Social Ties and Cognitive Function After Stroke

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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 its 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 Scoreg(cognition) e
• But the test has a maximum possible score
• Test Scoremin(15, g(cognition) e)

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Scaling Challenges
True Cognitive Status Values
Low
High
Maximum text score
Measured Test Score
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Measurement Ceilings
A ceiling on the dependent variable will bias the
regression coefficient away from the coefficient
for the true outcome variable.
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Ceilings with Longitudinal Data
Difference in True D 0
Observed -3
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Ceilings with Longitudinal Data
Difference in True D 0
Observed 3
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Medians vs Means
800
600
400
Cognitive Status
200
0
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
• 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

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Data Set

• AHEAD cohort of HRS
• Enrolled in 1993
• National sample of non-institutionalized
  survivors born pre-1924
• n7,542, Observations23,752
• Self-report years of education dichotomized at
  lt12 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 b00 b1Timeti b2Educationi
• b3TimetiEducationi
• bkOther Covariatesti ei
• Bootstrap (500 resamples) for standard errors,
  resampling on the individual (rather than the
  observation)

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Analysis

• Other covariates
• Age at enrollment, mothers education, fathers
  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
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Predicted Median TICS Score
From CLAD models, adjusted for sex, race, age at
baseline, Hispanic ethnicity, mothers and
fathers education
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Baseline Education Effect Estimates
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Slope Education Effect Estimates
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Loss to Follow-Up
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Effect at Alternative Quantiles
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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
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Unequal Scale Intervals
Do similar size increments have the same
meaning across all levels of the test?
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Unequal Scale Intervals
Do similar size increments have the same
meaning across all levels of the test?
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Unequal Scale Intervals
Do similar size increments have the same
meaning across all levels of the test?