average level of fatigue
Current level of fatigue
g
• Sca
Scale
e 0 to
o 10
0
• Alpha: .92
Statistical Analyses
• Linear Decline
– 1 Class
• Quadratic Decline
– 1 Class
– 2 Class
– 3 Class
Fit of Statistical Models
Free
Parameters
-2LL
Δ-2LL
BIC
ΔBIC
Linear-1
class
6
1746.20
---
3524.43
---
L + Q- 1
Class
10
1730.94
15.26
3516.94
-8.49
L+Q–2
Classes
20
1599.72
131.22
3309.55
-207.39
L+Q–3
Classes
30
1586.62
13.10
3338.39
+28.84
Model
Model Estimates
Growth Model
n
246
Estimate
Intercept
2.26 (.13)**
Li
Linear
Slope
Sl
-.14
14 (.02)**
( 02)**
Quadratic Slope
*, p <.01; ** p < .001
.05 (.01)*
Quadratic Mixture Models
4,5
4
35
3,5
3
2,5
,
2
1,5
1
0,5
0
O
Overall-Predicted
ll P di d
End of 2 Months 4 Months 6 Months
Treatment
Model Estimates
Growth Model
Growth Mixture Model
Class 1
Class 2
246
80
166
Intercept
2.26 (.13)**
.58 (.08)**
2.95 (.16)**
Li
Linear
Slope
Sl
-.14
14 (.02)**
( 02)**
-.05
05 (.02)**
( 02)**
-.17
17 (.04)**
( 04)**
.05 (.01)*
-.001 (.007)
.07 (.02)**
n
Estimate
Quadratic Slope
*, p <.01; ** p < .001
Quadratic Mixture Models
4,5
4
35
3,5
3
2,5
,
2
1,5
1
0,5
0
Overall-Predicted
Cl
Class
1 ((n = 80)
Class 2 (n = 166)
End of 2 Months 4 Months 6 Months
Treatment
Predictors of Class Membership
• Demographic
– Age, race, education, marital status, education
• Clinical
– Treatment
Treatment, disease stage ssurgery
rger ttype,
pe menopa
menopausal
sal
status, hormone therapy, BMI, Charlson comorbidity
• Psychosocial
– Fatigue
g catastrophizing,
p
g, exercise
Multivariate LR
Summary
• Growth Mixture Models allow us to identify
underlying homogeneity in heterogeneity of
change
• May be useful to identify those whose cognition
is most affected by the diagnosis of and
treatment
ea e for
o cancer.
ca ce
Latent Change Score Models
Latent Change Score Models
• Quite often we are interested in relating
changes in one variable with changes in
another
b. Lifestyle Activities
55
55
50
50
T-scorre
T-scorre
a. Cognitive Performance
45
40
45
40
Verbal Speed
Episodic Memory
Semantic Memory
Physical Activities
Social Activities
Cognitive Activities
35
35
0
2
4
6
8
Years of Follow-up
Follow up
10
12
0
2
4
6
8
Years of Follow-up
Follow up
10
12
Participants
T t l
Total
S
Sample
l 1
S
Sample
l 2
952
446
506
68 6 + 6.7
68.6
67
68 9 + 5.8
68.9
58
68 3 +7.5
68.3
+7 5
Gender (% Female)
63.4
59.6
66.8*
Education (M + SD)
14.2 + 3.1
13.4 + 3.1
14.8 + 3.1
N & Average Followup
n
M Yrs
n
M Yrs
n
M Yrs
Wave 2
714
3.1
320
2.9
394
3.2
Wave 3
569
6.3
241
5.9
328
6.6
Wave 4
171
8.9
171
8.9
Wave 5
126
12.28
126
12.28
--
--
Baseline n
Age (M + SD)
Cognitive Performance
Measures
• Processing Speed
– Lexical decision time
– Semantic decision time
• Episodic Memory
– Word recall
– Story recall
• Se
Semantic
a c Memory
e oy
– Fact recall
– Vocabulary
Bivariate Latent Change Score
Models
Lifestyle Activities
x0*
FXT1
x0
xs*
xs
x0
xs
x
x
xy
FXT2
XT2
x
xy
FXT3
…
XT3
…
YT3
…
FYT3
…
1
ys
ys*
y0*
y0
ys
y0
y
YT2
yx
y
y
FYT1
yx
FYT2
Cognitive Performance
McArdle JJ, Hamagami F: Latent difference score structural models for linear dynamic analyses
with incomplete longitudinal data, in Collins LM, Sayer AG (eds): New methods for the analysis of
change. Washington, DC, American Psychological Association, 2001, pp 139-175
Testable Models
•
•
•
•
No coupling
Activities predicting cognitive performance
Cognitive performance predicting activities
Dual coupling
• Models are independent of age, gender, years
off education
d
i and
d self-reported
lf
dh
health
l h at
baseline
No Coupling
Lifestyle Activities
x0*
FXT1
x0
xs*
xs
x0
xs
x
x
xy
FXT2
XT2
x
xy
FXT3
…
XT3
…
YT3
…
FYT3
…
1
ys
ys*
y0*
y0
ys
y0
y
YT2
yx
y
y
FYT1
yx
FYT2
Cognitive Performance
Lifestyle Activities Predicting
