Understanding the time course of interventions - amemory strategy example

March, 2018

Charles Driver

Max Planck Institute for Human Development

The study

Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.

Longitudinal study with 5 waves – though actually 8 waves!

Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).

book running

The study

Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.

Longitudinal study with 5 waves – though actually 8 waves!

Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).

book running

The study

Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.

Longitudinal study with 5 waves – though actually 8 waves!

Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).

book running

The study

Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.

Longitudinal study with 5 waves – though actually 8 waves!

Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).

book running

Longitudinal timeline

0 50 100 150 200 250

01

23

45

6Observations

Subject

Yea

rs fr

om s

tudy

sta

rt

Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:

Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.

Individual variation in timing too...

Longitudinal timeline

0 50 100 150 200 250

01

23

45

6Observations

Subject

Yea

rs fr

om s

tudy

sta

rt

Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:

Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.

Individual variation in timing too...

Longitudinal timeline

0 50 100 150 200 250

01

23

45

6Observations

Subject

Yea

rs fr

om s

tudy

sta

rt

Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:

Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.

Individual variation in timing too...

Longitudinal timeline

0 50 100 150 200 250

01

23

45

6Observations

Subject

Yea

rs fr

om s

tudy

sta

rt

Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:

Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.

Individual variation in timing too...

Research questions

Does the intervention have lasting effects?

How do the covariates moderate the findings?

Research questions

Does the intervention have lasting effects?

How do the covariates moderate the findings?

Research questions

Does the intervention have lasting effects?

How do the covariates moderate the findings?

Descriptive plots

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 asfa

Years

asfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 ashr

Years

ashr

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 itfa

Years

itfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 ithr

Years

ithr

Descriptive plots

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 asfa

Years

asfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 ashr

Years

ashr

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 itfa

Years

itfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0 ithr

Years

ithr

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:

wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:

wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:

wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:

wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:wide, SEM approach.

long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling - hierarchical Bayesian continuous time dynamic model.

Subject level latent dynamics driven by stochastic differential equation:

dη(t) =

(Aη(t) + b + Mχ(t)

)dt + GdW(t) (1)

Observations for each subject are described by:

y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)

Possible via:wide, SEM approach.long, Kalman-filter.

Frequentist SEM allows individual variation in intercepts,

With Bayesian formulation, everything can vary.

Modelling – take 2

Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.

Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.

On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.

0 1 2 3 4 5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81

Time

asfa

Modelling – take 2

Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.

Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.

On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.

0 1 2 3 4 5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81

Time

asfa

Modelling – take 2

Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.

Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.

On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.

0 1 2 3 4 5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81

Time

asfa

Modelling – take 2

Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.

Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.

On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.

0 1 2 3 4 5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81

Time

asfa

What do we gain with such an approach to interventions?

Continuous time accounts for variability in time interval betweenobservations.

Intervention as dynamic process allows estimating unknown shape /persistence parameters.

Hierarchical approach accounts for, allows understanding of, individualvariability.

What do we gain with such an approach to interventions?

Continuous time accounts for variability in time interval betweenobservations.

Intervention as dynamic process allows estimating unknown shape /persistence parameters.

Hierarchical approach accounts for, allows understanding of, individualvariability.

What do we gain with such an approach to interventions?

Continuous time accounts for variability in time interval betweenobservations.

Intervention as dynamic process allows estimating unknown shape /persistence parameters.

Hierarchical approach accounts for, allows understanding of, individualvariability.

What do we gain with such an approach to interventions?

Continuous time accounts for variability in time interval betweenobservations.

Intervention as dynamic process allows estimating unknown shape /persistence parameters.

Hierarchical approach accounts for, allows understanding of, individualvariability.

Results

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

asfa

Years

asfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ashr

Years

ashr

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

itfa

Years

itfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ithr

Years

ithr

Sig. intervention improvement for asfa, ashr, itfa.

Unclear if intervention effect persists across years – probably not in general.

Intervention gives greater gains for worse performers.

Results

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

asfa

Years

asfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ashr

Years

ashr

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

itfa

Years

itfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ithr

Years

ithr

Sig. intervention improvement for asfa, ashr, itfa.

Unclear if intervention effect persists across years – probably not in general.

Intervention gives greater gains for worse performers.

Results

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

asfa

Years

asfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ashr

Years

ashr

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

itfa

Years

itfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ithr

Years

ithr

Sig. intervention improvement for asfa, ashr, itfa.

Unclear if intervention effect persists across years – probably not in general.

Intervention gives greater gains for worse performers.

