identifying predictors of cognitive change when the outcome is measured with a ceiling
DESCRIPTION
Identifying Predictors of Cognitive Change When the Outcome Is Measured With a Ceiling. Gerontological Society of America 2004 Annual Meeting Maria Glymour, Jennifer Weuve, Lisa F. Berkman, James M. Robins Harvard School of Public Health. Outline. The question Why it’s difficult to answer - PowerPoint PPT PresentationTRANSCRIPT
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Identifying Predictors of Cognitive Change When the Outcome Is
Measured With a Ceiling
Gerontological Society of America
2004 Annual Meeting
Maria Glymour, Jennifer Weuve, Lisa F. Berkman, James M. Robins
Harvard School of Public Health
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Outline
• The question
• Why it’s difficult to answer
• How CLAD regression helps
• An example with HRS data
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The Question
• Does education affect cognitive change in old age?
• Earl attended 10 years of school and declined by 2 points on a cognitive test score from age 70 to 75.
Would Earl have experienced more or less cognitive change if he had, counter to fact, completed more
schooling?
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Indirect Measurement of Cognition
• Test is an indirect measure of our primary interest (cognitive function):
Test Score=g(cognition) +
• But the test has a maximum possible score:
Test Score=min(15, g(cognition) + )
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Scaling ChallengesTrue Cognitive Status Values
Measured Test Score
Low High
Maximum text score
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Measurement Ceilings
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X
A ceiling on the dependent variable will bias the regression coefficient away from the coefficient for the true outcome variable.
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0 1Time
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Difference in True = 0
Observed = -3
Ceilings with Longitudinal Data
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Difference in True = 0
Observed = 3
Ceilings with Longitudinal Data
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Medians vs Means
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Mean, Median
Co
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itiv
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tatu
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Sco
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Mean
Median
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CLAD Regression
The median is more robust to ceiling effects than the mean, so contrast medians by level of exposure
Use CLAD if believe the relationship between X and Y does not differ above (vs below) the ceiling
1. Calculate the median regression coefficients
2. Drop observations with a predicted value of Y over ceiling
3. Repeat steps 1 and 2 until all predicted values are below the ceiling.
Standard errors are messy: bootstrap.
Can use any quantile
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Data Set
• AHEAD cohort of HRS– Enrolled in 1993– National sample of non-institutionalized survivors born
pre-1924– n=7,542, Observations=23,752
• Self-report years of education: dichotomized at <12 years
• Telephone Interview for Cognitive Status (modified) – Possible range 0 (bad) -15 (good)– ~20% scored max at each interview– Assessed 1-5 times
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Analysis
TICSti = 00 + 1Timeti + 2Educationi
+ 3Timeti*Educationi
+ kOther Covariatesti + i
Bootstrap (500 resamples) for standard errors, resampling on the individual (rather than the observation)
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Analysis
• Other covariates:– Age at enrollment, mother’s education, father’s
education, Hispanic ethnicity
• Stratify by sex and race (black vs all other)
• Up to 5 cognitive assessments– Initial models treat time flexibly– Impose a linear model of time
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Summary of AHEAD Data
n 3,133 4,279
Age at baseline 77.7 (6.8) 76.0 (6.1)
Avg follow-ups 2.5 (1.4) 2.7 (1.4)
Male 36% 35%
Black 22% 7%
Hispanic 10% 2%
Mom 8+ years school 35% 67%
Pop 8+ years school 32% 62%
Education <=11 years
Education 12+ Years
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Predicted Median TICS Score
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1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Year
Pre
dic
ted
Sco
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From CLAD models, adjusted for sex, race, age at baseline, Hispanic ethnicity, mother’s and father’s education
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Baseline Education Effect Estimates
White women -1.39 (-1.55, -1.23) -1.37 (-1.58, -1.15)
Black women -2.46 (-2.99, -1.92) -2.60 (-3.25, -1.91)
White men -1.31 ( -1.51, -1.11) -1.08 (-1.35, -0.96)
Black men -2.83 ( -3.59, -2.07) -2.58 (-3.78, -1.48)
Mean Model Median Model
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Slope Education Effect Estimates
White women -0.03 (-0.05, -0.01) -0.07 (-0.11, -0.03)
Black women -0.07 (-0.13, -0.01) -0.08 (-0.20, 0.02)
White men -0.03 (-0.05, -0.00) 0.00 (-0.07, 0.02)
Black men 0.05 (-0.04, 0.15) 0.05 (-0.14, 0.25)
Mean Model Median Model
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Loss to Follow-Up
White women -0.07 (-0.11, -0.03) -0.09 (-0.13, -0.05)
Black women -0.08 (-0.20, 0.02) -0.03 (-0.11, 0.11)
White men 0.00 (-0.07, 0.02) 0.00 (-0.04, 0.04)
Black men 0.05 (-0.14, 0.25) 0.01 (-0.30, 0.17)
Median Model IPW Median Model
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Effect at Alternative Quantiles
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
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0.01
0 10 20 30 40 50 60
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(Less Desirable) Alternatives
• Baseline adjustment– Introduces new (and larger) biases
• Add the scales– Hides the ceiling– Hides the bias
• Tobit models– Stronger assumptions about the distribution
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Conclusions
• More educated respondents had much higher average cognitive scores for the duration of the study.
• Education associated with better evolution of cognitive function for white women.
• Ceilings introduced bias of unknown direction.
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Limitations & Future Work
• Discrete outcomes
• Missing data
• Complex sampling design
• Unequal scale intervals not due to ceilings
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Acknowledgements
• Dean Jolliffe, CLAD ado
• Funding:– National Institute of Aging
– Office for Behavioral and Social Science Research
– “Causal Effects of Education on Elder Cognitive Decline”
– AG023399
– NIA Training grant: AG00138
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END
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Unequal Scale Intervals
True Cognitive Status Values
Measured MMSE
Low High
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Do similar size increments have the same “meaning” across all levels of the test?
Unequal Scale Intervals
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Test Score
fun
ctio
n=
squ
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=ln
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0
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Test Score
fun
ctio
n=
squ
are
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rs
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0.5
1.0
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2.0
2.5
3.0
3.5
4.0
Fu
nct
ion
=ln
(sco
re)
Do similar size increments have the same “meaning” across all levels of the test?
Unequal Scale Intervals
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0
1
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0 5 10 15 20 25 30
Test Score
fun
ctio
n=
squ
are
root
of
erro
rs
-
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Fu
nct
ion
=ln
(sco
re)
Do similar size increments have the same “meaning” across all levels of the test?
Unequal Scale Intervals