Evidence Synthesis for Longitudinal Studies of Ageing

1. Evidence Synthesis for Longitudinal Studies of Ageing JassyMolitor, Nicky Best, and Sylvia Richardson In collaboration with Scott Hofer and Andrea Piccinin July 08 2010

2. Outline • Motivation • Data for Case Study • Model Set-Up • Results • Discussion

3. 1. Motivation

4. Main Goals of this project Overall aim: Develop and apply Bayesian hierarchical models for synthesis of multiple cross-national longitudinal datasets We tried to answer two following questions: • Evaluate effects of ageing on cognitive decline • Evaluate how different levels of education affect the rate of cognitive change over time (cognitive reserve) - cognitive reservedescribes the mind's resilience to neuropathological damage of the brain. In ageing study, researchers hypothesize that people with higher education tends to have better cognitive performance and a slower rate of brain damage as age increases.

5. Methodological issues • We used the random effects growth curves to model subject-specific trajectories. In the growth curve model, we would like to account for • Ceiling effect of outcome • Retest effect • Heterogeneity coming from different studies

6. 2. Data for Case Study

7. Where did we obtain the data? • Integrative Analysis of Longitudinal Studies on Aging (IALSA) http://www.ialsa.org/ • A collaborative research infrastructure for coordinated interdisciplinary, cross-national research aimed at the integrative understanding of within-person aging-related changes in health and cognition. • Comprised of over 25 longitudinal studies on aging, spanning eight countries (~70,000 individuals) • Mix of representative, volunteer, and special population samples • Collected individuals from birth to over 100 (focus on 50+), with birth cohorts ranging from 1880 to 1980 (mainly 1900-1920),

8. Studies description For the case study, we have five longitudinal data sets : Note: IALSA network contains at least 25 studies. We first focused the above five studies since they have common measurement of outcomes (MMSE) and covariates.

9. Data with no missing values • We create two sets of data sets • Non-Restricted Data: every subject has at least 2 observations • Restricted Data: every subject has at least 2 observation andall their mmse > 19 (to avoid demented individuals.)

10. Key Variables • Outcome: MMSE (Mini Mental State Examination) • Scores range from 0 to 30 (for non-restricted data) • Scores range from 20 to 30 (for restricted data) • Main effect: Age (continuous, centered at 75) • Time independent Covariates: • Education ( 1:Low, 2:Medium, 3:High) • Gender (0: females, 1: males) • Baseline age (continuous value)

11. Criteria of classifying education • We used the historical information of education across counties which obtained from the wikipedia.org (http://en.wikipedia.org/wiki/) and distribution of education year of current data to classify the education into low, medium, and high. Note: the education variable in SATSA was measured as categorical variables with 4 levels.

12. 3. Model Set Up

13. Single Study – schematic diagram We build up our model based on answering two questions : Cognitive Performance Education Effect Aging Effect Question 2 Does higher education slow cognitive decline over time? Question 1 Does cognitive performance decline as age increases?

14. Diagram for age-based linear latent growth curve model (stage 1)Model cognitive performance as a function of subject-specific trajectories Subject’s specific Initial level of cognitive performance (intercept i ) Subject’s specific Linear Rate of change of cognitive performance (slope i ) MMSE (yij) As one of surrogate measurements of cognitive performance AGE (Aij) We model subjects’ cognitive performance as a function of their trajectories,intercept and slope.

15. Diagram for age-based latent growth curve model (stage 2) ( joint model for subject-specific trajectories) correlation Education (Ei) Other Covariates( Ci) Subject’s specific Initial level of cognitive performance (intercept i ) Subject’s specific Linear Rate of change of cognitive performance (slope i ) MMSE (yij) As one of surrogate measurements of cognitive performance AGE (Aij) • We can consider individual initial level and cognitive rate of change • as influenced by their education and other covariates • We also allow for the correlationbetween initial level and rate of change • The association between individual cognitive rate of change (slopei) and • education allows for examination of cognitive reserve

16. Mathematical presentation of the two stage latent growth curve model • Assume subject i has j repeated measurements (j=1,…Ni) • First stage: model cognitive performance as subject-specific trajectory • Second Stage: joint model for subject-specific trajectories. Subject’s specific linear rate (slope i ) Subject’s specific initial level (intercept i ) AGE (Aij) MMSE (yij) Decline in cognitive function with age b d Other Covariates ( Ci) Education ( Ei) Subject’s specific initial level (intercept i ) Subject’s specific linear rate (slope i ) correlation Cognitive reserve

17. Accounting for ceiling effect of MMSE Subject’s specific Initial level of cognitive performance (intercept i ) Subject’s specific Linear Rate of change of cognitive performance (slope i ) Observed MMSE (yij) AGE (Aij) True MMSE (y*ij) Observed MMSE (yij)

18. Elaborating the basic model3. Extend age-based latent linear growth curve model by including retest correlation Other Covariates( Ci) Education (Ei) b d Subject’s specific (retest i ) Subject’s specific (intercept i ) Subject’s specific (slope i ) OCCASION (Xij) MMSE (yij) As one of surrogate measurements of cognitive performance AGE (Aij)

19. Extension of Model: combined studies Global intercept Global slope Study specific (intercepts) Study specific (slopes) Study s Other Covariates( Csi) Education (Esi) b d correlation Subject specific (interceptsi) Subject specific (slopesi) Subject i AGE (Asij) True MMSE (y*sij) observed MMSE (ysij) Occasion j

20. 4. Results • Five studies (CLS, HOPE,LASA, OCTO, and SATSA) will be combined. • We will present two sets of results based on restricted (observation>=2 and all mmse>19) and non-restricted (observations >=2) data sets. • We used three different methods to perform the joint-analysis • Meta (fixed) • Meta (Random) • Bayesian Unified

21. Single study (Linear Model+ with adjustment of ceiling effect ) Non-restricted data (observation >=2) #: posterior mean (95% credible interval) For all studies, there was a significant decline in the performance over time on the tests of Mini- Mental State Examination (MMSE). For both LASA and SATSA, the low educated group showed faster and more significant decline in MMSE when compared to the medium-educated group. For HOPE, the rate of cognitive change over time in the high educated group showed faster decline when compared to the medium educated group, and the effect was significant.

