Separation of Longitudinal
Change from Re-Test Effect
using a Multiple-Group
Latent Growth Model
Richard N. Jones, John N. Morris, Adrienne
N. Rosenberg, Research and Training
Institute, Hebrew Rehabilitation Center for
Aged, Research and Training Institute,
Boston MA
Data acquisition and research supported by the NIA and NINR
Objective
• Describe a commonly occurring challenge
in longitudinal studies of cognitive aging:
the re-test effect
• Present a general latent variable modeling
framework for statistically separating aging
and re-test effects
• Demonstrate the modeling approach in
real data (ACTIVE Cognitive intervention
study)
Hypothesized Longitudinal Course
50
45
40
35
30
0
1
2
Time
3
Hypothesized and Observed Longitudinal Course
55
50
45
40
35
30
0
1
2
Time
3
Bias in Estimate of Baseline Level and Change
55
50
45
40
35
30
0
1
2
Time
3
Hypothesized Longitudinal Course
55
Retest + Aging
Effect
Performance
50
Aging +
Residual
Retest
45
40
35
30
0
1
2
Time
3
Latent Growth Model
Performance
50
45
40
35
30
0
1
2
Time
yij  1i   2i  TIMEi   ij
1i  1   1i
 2i   2   2i
3
1
2
3
4
y1 y2 y3 y4


Latent Growth Curve Model for Linear Change
1
2
3
4
*
*
*
*
y1 y2 y3 y4
[0]
1
*
1
[0]
1
1
1
2
3


[1=*]
[0]
[0]
*
[2=*]
*
Hypothesized Longitudinal Course
55
Performance
50
45
40
35
30
0
1
2
3

Time
yij  1i   2i  TIMEi  3i  RETESTi   ij
1i  1   1i
 2i   2   2i
 3i   3   3 i
1
2
3
4
y1 y2 y3 y4


Latent Growth Curve Model for Linear Change
with second intercept (learning factor)

[3=*]
?
1
1 1
1
2
3
4
*
*
*
*
y1 y2 y3 y4
[0]
1
*
1
[0]
1
1
1
2
3


[1=*]
[0]
[0]
*
[2=*]
*
Adding Background and Explanatory Variables
yij  1i   2i  TIMEi  3i  RETESTi   ij
1i  1   iq  xq   1i
 2i   2   iq  xq   2i

3i   3   iq  xq   3i
1
2
3
4
y1 y2 y3 y4





x
x
x
Background
Variables
Example: ACTIVE
• Advanced Cognitive Training for Vital and
Independent Elderly
• Six sites (AL, IN, MA, MI, MD, PA)
• Random assignment to one of four
intervention arms, 4-group pre-post design
– Speed of Processing, Memory, Logical
Reasoning, No Training Control
• Healthy older adults (n=2,428) aged 65-83
Outcome Measure
• Speed of Processing Composite
– Ball, et al. Jama, 2002; 288:2271-81.
– Regression-method factor score for multiple
speeded tests
– Based on minimum stimulus duration at which
participants could identify and localize
information with 75% accuracy, under different
cognitive demand conditions
– Lower is better (faster speed of processing)
150
100
50
0
-5
0
5
Speed of Processing Composite
Measurement Schedule
Assessment
Study Year
Baseline
0
(intervention)
Post-Test
0.23
Follow-up 1
1.00
Follow-up 2
2.00
Speed as a Function of Age
(Baseline only, All Participants)
2
1
0
-1
-2
65
75
Age
85
Conflicting Estimates of Change
Model
Estimated
Annual Change
Baseline age-diff.
Repeated Measures†
Post-Test Part
FU1 -> FU2
†
speed-trained subjects excluded
+0.19
-3.80
-0.01
Multiple Group LGM
• Use age as a cohort indicator
• Model change as a function of age rather
than study time
• Assume (initially) no cohort differences in
– growth
– re-test effects, and the
– influence of background variables
Cross-Sequential Cohort Design
Year of Obs '95 '96 '97
Observation
1
2
3
-----------------------Cohort
Age
1
65 66 67
2
66 67 68
3
67 68 69
Hypothesized and Observed Longitudinal Course
60
50
40
30
20
hypothesized
observed
10
65
66
67
Age
68
69
Mean Scores On Repeat Testing
(Non-Speed Trained Group)
2
1
0
-1
-2
0
1
2
Study Year
GEE model using ordinal time adjustment for baseline age
Parameterization of Multiple Group LGM
1
baseline
12-week
post-test
2
(aget )
year 1
follow-up
3
(aget )
(aget )
y1 y2 y3
1
(4)

[ 1](1)
year 2
follow-up
4
(aget )
y4
1
1
1
0.23 *
*
*
*



[ 2](2)

