Evidence Synthesis for Longitudinal Studies of Ageing

Jassy Molitor, Nicky Best, and Sylvia Richardson

In collaboration with Scott Hofer and Andrea Piccinin

July 08 2010

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

1. Motivation

Main Goals of this projectOverall aim: Develop and apply Bayesian hierarchical models

for synthesis of multiple cross-national longitudinal datasets

We tried to answer two following questions:

1. Evaluate effects of ageing on cognitive decline

2. Evaluate how different levels of education affect the rate of cognitive change over time (cognitive reserve)

- cognitive reserve describes 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.

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

2. Data for Case Study

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),

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.

Study (country) Sampling designCanberra Longitudinal Study (CLS, Australia) Community sample (electoral role),

institutional care, oversampling of very old

Healthy Old People in Edinburgh(HOPE, UK )

Medical registry

Longitudinal Aging Study Amsterdam (LASA, Netherlands )

Urban and rural municipal registries

Origins of Variance in the Oldest-Old:Octogenarian Twins (OCTO-Twin, Swiss )

Swedish Twin Registry

Swedish Adoption Twin Study of Aging (SATSA)

Swedish Twin Registry

Data with no missing values• We create two sets of data sets

1. Non-Restricted Data: every subject has at least 2 observations

2. Restricted Data: every subject has at least 2 observation and all their mmse > 19 (to avoid demented individuals.)

Non-restrict restrict % of dropingcls 1762 1710 3.00

hope 1281 1261 2.00lasa 9015 8662 4.00octo 1863 1460 22.00satsa 2560 2524 1.00

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)

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.

Education CLS (Australia)

HOPE(Scotland)

LASA(Netherland)

OCTO(Sweden)

SATSA(Sweden)

Low 1-9 yrs 1-9 yrs 1-9 yrs 1-7 yrs Level 1

Medium 10-12 yrs 10-12 yrs 10-12 yrs 8-12 yrs Level 2-3

high >=13 yrs >=13 yrs >=13 yrs >=13 yrs Level 4

Note: the education variable in SATSA was measured as categorical variables with4 levels.

3. Model Set Up

Cognitive Performance

Aging Effect

Question 1Does cognitive performance decline as age

increases?

Education Effect

Question 2Does higher education slow cognitive

decline over time?

Single Study – schematic diagram

We build up our model based on answering two questions :

MMSE (yij)As one of surrogate measurements

of cognitive performance

Subject’s specific Linear Rate of change of cognitive performance

(slope i )

Subject’s specific Initial level of cognitive performance

(intercept i )

We model subjects’ cognitive performance as a function of their trajectories, intercept and slope.

Diagram for age-based linear latent growth curve model (stage 1)Model cognitive performance as a function of subject-specific trajectories

AGE (Aij)

MMSE (yij)As one of surrogate measurements

of cognitive performance

Subject’s specific Linear Rate of change of cognitive performance

(slope i )

Subject’s specific Initial level of cognitive performance

(intercept i )

correlation

Diagram for age-based latent growth curve model (stage 2) ( joint model for subject-specific trajectories)

• We can consider individual initial level and cognitive rate of change as influenced by their education and other covariates

Education (Ei)Other

Covariates ( Ci )

• We also allow for the correlation between initial level and rate of change

• The association between individual cognitive rate of change (slopei) and education allows for examination of cognitive reserve

AGE (Aij)

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.

2

* *0 1

~ ( , )ij ij

ij i i ij

y N

A

*00

*11

0 0 2 3

1 1 1 2

~ ,ii

ii

Ti i i

Ti i i

MVN

C E

C E

21 12

22

MMSE (yij)

Subject’s specific initial level

(intercept i )

Other Covariates ( Ci )

Education ( Ei )

correlation

Subject’s specific linear rate

(slope i ) *1i

AGE (Aij)

Subject’s specific initial level

(intercept i )

*0i

Subject’s specific linear rate

(slope i ) *1i

*0i

Decline in cognitive function

with age

Cognitive reserve

Observed MMSE (yij)

Subject’s specific Linear Rate of change of cognitive performance

(slope i )

Subject’s specific Initial level of cognitive performance

(intercept i )

Accounting for ceiling effect of MMSE

AGE (Aij)

Observed MMSE (yij)

True MMSE (y*ij)

* *1

*1 1

* 2

* *0 1

~ ( , )

ij

ij

ij ij

ij

ij ij

ij i i ij

y y if y c

y c if y c

y N

A

MMSE (yij)As one of surrogate measurements

of cognitive performance

Subject’s specific (slope i )

Subject’s specific

(intercept i )

correlation

Elaborating the basic model3. Extend age-based latent linear growth curve model by including retest

