timms - defense slides - a novel engineering approach to modeling and optimizing smoking cessation...

Control Systems Engineering LaboratoryCSEL

Kevin P. Timms!

!Biological Design Program!

School of Biological & Health Systems Engineering,!!

Control Systems Engineering Laboratory!School for Engineering of Matter, Transport, & Energy!

!Arizona State University

A Novel Engineering Approach to Modeling and Optimizing Smoking Cessation Interventions

PhD Dissertation Defense!November 10, 2014

Control Systems Engineering LaboratoryCSEL Agenda

2

• Motivation, research goals & contributions!

• Self-regulation model development & estimation!

• Formulation of an adaptive smoking cessation intervention!

• Evaluation of nominal & robust performance!

• Extensions, summary, & conclusions


3






Control Systems Engineering LaboratoryCSEL Motivation

• Cigarette smoking remains a major global public health issue!

- ~ 20% of adults are smokers!

- Leading cause of preventable death in the U.S. (2014 Surgeon General’s Report)

• Chronic, relapsing disease: ~90% of quit attempts fail (Fiore & Baker, 2011; Fiore et al., 2000)

4

Control Systems Engineering LaboratoryCSEL Motivation

• Cigarette smoking remains a major global public health issue!

- ~ 20% of adults are smokers!

- Leading cause of preventable death in the U.S. (2014 Surgeon General’s Report)

• Chronic, relapsing disease: ~90% of quit attempts fail (Fiore & Baker, 2011; Fiore et al., 2000)

• Smoking cessation intervention: Any program intended to support a successful quit attempt!

- “Fixed” interventions met with limited success (Fish et al., 2010)!

- Success rates of combination pharmacotherapies < 35% (Piper et al., 2009)

4

Control Systems Engineering LaboratoryCSEL Motivation (cont.)

• Alternative treatment paradigm: Time-varying, adaptive smoking cessation intervention (Collins et al., 2004; Nandola & Rivera, 2013)!

- Tailor treatment dosages over time to the changing needs of an individual smoker trying to quit!

- Consists of a control system with feedback/feedforward action

5

Control Systems Engineering LaboratoryCSEL Motivation (cont.)

• Alternative treatment paradigm: Time-varying, adaptive smoking cessation intervention (Collins et al., 2004; Nandola & Rivera, 2013)!

- Tailor treatment dosages over time to the changing needs of an individual smoker trying to quit!

- Consists of a control system with feedback/feedforward action

• Dissertation goal: Explore the utility of an engineering approach to design of adaptive smoking cessation interventions!

- Use dynamical systems modeling & system identification methods to better understand smoking as a process of behavior change!

- Lay the conceptual & computational groundwork for an optimized, adaptive smoking cessation intervention based in control theory

5

Control Systems Engineering LaboratoryCSEL Research Contributions

• Modeling!

- Development & estimation of models describing smoking cessation behavior change as a self-regulatory process!

- Demonstration that engineering models can describe group average and single subject behavioral dynamics, provide insight into treatment effects!

- Dynamic mediation model development & estimation (not shown)!

• Adaptive intervention design (controller design)!

- Translation of the clinical requirements of a cessation intervention into a control systems problem!

- Formulation of an intervention algorithm in the form of a Hybrid Model Predictive Controller!

- Evaluation of nominal & robust performance through simulation!

- Assessment of a clinician-friendly controller tuning strategy

6


7






Control Systems Engineering LaboratoryCSEL Intensive Longitudinal Data (ILD)

• Design of an intervention with rapid and effective adaptation requires an improved understanding of the cessation process

8



• Computerized, mobile technologies facilitate collection of intensive longitudinal data (ILD) — Frequent measurements of behaviors over time!

- Captures dynamic nature of behavioral constructs!

- Contrasts traditional behavioral science data sets!

- Rate at which ILD available has outpaced the rate at which appropriate analytical methods emerge

8



• Computerized, mobile technologies facilitate collection of intensive longitudinal data (ILD) — Frequent measurements of behaviors over time!

- Captures dynamic nature of behavioral constructs!

- Contrasts traditional behavioral science data sets!

- Rate at which ILD available has outpaced the rate at which appropriate analytical methods emerge

• Here, secondary analysis of ILD from a U. of Wisconsin smoking cessation clinical trial (McCarthy et al., 2008)

8

Control Systems Engineering LaboratoryCSEL McCarthy et al., 2008

• McCarthy et al., Nicotine & Tobacco Research, Vol. 10, No. 4, pgs. 717-729, 2008.

