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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. Outline. The question Why it’s difficult to answer

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slide1

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
Outline
  • The question
  • Why it’s difficult to answer
  • How CLAD regression helps
  • An example with HRS data
the question
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?

indirect measurement of cognition
Indirect Measurement of Cognition
  • Test is an indirect measure of our primary interest (cognitive function):

Test Score=g(cognition) + e

  • But the test has a maximum possible score:

Test Score=min(15, g(cognition) + e)

scaling challenges
Scaling Challenges

True Cognitive Status Values

Low

High

Maximum text score

Measured Test Score

measurement ceilings
Measurement Ceilings

A ceiling on the dependent variable will bias the regression coefficient away from the coefficient for the true outcome variable.

ceilings with longitudinal data

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Time

Ceilings with Longitudinal Data

Difference in True D = 0

Observed = -3

ceilings with longitudinal data1

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Time

Ceilings with Longitudinal Data

Difference in True D = 0

Observed = 3

medians vs means

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Test Score

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Median

Mean

Medians vs Means

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600

400

Cognitive Status

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Mean, Median

clad regression
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
    • Calculate the median regression coefficients
    • Drop observations with a predicted value of Y over ceiling
    • Repeat steps 1 and 2 until all predicted values are below the ceiling.
  • Standard errors are messy: bootstrap.
  • Can use any quantile
data set
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
analysis
TICSti = b00 + b1Timeti + b2Educationi

+ b3Timeti*Educationi

+ bkOther Covariatesti + ei

Bootstrap (500 resamples) for standard errors, resampling on the individual (rather than the observation)

Analysis
analysis1
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

Analysis
predicted median tics score
Predicted Median TICS Score

From CLAD models, adjusted for sex, race, age at baseline, Hispanic ethnicity, mother’s and father’s education

less desirable alternatives
(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
conclusions
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.
limitations future work
Limitations & Future Work
  • Discrete outcomes
  • Missing data
  • Complex sampling design
  • Unequal scale intervals not due to ceilings
acknowledgements
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
unequal scale intervals1

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4.0

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function=square root of errors

Function=ln(score)

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2.0

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Test Score

Unequal Scale Intervals

Do similar size increments have the same “meaning” across all levels of the test?

unequal scale intervals2
Unequal Scale Intervals

Do similar size increments have the same “meaning” across all levels of the test?

unequal scale intervals3
Unequal Scale Intervals

Do similar size increments have the same “meaning” across all levels of the test?

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