[ 3](3)
NOTE: "Age" is age at baseline assessment.
non-Speed trained subjects only.
Model relevant to
Parameterization of Multiple Group LGM
=
y1
y2
y3
y4
1
2
3
1
age-65
0
1
age-65 0.23
1
age-64 0.23
1
age-63 0.23
where yt (t=1,2,3,4) refer to speed composite scores at
baseline, 12-week post-test, 1-year follow-up and 2-year
follow-up, and age is age at baseline assessment.
Parameterization of Multiple Group LGM
=
y1
y2
y3
y4
1
2
3
1
age-65
0
1
age-65 0.23
1
age-64
*
1
age-63
*
where yt (t=1,2,3,4) refer to speed composite scores at
baseline, 12-week post-test, 1-year follow-up and 2-year
follow-up, and age is age at baseline assessment.
Model 1: Maximum Likelihood Estimation, Complete
Sample Analysis Assuming MAR; Excluding those who
received speed training (4 y’s, 3 ’s)
N=1,801; Number of groups = 19 (n=31 to 131)
Model 2(df), P
277.353 (218) P=.004
CFI, TFI
0.985, 0.992
RMSEA (90% CI)
0.054 (.032-.072)
Model Part
Estimate SE
P
Time Steps for Recall Effect
post-test
0.23 --first annual follow-up
0.28
(.01) <.001
second annual follow-up
0.34
(.02) <.001
Latent Variable Means/Intercepts
Baseline
-1.83 (0.10) <.001
Age-related change
+0.18 (0.01) <.001
Retest effect
-3.01 (0.22) <.001
Regressions
Re-test effect on Baseline
0.44 (0.07) <.001
Age-related change on Baseline -0.01 (0.00) <.001
Model 2: ...adding educational attainment (years of
education centered at grade 12) to model
Model 2(df), P
335.963 (291) P=.04
CFI, TFI
0.976, 0.984
RMSEA (90% CI)
0.057 (.016-.083)
Model Part
Estimate SE
P
Time Steps for Recall Effect
post-test
0.23 --first annual follow-up
0.29
(.02) <.001
second annual follow-up
0.33
(.02) <.001
Latent Variable Means/Intercepts
Baseline
-1.50 (0.15) <.001
Age-related change
+0.18 (0.02) <.001
Retest effect
-2.88 (0.32) <.001
Regressions
Re-test effect on Baseline
Age-related change on Baseline
Baseline on years of education
Re-test on years of education
Age-related change on education
0.51
-0.01
-0.19
0.02
0.00
(0.12)
(0.01)
(0.05)
(0.07)
(0.00)
<.001
0.061
<.001
0.766
0.394
Results: Cohort-Specific and Model Implied
Trajectories
Speed compsite
(SD units marked)
2
0
-2
-4
65
70
75
80
age
Model-Implied Age-Related Change
Observed Cohort-Specific Trajectories
Age differences (baseline)
85
Hypothesized Longitudinal Course
55
Retest + Aging
Effect
Performance
50
Aging +
Residual
Retest
45
40
35
30
0
1
2
Time
3
Conclusion
• MGLGM one method for modeling re-test
effect and aging effect separately
• LGM feature of “freely estimating time
scores” useful for capturing “residual” retest effects
• Examine relationship of background
characteristics and variance in retest and
aging effects
• Relationship of retest and learning to
clinically meaningful outcomes
Acknowledgement
•
•
•
ACTIVE study (Advanced Cognitive Training for Independent and Vital
Elderly) is a multi-site collaborative cognitive intervention trial supported by
the National Institute on Aging and the National Institute on Nursing
Research.
Sharon Tennstedt is the principal investigator at the coordinating center,
New England Research Institutes, Watertown, Massachusetts (AG14282).
The principal investigators and field sites include
– Karlene Ball, University of Alabama at Birmingham (AG14289);
– Michael Marsiske, Institute on Aging, University of Florida, Gainesville
(AG14276);
– John Morris, Hebrew Rehabilitation Center for Aged Research and
Training Institute, Boston (NR04507);
– George Rebok, Johns Hopkins University Bloomberg School of Public
Health (AG14260);
– Sherry Willis, Penn State University, Gerontology Center (AG14263).
– David Smith was the principal investigator at Indiana University School
of Medicine, Regenstrief Institute, Indianapolis (NR04508) at the time
of initial award, currently Fred Unverzagt is currently the principal
investigator.
Age Differences in MSQ Score (Baseline EPESE)
5.10
5.00
4.90
4.80
4.70
b = -.02 SD units per year
4.60
65
70
75
80
85
Age
Baseline data from EPESE/ICPSR public use data file, baseline data only, listwise complete on Mental Status Questionnaire
(MSQ) scores at first, fourth and seventh assessment
Age Differences in MSQ Score (Baseline EPESE)
5.1
b = -0.02 SD/year
4.9
b = -0.10 SD/year
b = -0.06 SD/year
4.7
4.5
0
3
6
Study Year
Baseline data from EPESE/ICPSR public use data file, baseline data only, listwise complete on Mental Status Questionnaire
(MSQ) scores at first, fourth and seventh assessment