• Bupropion & counseling treatment study!

- “AC” group: Active bupropion, counseling (n=100)!- “PNc” group: Placebo bupropion, no counseling (n=99)

9

Control Systems Engineering LaboratoryCSEL McCarthy et al., 2008

• McCarthy et al., Nicotine & Tobacco Research, Vol. 10, No. 4, pgs. 717-729, 2008.

• Bupropion & counseling treatment study!

- “AC” group: Active bupropion, counseling (n=100)!- “PNc” group: Placebo bupropion, no counseling (n=99)

• ILD collected via nightly self-reports, “Since last report”:!- CPD [0-99]: Number of cigarettes smoked / day!

- Craving [4-44]: Σ Urge, Cigonmind, Thinksmk, Bother!

- Urge [1-11]: Average, Bothered by urges?!

- Cigonmind [1-11]: Average, Cigarettes on my mind?!

- Thinksmk [1-11]: Average, Thinking about smoking a lot?!

- Bother [1-11]: Average, Bothered by desire to smoke?

9

Control Systems Engineering LaboratoryCSEL McCarthy et al., 2008 (cont.)

10

AC group averagePNc group average

AC single subject exPNc single subject ex

0 5 10 15 20 25 30 350

5

10

15

CPD

0 5 10 15 20 25 30 35

5

15

25

35

Craving

0 5 10 15 20 25 30 350

1

Day

Quit

TQD

TQD

TQD

# Ci

gare

ttes

Poin

ts


• Data sets

• Target Quit Date = TQD

• Quit represents initiation of a quit attempt

• Our focus: 36 days (7 pre-TQD, 28 post-TQD)

10



0 5 10 15 20 25 30 350

5

10

15

CPD

0 5 10 15 20 25 30 35

5

15

25

35

Craving

0 5 10 15 20 25 30 350

1

Day

Quit

TQD

TQD

TQD

# Ci

gare

ttes

Poin

ts


• Data sets

• Target Quit Date = TQD

• Quit represents initiation of a quit attempt

• Our focus: 36 days (7 pre-TQD, 28 post-TQD)

• Dynamical systems modeling & system identification offer a means to represent smoking cessation as a process of behavior change 10



0 5 10 15 20 25 30 350

5

10

15

CPD

0 5 10 15 20 25 30 35

5

15

25

35

Craving

0 5 10 15 20 25 30 350

1

Day

Quit

TQD

TQD

TQD

# Ci

gare

ttes

Poin

ts

Control Systems Engineering LaboratoryCSEL Self-Regulation Within Cessation

• Connection between ILD and engineering models ➔ Psychological theory!

• Self-regulation is a prominent concept within behavioral science research (Carver & Scheier, 1998; Solomon, 1977; Solomon, 1974; Velicer, 1992)!

- Largely described in tobacco use settings in conceptual terms

11

Control Systems Engineering LaboratoryCSEL Self-Regulation Within Cessation

• Connection between ILD and engineering models ➔ Psychological theory!

• Self-regulation is a prominent concept within behavioral science research (Carver & Scheier, 1998; Solomon, 1977; Solomon, 1974; Velicer, 1992)!

- Largely described in tobacco use settings in conceptual terms

11

Pd

+

-Self-

Regulatore

++ Pr

Disturbances e.g., intervention,

emotional/cognitive state, smoking cues

Biological or psychological

outcomee.g., blood nicotine,

urge level

Cigarette smoking

• Hypothesized set points (r): blood nicotine, affect, urge levels!

• Disturbances: Interventions, emotional/cognitive states, context cues

Control Systems Engineering LaboratoryCSEL Self-Regulation Models

• Cessation process from a control systems engineering perspective:

12

Pd (s)

+

-C(s)

e+

+P(s)rcrav

Quit

CPD Craving

CPD =

✓C

1 + PC

◆rcrav +

✓Pd

1 + PC

◆Quit

Craving =

✓PC

1 + PC

◆rcrav +

✓PPd

1 + PC

◆Quit

Closed-loop identification problem

Control Systems Engineering LaboratoryCSEL Model Estimation

• Continuous-time model estimation using prediction-error methods!

- P(s): Single-input / single-output problem!

- Pd(s), C(s): Two-input / one-output problem!