22. Combined studies (Linear Model+ with adjustment of ceiling effect ) Non-restricted data (observation >=2) $ : posterior mean (95% credible interval) • In the combined studies: • There was a significant decline in the performance over time on the tests of Mini-Mental State Examination (MMSE) for all three methods. • In the combined studies, the rate of cognitive change over time in the low educated group show faster and significant decline when compared to the medium educated group for all three methods. • By combing studies, the rate of cognitive change over time in the high educated group show faster and decline when compared to the medium educated group for all three methods. However, the effect is not significant.

23. Single study (Linear Model+ with adjustment of ceiling effect ) Restricted data (observation >=2 and all mmse >19) #: posterior mean (95% credible interval) For all studies, there was a significant decline in the performance over time on the tests of Mini- Mental State Examination (MMSE). For both LASA and SATSA, the rate of cognitive change over time in the low educated group showed faster decline when compared to the medium educated group, and the effect was significant. For most studies except OCTO, the rate of cognitive change over time in the high educated group shows faster decline when compared to the medium educated group. However, the effects were not significant.

24. Combined studies (Linear Model+ with adjustment of ceiling effect ) Restricted data (observation >=2 and all mmse >19) $: posterior mean (95% credible interval) • In the combined studies: • There was a significant decline in the performance over time on the tests of Mini- Mental State Examination (MMSE) for all three methods. • In the combined studies, the rate of cognitive change over time in the low educated group showed faster and significant decline when compared to the medium educated group for all three methods. • By combing studies, the rate of cognitive change over time in the high educated group showed faster decline when compared to the medium educated group for all three methods. However, the effect is not significant.

25. Forest plot 1 Non-Restricted Data Restricted Data

26. Forest Plot 2 Non-Restricted Data Restricted Data

27. Forest plot 3 Non-Restricted Data Restricted Data

28. 5. Discussion

29. Discussion For both data sets: • There was a significant decline in the performance over time on the tests of Mini- Mental State Examination (MMSE). (Though, as discussed yesterday, we may not want to think of age as being causal.) • People in the low-educated group show faster rate of cognitive decline compared with those in the medium-educated group. More education seems to slow measured decline in cognitive function. • People in the high-educated group tend to show a faster rate of decline compared to those in the medium-educated group, though the effect is not significant. However, decline in cognition for people in the high-educated group seems to be non-linear, with a flat trajectory followed by a sharp decline. This suggests that a non-linear model, such as a change-point model, should be used to capture this decline pattern.

31. 6. Future Work

32. Future work • Include more studies (ie. ALSA, H-70, NAS) • Some current results inconclusive, so more data would increase power. • Change point model • Interest in whether high education (cognitive reserve) delays ageing-related cognitive decline. • But, may be too few observations per subject to fit model • Include more information related to study quality (e.g. sample size, sample method, participants, health status,..) to help model and explain heterogeneity across studies • Meta-regression • Subjective “bias” adjustment (e.g. Turner et al, 2009)

33. Thank You

34. Elaborating the basic model1. Non-linear trajectories • Include quadratic age term • But, only have maximum of 3 to 5 observations per subject, so difficult to estimate Other Covariates( Ci) d Education (Ei) g b Subject’s specific (intercept i ) Subject’s specific (slope i ) Subject’s specific (curve i ) MMSE (yij) As one of surrogate measurements of cognitive performance AGE (Aij)

35. Study characteristics

36. Elaborating the basic model2. Ceiling Effect • From the test material (ie. MMSE) it is relative easy to obtain the maximum score of test. • For example, if we gave an elementary school math test to adults, many would score at ceiling. Similarly, because the MMSE is actually a screen for dementia, rather than a test of ability, someone of average ability with no dementia or other brain damage should be able to score 30 on the MMSE. Model response (MMSE) as normal, treat MMSE scores = 30 as censored.

37. Elaborating the basic model3. Retest Effect • A retest effect occurs when an individual's score improves with repeated administration of the same test. • For example, they may learn strategies or remember details from the earlier administrations that help their score subsequently. This is a problem because we assume they are not getting "smarter", it is just that their score is increasing. • The largest retest effect is generally seen at the second occasion, but increases have been seen for up to as many as 5 (yearly) or 8 (weekly) occasions. Include dummy variable indicating first or subsequent measurement occasion for each subject (Ferrer et. al. 2004). Note: we assumed that retest effect happened at second occasion and became constant afterward. • Since retest effect is assumed to be positive, specify truncated (normal) prior for associated regression coefficient

38. Elaborating the basic model4. Heterogeneity across different studies • Why do we need to combine studies? • The effect of education on cognitive reserve is inconclusive from study to study. Therefore, combing studies is needed to increase power Extend single study model by adding 3rd hierarchical level and assuming studies are exchangeable • Need careful choice of priors on between-study random effects variances, since only 5 studies • We use half normal or half-Cauchy (Gelman 2006) priors.