Education (Ei)Other

Covariates ( Ci )

AGE (Aij)

Subject’s specific (retest i )

OCCASION (Xij)

Extension of Model: combined studies

True MMSE (y*sij)

Subject specific(slopesi)

Subject specific(interceptsi)

Education (Esi)Other

Covariates ( Csi )

observed MMSE (ysij)

Study specific(intercepts)

Study specific(slopes)

Global intercept Global slope

AGE (Asij)

correlation

Occasion j

Subject i

Study s

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

Single study (Linear Model+ with adjustment of ceiling effect )

ClS # HOPE# LASA# OCTO# SATSA#

intercept 28.71 ( 28.36 , 29.06 ) * 29.09 ( 28.75 , 29.44 ) * 28.37 ( 28.12 , 28.62 ) * 28.53 ( 25.62 , 31.16 ) * 28.25 ( 27.79 , 28.71 ) *

slope(age) -0.199 ( -0.252 , -0.143 ) * -0.124 ( -0.19 , -0.055 ) * -0.114 ( -0.136 , -0.092 ) * -0.837 ( -1.087 , -0.587 ) * -0.118 ( -0.15 , -0.087 ) *

low.education -0.932 ( -1.401 , -0.438 ) * -0.64 ( -1.047 , -0.214 ) * -1.758 ( -2.005 , -1.494 ) * -0.331 ( -2.8 , 2.437 ) -0.812 ( -1.279 , -0.358 ) *high.education 0.506 ( 0.061 , 0.954 ) * 1.176 ( 0.632 , 1.736 ) * 0.201 ( -0.171 , 0.566 ) -1.301 ( -7.611 , 4.983 ) 0.895 ( -0.116 , 1.995 )

baseage 0.095 ( 0.039 , 0.153 ) * 0.02 ( -0.049 , 0.091 ) 0.033 ( 0.018 , 0.049 ) * 0.904 ( 0.657 , 1.148 ) * 0.062 ( 0.038 , 0.086 ) *male -0.336 ( -0.718 , 0.011 ) -0.583 ( -0.95 , -0.196 ) * -0.339 ( -0.52 , -0.154 ) * 0.092 ( -1.095 , 1.206 ) 0.166 ( -0.134 , 0.467 )

age*low.education -0.053 ( -0.131 , 0.033 ) -0.005 ( -0.093 , 0.085 ) -0.068 ( -0.091 , -0.042 ) * -0.283 ( -0.55 , 0.002 ) -0.045 ( -0.083 , -0.009 ) *

age*high.education -0.002 ( -0.078 , 0.075 ) -0.136 ( -0.241 , -0.034 ) * -0.03 ( -0.065 , 0.006 ) 0.398 ( -0.299 , 1.118 ) -0.001 ( -0.078 , 0.082 )

Non-restricted data (observation >=2)

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.

#: posterior mean (95% credible interval)

Combined studies (Linear Model+ with adjustment of ceiling effect )

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.

Non-restricted data (observation >=2) Meta Fixed Meat Random Bayesian Unified pool.mean pool.ci pool.mean pool.ci pool.mean$ pool.ci $

intercept 28.6 ( 28.4 , 28.8 )* 28.6 ( 28.3 , 29 )* 30.09 ( 28.06 , 31.98 ) *slope(age) -0.127 ( -0.144 , -0.11 )* -0.176 ( -0.242 , -0.11 )* -0.295 ( -0.582 , -0.011)*

low.education -1.27 ( -1.45 , -1.08 )* -1.02 ( -1.6 , -0.44 )* -1.258 ( -1.426 , -1.094 ) *high.education 0.529 ( 0.283 , 0.776 )* 0.619 ( 0.178 , 1.06 )* 0.48 ( 0.259 , 0.696 ) *

base.age 0.047 ( 0.0342 , 0.0598 )* 0.0984 ( 0.0343 , 0.163 )* 0.04 ( 0.027 , 0.054 ) *male -0.263 ( -0.396 , -0.13 )* -0.247 ( -0.518 , 0.0246 ) -0.253 ( -0.383 , -0.114 ) *

age*low.education -0.0586 ( -0.0785 , -0.0387 )* -0.0567 ( -0.0813 , -0.032 )* -0.048 ( -0.065 , -0.031 ) *

age*high.education -0.0298 ( -0.0592 , -0.000399 ) -0.0313 ( -0.0779 , 0.0153 ) -0.024 ( -0.048 , 0.001 )

$ : posterior mean (95% credible interval)

Single study (Linear Model+ with adjustment of ceiling effect )

Restricted data (observation >=2 and all mmse >19)

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.