• Estimate P(s), Pd(s), & C(s) for each set of group average signals!

• Validation!

- Goodness-of-fit index:!

- Model parsimony!

- Parameter plausibility13

Fit [%] = 100 ⇤✓1� ||y(t)� y(t)||2

||y(t)� y||2

◆

Pd (s)

+

-C(s)

e+

+P(s)rcrav

Quit

CPD Craving

Control Systems Engineering LaboratoryCSEL Estimated Group-Average Models

• Low-order model structures:

!

!

• AC group average!- Craving: 87.8%!- CPD: 89.2%!

• PNc group average!- Craving: 64.72%!- CPD: 84.4%!

• Models reflect major features of both groups’ signals!

- CPD drop, resumption!

- Inverse response in Craving 14

AC data PNc data

AC model PNc modelP (s) =K1(⌧as+ 1)

⌧1s+ 1

Pd(s) = Kd

C(s) =Kc

⌧cs+ 1

Control Systems Engineering LaboratoryCSEL Self-Regulation Models (cont.)

• Simulation, theory, & fits suggest the estimated models accurately represent the psychological phenomenon!

- Reverse-engineering, estimation of self-regulation models of smoking behavior using clinical data not seen within behavioral science settings!

• A control engineering perspective offers unique insights intothe self-regulatory process

15


• Insights offered by a control engineering perspective!

- rcrav found to be average Craving level pre-TQD

16

Pd (s)

+

-C(s)

e+

+P(s)rcrav

Quit

CPD Craving



- rcrav found to be average Craving level pre-TQD !

- Reduction in CPD on TQD modeled by Pd path!

- Small, slow resumption modeled by feedback path

17

Pd (s)

+

-C(s)

e+

+P(s)rcrav

Quit

CPD Craving 0 5 10 15 20 25 30 350

5

10

15

CPD

0 5 10 15 20 25 30 3515

20

25

30Craving

0 5 10 15 20 25 30 350

1

Day

Quit





- Small, slow resumption modeled by feedback path!

- Craving self-regulator acts as a proportional-with-filter controller

18

Pd (s)

+

-C(s)

e+

+P(s)rcrav

Quit

CPD Craving C(s) =Kc

⌧cs+ 1





- Small, slow resumption modeled by feedback path!

- Craving self-regulator acts as a proportional-with-filter controller!

- Zero term in P(s) suggests Craving results from two competing sub-processes

Self-Regulation Models (cont.)

19

Quit

Cigsmked

Pd (s)

Craving+

-C(s)rcrav

e

P2(s)

P1(s)

P(s)

++ +

+rcrav

Quit

CPD Craving


• Insights offered by a control engineering perspective (cont.)!

- Compare parameter estimates from group average models to help evaluate bupropion & counseling effects!• Active treatment supports greater reduction in CPD on TQD: Kd =

-15.0, AC; = -10.2, PNc!

• Active treatment increases the speed at which Craving responds to unit change in CPD: !1 = 8.2 days, AC; = 26.8 days, PNc!

• Active treatment diminishes relative contribution of feedback path to CPD dynamics: PNc’s Kc 73% larger than AC’s

20

Pd (s)

+

-C(s)

e+

+P(s)rcrav

Quit

CPD Craving


0 5 10 15 20 25 30 35

0

5

10

15

20CPD

0 5 10 15 20 25 30 350

10

20

30

40Craving

0 5 10 15 20 25 30 350

1

Day

Quit


21

AC subject dataAC subject model PNc subject model

PNc subject data

CPD

• Straightforward extension to modeling single subjects!

• Same low order structures as before!

• AC single subject example!

- Craving: 66.9%!- CPD: 77.1%!

• PNc single subject example!

- Craving: 57.6%!- CPD: 63.0%


22






Control Systems Engineering LaboratoryCSEL Adaptive Intervention Structure

23

Treatment Goals

TreatmentDosages Measured

Outcomes

Measured Disturbances

Decision Rules

Behavior Change

Mechanisms

• Connecting clinical concepts to control systems engineering


• Connecting clinical concepts to control systems engineering!- Treatment goals ⇔ set points!

1. CPD = 0, t ⩾ TQD!

2. Craving = 0, t ⩾ TQD

Adaptive Intervention Structure

24

Intervention Algorithm

CPD target

Craving target

TreatmentDosages Measured

Outcomes

Measured Disturbances

Behavior Change

Mechanisms



- Tailoring variables ⇔ measured outcomes & disturbances!• Controlled variables!