Results

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

asfa

Years

asfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ashr

Years

ashr

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

itfa

Years

itfa

0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

ithr

Years

ithr

Sig. intervention improvement for asfa, ashr, itfa.

Unclear if intervention effect persists across years – probably not in general.

Intervention gives greater gains for worse performers.

Individual differences - age effects

20 30 40 50 60 70

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

AgeT1

Effect

TD_asfa_intTD_ashr_intTD_itfa_intTD_ithr_int

20 30 40 50 60 70

−0.2

−0.1

0.0

0.1

0.2

0.3

AgeT1

Effect

slope_asfaslope__ashrslope__itfaslope__ithr

20 30 40 50 60 70

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6

0.8

AgeT1

Effect

manifestmeans_asfamanifestmeans_ashrmanifestmeans_itfamanifestmeans_ithr

20 30 40 50 60 70

0.6

0.8

1.0

1.2

AgeT1

Effect

manifestvar_asfamanifestvar_ashrmanifestvar_itfamanifestvar_ithr

20 30 40 50 60 70

−10

−8−6

−4−2

02

AgeT1

Effect

dr_memInt

20 30 40 50 60 70

−4−2

02

4

AgeT1

Effect

TD_memInt2TD_memInt3

Individual differences - age effects

20 30 40 50 60 70

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

AgeT1

Effect

TD_asfa_intTD_ashr_intTD_itfa_intTD_ithr_int

20 30 40 50 60 70−0.2

−0.1

0.0

0.1

0.2

0.3

AgeT1

Effect

slope_asfaslope__ashrslope__itfaslope__ithr

20 30 40 50 60 70

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6

0.8

AgeT1

Effect

manifestmeans_asfamanifestmeans_ashrmanifestmeans_itfamanifestmeans_ithr

20 30 40 50 60 70

0.6

0.8

1.0

1.2

AgeT1

Effect

manifestvar_asfamanifestvar_ashrmanifestvar_itfamanifestvar_ithr

20 30 40 50 60 70

−10

−8−6

−4−2

02

AgeT1

Effect

dr_memInt

20 30 40 50 60 70

−4−2

02

4

AgeT1

Effect

TD_memInt2TD_memInt3

Discussion points - different shapes of intervention effect

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

Basic impulse effect

Time

Stat

e

Base process

0 5 10 15 20

0.0

0.5

1.0

1.5

2.0

2.5

Persistent level change

Time

Stat

e

Base processInput process

0 5 10 15 20

0.0

0.5

1.0

1.5

Dissipative impulse

Time

Stat

e

Base processInput process

0 5 10 15 20

-0.5

0.0

0.5

1.0

Oscillatory dissipation

Time

Stat

e

Base processInput processMediating input process

Discussion points - interventions on a trend

0 5 10 15 20

01

23

45

6

Time

Stat

e

Process without interventionProcess with interventionIntervention

Discussion points - system identification

0 5 10 15 20

−0.

50.

00.

51.

01.

52.

0

Natural state

Time

Sta

te

Process 1Process 2

0 5 10 15 20−

0.5

0.0

0.5

1.0

1.5

2.0

State with interventions

Time

Sta

te

Process 1Process 2

Discussion points - absolute model fit

Fits are better than saturated covariance structure.

Are there formalised approaches for model fit with person specific meanand or covariance?

Is absolute fit actually important?

Discussion points - absolute model fit

Fits are better than saturated covariance structure.

Are there formalised approaches for model fit with person specific meanand or covariance?

Is absolute fit actually important?

Discussion points - absolute model fit

Fits are better than saturated covariance structure.

Are there formalised approaches for model fit with person specific meanand or covariance?

Is absolute fit actually important?

Summary

The effect of interventions can change in time, and across people.

Analyses and plots via ctsem R package.

Chapter: Understanding the time course of interventions with continuoustime dynamic models.

Thanks!

Summary

The effect of interventions can change in time, and across people.

Analyses and plots via ctsem R package.

Chapter: Understanding the time course of interventions with continuoustime dynamic models.

Thanks!

Summary

The effect of interventions can change in time, and across people.

Analyses and plots via ctsem R package.

Chapter: Understanding the time course of interventions with continuoustime dynamic models.

Thanks!

Summary

The effect of interventions can change in time, and across people.

Analyses and plots via ctsem R package.

Chapter: Understanding the time course of interventions with continuoustime dynamic models.

Thanks!

Summary

The effect of interventions can change in time, and across people.

Analyses and plots via ctsem R package.

Chapter: Understanding the time course of interventions with continuoustime dynamic models.

Thanks!