Cognition
Lifestyle Activities
x0*
FXT1
x0
xs*
xs
x0
xs
x
x
xy
FXT2
XT2
x
xy
FXT3
…
XT3
…
YT3
…
FYT3
…
1
ys
ys*
y0*
y0
ys
y0
y
YT2
yx
y
y
FYT1
yx
FYT2
Cognitive Performance
Cognition Predicting Lifestyle
Activities
Lifestyle Activities
x0*
FXT1
x0
xs*
xs
x0
xs
x
x
xy
FXT2
XT2
x
xy
FXT3
…
XT3
…
YT3
…
FYT3
…
1
ys
ys*
y0*
y0
ys
y0
y
YT2
yx
y
y
FYT1
yx
FYT2
Cognitive Performance
Dual Coupling
Lifestyle Activities
x0*
FXT1
x0
xs*
xs
x0
xs
x
x
xy
FXT2
XT2
x
xy
FXT3
…
XT3
…
YT3
…
FYT3
…
1
ys
ys*
y0*
y0
ys
y0
y
YT2
yx
y
y
FYT1
yx
FYT2
Cognitive Performance
Results
Summary
• Models suggested that cognitive activities
buffer cognitive decline, but reverse causation
was present
• Latent Change Score models allow us to
examine how processes change together
• Leading and lagging relationships can be
posed, where experimental manipulation may
be difficult
Integrative Data Analysis
What is Integrative Data
Analysis?
• Similar to a meta-analysis, but with raw data
• Information from multiple samples is combined
in one data analysis
• There are numerous advantages, but also
challenges to this method of data analysis
Advantages
• Increased
frequencies of low
base rate outcomes
base-rate
• Increased statistical
power
• Replication
• Broader
psychometric
assessment of
constructs
• Increased sample
heterogeneity
Curran, P. J. & Hussong, A. M (2009). Integrative data analysis: The simultaneous
analysis of multiple data sets. Psychological Methods, 14, 81-100
Challenges
• Heterogeneity due to
sampling
• Heterogeneity due to
measurement
• Heterogeneity due to
geographic region
• Heterogeneity due to
study design
• Heterogeneity due to
history
Curran, P. J. & Hussong, A. M (2009). Integrative data analysis: The simultaneous
analysis of multiple data sets. Psychological Methods, 14, 81-100
Latent Variables as an Approach
• “Structural equation models do not require all
variables to be measured on all individuals
under all conditions
conditions” (McArdle,
(McArdle 1994)
• Absent data is treated as incomplete or missing
• Sensitivity analyses can be conducted that
evaluate assumptions of incompleteness
Latent Variables as Measures
Verbal Ability: Study 1
Verbal Ability: Study 2
COWA
Verbal
Ability
Boston Naming
Vocabulary
COWA
Verbal
Ability
Boston Naming
Vocabulary
Illustration
McArdle JJ, Grimm KJ, Hamagami F, et al: Modeling Life-Span Growth Curves of Cognition Using
Longitudinal Data With Multiple Samples and Changing Scales of Measurement. Psychological
Methods 14:126-149, 2009
Illustration
McArdle JJ, Grimm KJ, Hamagami F, et al: Modeling Life-Span Growth Curves of Cognition Using
Longitudinal Data With Multiple Samples and Changing Scales of Measurement. Psychological
Methods 14:126-149, 2009
Summary
• Integrative data analysis is receiving
considerable attention by scientists and
funding agencies
• Groups like the ICCTF may be in a strong
position to advocate for these projects and
bring
b
g together
oge e interested
e es ed sc
scientists
e ss
Conclusions
• Test the models that reflect the underlying
processes
• Random effects models allow longitudinal data
to be treated flexibly and innovatively
• Make friends with your local statistician
Acknowledgements
•
•
•
•
•
•
•
•
Paull JJacobsen,
P
b
M
Moffitt
ffitt C
Cancer C
Center
t
Heather Jim, Moffitt Cancer Center
Roger
g Dixon, University
y of Alberta
Christopher Hertzog, Georgia Institute of Technology
Jack McArdle, University of Southern California
Cathy McEvoy
McEvoy, University of South Florida
Funding
– ACS RCS 01-070-01 (Booth-Jones, PI)
– R01 CA82822 (Jacobsen, PI)
– R03 AG024082 (Small, PI)
– R37 AG008235 (Victoria Longitudinal Study: Dixon, PI)
Contact Information:
– [email protected]