1. CPD reported via smartphone!2. Craving reported via smartphone!

• Measured disturbances!1. Quit!2. Stress reported via smartphone


25

CPD

Craving

Quit Stress

Intervention Algorithm

CPD target

Craving target

TreatmentDosages Behavior

Change Mechanisms



- Tailoring variables ⇔ measured outcomes & disturbances!

- Treatment components & clinical use guidelines ⇔ manipulated variables & constraints!

1. ucouns [# cessation counseling sessions / day]!

2. ubup [# 150 mg bupropion doses / day]!

3. uloz [# nicotine lozenges / day]


26

ucouns Intervention Algorithm

CPD

Craving

Behavior Change

Mechanisms

Quit Stress

ubup uloz

CPD target

Craving target



- Tailoring variables ⇔ measured outcomes & disturbances!

- Treatment components & clinical use guidelines ⇔ manipulated variables & constraints!

- Behavior change process ⇔ open-loop dynamical model

27

ucouns Intervention Algorithm

CPD

Craving

Behavior Change Models

Quit Stress

ubup uloz

CPD target

Craving target

CPD

Craving

�=

Pcpdc

(s) Pcpdb(s) Pcpdl

(s)Pcravc(s) Pcravb(s) Pcravl(s)

�2

4uc

ub

ul

3

5+

PcpdQ

(s) PcpdS(s)

PcravQ(s) PcravS (s)

� QuitStress

�


• Hybrid Model Predictive Control (HMPC) framework!

- Manages discrete-leveled nature of ucouns, ubup, & uloz!

- Clinically-advantageous features of predictive control!• Combined feedback-feedforward action!

• Explicit constraint handling!

• Optimized manipulated variable adjustment!

• Systematically manages multiple inputs, multiple outputs!

• Moving horizon implementation, robust decision-making

ucouns HMPC

Algorithm

CPD

Craving

Behavior Change Models

Quit Stress

ubup uloz

CPD target

Craving target

28

Control Systems Engineering LaboratoryCSEL HMPC Decision-Making

29

Specify intervention targets, components,

constraints

Supply dynamic models

Offline Online (done each review period)


29


constraints


Offline

Obtain CPD, Craving, & Stress measurements

Online (done each review period)


29


constraints


Offline


Predict how CPD & Craving will deviate from targets over the next p days using measurements,

models, and prior dose assignments



29


constraints


Offline




Determine the best set of ucouns, ubup, & uloz

adjustments for the following m days by minimizing an objective function subject to constraints



29


constraints


Offline







Assign only the next set of dosage adjustments (moving horizon component)


29

Wait until the next review period


constraints


Offline







Assign only the next set of dosage adjustments (moving horizon component)

Control Systems Engineering LaboratoryCSEL Nominal Models

• Quit-response models!- Describes patient unable to successfully quit on their own!- Patterned after single subject from McCarthy et al., 2008 study!- Based in closed-loop models describing self-regulation process!

!

!

!

!

!

!

!

• Dose-, Stress-response models informed by data, literature, step/impulse responses

30

0 5 10 15 20 25 30 35 40 45 500

5

10

CPD

0 5 10 15 20 25 30 35 40 45 500102030

Craving

0 5 10 15 20 25 30 35 40 45 500

1Quit

Day

0

0

Baseline CPD

Baseline Craving

Representative patient model

Control Systems Engineering LaboratoryCSEL MLD Representation

• Manipulated variables can only be assigned in pre-determined, discrete levels!

• Represent the open-loop system as a linear hybrid system in Mixed Logical Dynamical (MLD) form (Bemporad & Morari, 1999)

31

x(k + 1) = Ax(k) +B1u(k) +B2�(k) +B3z(k) +Bdd(k)

y(k) = Cx(k) + d

0(k) + ⌫(k)

E2�(k) + E3z(k) E5 + E4y(k) + E1u(k)� Edd(k)

where:!x(k), u(k), and y(k) are state, input, and output variables, respectively,!d(k), d′(k), and ν(k) are measured disturbance, unmeasured disturbance, and measurement noise signals, respectively, and!δ(k) and z(k) are discrete and continuous auxiliary variables.! !

Control Systems Engineering LaboratoryCSEL MLD Representation (cont.)

