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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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0 1Time

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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

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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

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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

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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

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Test Score

fun

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2.5

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Fu

nct

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=ln

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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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0

1

2

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6

0 5 10 15 20 25 30

Test Score

fun

ctio

n=

squ

are

root

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erro

rs

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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