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1 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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2 Outline The question Why its difficult to answer How CLAD regression helps An example with HRS data

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3 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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4 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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5 Scaling Challenges True Cognitive Status Values Measured Test Score LowHigh Maximum text score

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6 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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7 16 18 20 22 24 26 28 30 32 34 36 01 Time 16 18 20 22 24 26 28 30 32 34 36 Difference in True = 0 Observed = -3 Ceilings with Longitudinal Data

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8 16 18 20 22 24 26 28 30 32 34 36 01 Time 16 18 20 22 24 26 28 30 32 34 36 Difference in True = 0 Observed = 3 Ceilings with Longitudinal Data

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9 Medians vs Means 0 200 400 600 800 Mean, Median Cognitive Status Test Score 0 200 400 600 800 Mean Median

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10 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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11 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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12 Analysis TICS ti = 00 + 1 Time ti + 2 Education i + 3 Time ti *Education i + k Other Covariates ti + i Bootstrap (500 resamples) for standard errors, resampling on the individual (rather than the observation)

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13 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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14 Summary of AHEAD Data

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15 Predicted Median TICS Score From CLAD models, adjusted for sex, race, age at baseline, Hispanic ethnicity, mothers and fathers education

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16 Baseline Education Effect Estimates

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17 Slope Education Effect Estimates

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18 Loss to Follow-Up

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19 Effect at Alternative Quantiles

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20 (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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21 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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22 Limitations & Future Work Discrete outcomes Missing data Complex sampling design Unequal scale intervals not due to ceilings

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23 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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24 END

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25 Unequal Scale Intervals True Cognitive Status Values Measured MMSE LowHigh

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26 Do similar size increments have the same meaning across all levels of the test? Unequal Scale Intervals

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27 Do similar size increments have the same meaning across all levels of the test? Unequal Scale Intervals

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28 Do similar size increments have the same meaning across all levels of the test? Unequal Scale Intervals

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