• Logical representations of the available dosages!

- ucouns(k) ∈ {0, 1} sessions/day!

!

!

- ubup(k) ∈ {0, 1, 2} 150 mg doses/day!

!

!

- uloz(k) ∈ {0, 1, 2, … , 20} lozenges/day

32

�i

(k) = 1 , zi

(k) = i; i 2 {0, 1}

ucouns

=1X

i=0

zi

(k),1X

i=0

�i

(k) = 1

�j(k) = 1 , zj(k) = j � 2; j 2 {2, 3, 4}

ubup =4X

j=2

zj(k),4X

j=2

�j(k) = 1

�k

(k) = 1 , zk

(k) = k � 5; k 2 {5, ..., 25}

uloz

=25X

k=5

zk

(k),25X

k=5

�k

(k) = 1


where:!r indicates reference values based around a pre-defined TQD!Qy is the penalty weight for the control error, !QΔu is a penalty weight for manipulated variable move suppression, andQu, Qd, and Qz are the penalty weights on the manipulated and auxiliary variables. !

HMPC Features

33

• Daily dosing decisions calculated by minimizing an objective function (J) subject to constraints:

• Solved as a mixed integer quadratic programming (MIQP) problem!

min{[u(k+i)]m�1

i=0 ,[�(k+i)]p�1i=0 ,[z(k+i)]p�1

i=0 }J ,

pX

i=1

||y(k + i)� yr(k + i)||2Qy+

m�1X

i=0

||�u(k + i)||2Q�u

+m�1X

i=0

||u(k + i)� ur||2Qu+

p�1X

i=0

||�(k + i)� �r||2Q�

+p�1X

i=0

||z(k + i)� zr||2Qz


where:!r indicates reference values based around a pre-defined TQD!Qy is the penalty weight for the control error, !QΔu is a penalty weight for manipulated variable move suppression, andQu, Qd, and Qz are the penalty weights on the manipulated and auxiliary variables. !

HMPC Features

33

• Daily dosing decisions calculated by minimizing an objective function (J) subject to constraints:

• Solved as a mixed integer quadratic programming (MIQP) problem!

min{[u(k+i)]m�1

i=0 ,[�(k+i)]p�1i=0 ,[z(k+i)]p�1

i=0 }J ,

pX

i=1

||y(k + i)� yr(k + i)||2Qy+

m�1X

i=0

||�u(k + i)||2Q�u

+m�1X

i=0

||u(k + i)� ur||2Qu+

p�1X

i=0

||�(k + i)� �r||2Q�

+p�1X

i=0

||z(k + i)� zr||2Qz

• Basing dosing decisions in a quantified optimality criterion represents a significant departure from current treatment methods!

Control Systems Engineering LaboratoryCSEL HMPC Features (cont.)

34

• Optimized dosing subject to constraints!

- High, low dosage bounds

- Move size constraints

- Lower CPD, Craving bound = 0

0 ucouns

(k) 1

0 ubup

(k) 2

0 uloz

(k) 20

0 kX

i=0

ucouns

(k � i) 5

�1 �ucouns

(k) 1

0 �ubup

(k) 0, k 6= 4 + nTsw

0 1, k = 4 + nTsw

, n = 0, 1, 2, ...

�20 �uloz

(k) 20


35






Control Systems Engineering LaboratoryCSEL Nominal Performance

• Evaluating nominal performance!

- Patient receiving the intervention is the same patient around whom the intervention was designed!

- Nominal patient!

• Patterned after PNc single subject previously shown (McCarthy et al., 2008)!

• Unable to quit smoking on their own!

• Baseline CPD = 9.3, Craving = 16.1

36

Control Systems Engineering LaboratoryCSEL Nominal Performance

• Evaluating nominal performance!

- Patient receiving the intervention is the same patient around whom the intervention was designed!

- Nominal patient!

• Patterned after PNc single subject previously shown (McCarthy et al., 2008)!

• Unable to quit smoking on their own!


• Simulation time frame!

- Patient-reports of CPD, Craving, & Stress start on day 0 ➔ Dosage decisions made each day starting on day 0!

- Intervention implemented through day 50!