ClS # HOPE# LASA# OCTO# SATSA#

intercept 28.54 ( 28.23 , 28.86 ) * 29.03 ( 28.73 , 29.35 ) * 28.17 ( 27.99 , 28.36 ) * 30.69 ( 29.34 , 32.01 ) * 28.03 ( 27.67 , 28.36 ) *slope(age) -0.134 ( -0.177 , -0.092 ) * -0.102 ( -0.151 , -0.05 ) * -0.073 ( -0.089 , -0.057 ) * -0.264 ( -0.375 , -0.148 ) * -0.085 ( -0.108 , -0.064 ) *

low.education -0.869 ( -1.287 , -0.456 ) * -0.666 ( -1.046 , -0.281 ) * -1.365 ( -1.541 , -1.182 ) * -0.628 ( -1.955 , 0.724 ) -0.645 ( -0.976 , -0.316 ) *high.education 0.478 ( 0.081 , 0.884 ) * 0.989 ( 0.509 , 1.475 ) * 0.216 ( -0.033 , 0.471 ) 0.851 ( -2.148 , 4.145 ) 0.652 ( -0.12 , 1.412 )

baseage 0.05 ( 0.006 , 0.096 ) * -0.004 ( -0.055 , 0.045 ) -0.007 ( -0.019 , 0.006 ) 0.02 ( -0.089 , 0.135 ) 0.029 ( 0.012 , 0.048 ) *male -0.268 ( -0.563 , 0.038 ) -0.56 ( -0.877 , -0.243 ) * -0.272 ( -0.428 , -0.128 ) * -0.532 ( -1.03 , -0.012 ) * 0.139 ( -0.11 , 0.389 )

age*low.education -0.009 ( -0.07 , 0.053 ) 0.007 ( -0.063 , 0.072 ) -0.027 ( -0.046 , -0.009 ) * -0.02 ( -0.145 , 0.113 ) -0.031 ( -0.06 , -0.005 ) *age*high.education -0.015 ( -0.069 , 0.042 ) -0.038 ( -0.122 , 0.041 ) -0.023 ( -0.05 , 0.004 ) 0.058 ( -0.252 , 0.341 ) -0.011 ( -0.071 , 0.049 )

#: posterior mean (95% credible interval)

Combined studies (Linear Model+ with adjustment of ceiling effect )

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.

Restricted data (observation >=2 and all mmse >19)

$: posterior mean (95% credible interval)

Meta Fixed Meat Random Bayesian Unified pool.mean pool.ci pool.mean pool.ci pool.mean$ pool.ci $

intercept 28.4 ( 28.3 , 28.5 )* 28.6 ( 28.2 , 29.1 )* 28.91 ( 27.93 , 29.97 ) *slope(age) -0.0852 ( -0.0973 , -0.073 )* -0.106 ( -0.138 , -0.0734 )* -0.123 ( -0.205 , -0.042 ) *

low.education -1.09 ( -1.22 , -0.949 )* -0.886 ( -1.28 , -0.489 )* -1.011 ( -1.136 , -0.888 ) *high.education 0.438 ( 0.247 , 0.629 )* 0.535 ( 0.201 , 0.868 )* 0.487 ( 0.319 , 0.661 ) *

base.age 0.00633 ( -0.00346 , 0.0161 ) 0.0155 ( -0.0103 , 0.0413 ) 0.005 ( -0.005 , 0.016 )male -0.241 ( -0.346 , -0.136 )* -0.268 ( -0.499 , -0.0365 )* -0.24 ( -0.353 , -0.137 ) *

age*low.education -0.0256 ( -0.04 , -0.0113 )* -0.0256 ( -0.04 , -0.0113 )* -0.022 ( -0.035 , -0.008 ) *age*high.education -0.0209 ( -0.0425 , 0.00059 ) -0.0209 ( -0.0425 , 0.00059 ) -0.015 ( -0.035 , 0.005 )

Non-Restricted Data Restricted Data

Forest plot 1

Forest Plot 2Non-Restricted Data Restricted Data

Forest plot 3Non-Restricted Data Restricted Data

5. 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.

Discussion

6. 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)

Future work

THANK YOU

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

MMSE (yij)As one of surrogate measurements

of cognitive performance

Subject’s specific (slope i )

Subject’s specific

(intercept i )

Education (Ei)Other

Covariates ( Ci )

AGE (Aij)

Subject’s specific (curve i )

g

Study characteristics

study title start yr N(T 1)

Age(T 1)

follow-up(yr)

occ interval

CLS 1991 897 70-93 14 3.5

HOPE 1990 603 70+ 12 4

LASA 1991 3107 55-85 9 3

OCTO 1990 702 80+ 8 2

SATSA 1984 1500 40-84 6 3

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.

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

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.