- TQD = day 15

• p = 30 days, m = 8 days36


0 5 10 15 20 25 30 35 40 45 50

0

5

10

CPD

0 5 10 15 20 25 30 35 40 45 500

10

20

Craving

0 5 10 15 20 25 30 35 40 45 500

1

2Bupropion Dose

0 5 10 15 20 25 30 35 40 45 500

1Counseling Dose

0 5 10 15 20 25 30 35 40 45 500

10

20Lozenge Dose

0 5 10 15 20 25 30 35 40 45 500

1

Disturbance Signals

0 5 10 15 20 25 30 35 40 45 50−2

0

2

Nominal Performance, Simulation 1

• Objective function penalties: Qcpd = 10, Qcrav = 10, Qtotal(u) = 1!

• Able to promote successful quit attempt!

- Post-TQD cigs: 11.9!

- # days CPD=0: 14!

- Day 50 Craving: 3.2 points!

- 242 lozenges assigned

37 Day

Quit

Stress

CPD

CravingResponses w/ interventionResponse, no intervention

Target level


0 5 10 15 20 25 30 35 40 45 50

0

5

10

0 5 10 15 20 25 30 35 40 45 500

10

20

0 5 10 15 20 25 30 35 40 45 500

1

2Bupropion Dose

0 5 10 15 20 25 30 35 40 45 500

1Counseling Dose

0 5 10 15 20 25 30 35 40 45 500

10

20Lozenge Dose

0 5 10 15 20 25 30 35 40 45 500

1

Disturbance Signal(s)

0 5 10 15 20 25 30 35 40 45 50−2

0

2

Nominal Performance, Simulation 2



- Post-TQD cigs: 9.6!

- # days CPD=0: 23!


- 99 lozenges assigned!

• Additional ucouns, ubup doses!

• Illustrates flexibility of this approach

38 Day

Quit

Stress

CPD

CravingResponses w/ interventionResponse, no intervention

Target level

Control Systems Engineering LaboratoryCSEL Robust Performance:

Alternate Patient• Evaluating robust performance!

- Patient receiving the intervention is not the patient around whom the intervention was designed, ie, plant-model mismatch introduced!

- Alternate patient who receives the intervention (“plant”)!

• Patterned after a different subject from McCarthy et al. (2008) study!


39

0 5 10 15 20 25 30 35 40 45 500

5

10

CPD

0 5 10 15 20 25 30 35 40 45 500

10

20

30

Craving

Nominal (representative) patient modelAlternate patient model

DayTQD

TQD


Alternate Patient, Simulation 1



- CPD=0, t ⩾ day 17!


- Steady-state uloz: 16 loz/day!

• Higher Craving baseline leads to sustained high lozenge dosing

40

0 5 10 15 20 25 30 35 40 45 500

5

10

0 5 10 15 20 25 30 35 40 45 500

10

20

30

0 5 10 15 20 25 30 35 40 45 500

1

2Bupropion Dose

0 5 10 15 20 25 30 35 40 45 500

1Counseling Dose

0 5 10 15 20 25 30 35 40 45 500

10

20Lozenge Dose

0 5 10 15 20 25 30 35 40 45 500

1


0 5 10 15 20 25 30 35 40 45 50−1

0

1

Day

Quit

Stress

CPD

Craving Responses w/ interventionResponse, no intervention

Target level


Alternate Patient, Simulation 2



- CPD=0, t ⩾ day 17!


- Steady-state uloz: 4 loz/day!

• Trade-off between Craving offset and steady-stateuloz assignment

41

0 5 10 15 20 25 30 35 40 45 500

5

10

0 5 10 15 20 25 30 35 40 45 500

10

20

30

0 5 10 15 20 25 30 35 40 45 500

1

2Bupropion Dose

0 5 10 15 20 25 30 35 40 45 500

1Counseling Dose

0 5 10 15 20 25 30 35 40 45 500

10

20Lozenge Dose

0 5 10 15 20 25 30 35 40 45 500

1


0 5 10 15 20 25 30 35 40 45 50−1

0

1

Day

Quit

Stress

CPD

Craving Responses w/ interventionResponse, no intervention

Target level


42






Control Systems Engineering LaboratoryCSEL Summary & Conclusions

• Dynamical systems models offer a means to describe smoking cessation as a behavior change process!

- System identification methods (e.g., pem) used in conjunction with ILD to estimate parsimonious behavior change models!

• Group average, single subject perspectives!

• Parameter estimates provide insight into treatment effects!

- Reverse-engineered & estimated models describing cessation as a self-regulation process!

• Departure from traditional descriptions of self-regulated behaviors!

• Smoking activity meant to regulate Craving!

• Changes in CPD result of a Quit disturbance, feedback path!

• Psychological self-regulator acts as a P w/ Filter controller

43

Control Systems Engineering LaboratoryCSEL Summary & Conclusions (cont.)

• Laid the conceptual & computational groundwork for a clinically-relevant, optimized, adaptive cessation intervention!

- Established a connection between clinical aspects of an adaptive smoking intervention & control systems engineering!

- Formulated an intervention algorithm based in an HMPC framework!

- Simulations indicate this intervention can support a successful quit attempt!

• Intervention formulation features tuning such that a clinician can flexibly adjust performance/dosing!

• Tuning for nominal performance generally involves subtle trade-off between lozenge demands and post-TQD lapses!

• Inter-connected nature of CPD & Craving helps facilitate robust decision-making despite plant-model mismatch

44

Control Systems Engineering LaboratoryCSEL Additional Work Not Shown Today

• Development & estimation of dynamic mediation models!

• Illustration of analytical opportunities afforded by simulation &

dynamical systems models (e.g., modes of intervention action) !

• Exploration of self-regulation on a within-day time scale!

• Details of nominal model development, capacity constructs!

• Incorporation of 3-degree-of-freedom tuning functionality!

• Detailed analysis of tuning functionality, additional nominal and robust

performance scenarios!

• Outline of future directions (eg, within-day dosing)

45

Control Systems Engineering LaboratoryCSEL Publications

- K.P. Timms, D.E. Rivera, L.M. Collins, & M.E. Piper (2012). “System identification modeling of a smoking cessation intervention,” Proceedings of the 16th IFAC Symposium on System Identification: 786-791.!

- K.P. Timms, D.E. Rivera, L.M. Collins, & M.E. Piper (2013). “Control systems engineering for understanding and optimizing smoking cessation interventions,” Proceedings of the 2013 American Control Conference: 1967-1972.!

- K.P. Timms, D.E. Rivera, L.M. Collins, & M.E. Piper (2014). “A dynamical systems approach to understanding self-regulation in smoking cessation behavior change,” Nicotine & Tobacco Research, 16 (Suppl 2): S159-S168. doi: 10.1093/ntr/ntt149!

- K.P. Timms, D.E. Rivera, L.M. Collins, & M.E. Piper (2014). “Continuous-time system identification of a smoking cessation intervention,” International Journal of Control, 87 (7): 1423-1437!

- K.P.Timms, C.A. Martin, D.E. Rivera, E.B. Hekler, & W. Riley (2014). “Leveraging intensive longitudinal data to better understand health behaviors,” Proceedings of the 36th Annual IEEE EMBS Conference: 6888-6891.!

- K.P. Timms, D.E. Rivera, L.M. Collins, & M.E. Piper. “Dynamic modeling and system identification of mediated behavior change with a smoking cessation intervention case study,,” Multivariate Behavioral Research (In Revisions).!

- K.P. Timms, D.E. Rivera, M.E. Piper, & L.M. Collins (2014). “A Hybrid Model Predictive Control strategy for optimizing a smoking cessation intervention,” Proceedings of the 2014 American Control Conference: 2389-2394.!

!Additional publications being prepared for venues such as

Journal of Consulting & Clinical Psychology and Control Engineering Practice

46

Control Systems Engineering LaboratoryCSEL Acknowledgements

• This work was supported by the Office of Behavioral and Social Sciences Research and NIDA at the NIH (K25 DA021173, R21 DA024266, P50 DA10075, F31 DA035035), American Heart Association!

• Advisor: Dr. Rivera!

• Committee members: Dr. Frakes & Dr. Nielsen!

• Collaborators: Dr. Linda Collins (PSU), Dr. Megan Piper (UW)!

• Professors, BDGP advisors & administrative staff!

• Lab colleagues: Sunil Deshpande, Yuwen Dong, Cesar Martin!

• Family & friends

47


Thank you! !

www.kevintimms.com!!

http://csel.asu.edu/?q=AdaptiveIntervention

48

http://www.kevintimms.com

http://csel.asu.edu/?q=AdaptiveIntervention

Control Systems Engineering LaboratoryCSEL Robust Performance,

Alternate Patient A, Sim 1

50

• Alternate Patient!

• Able to quit on their own!

- Baseline CPD = 20.3!

- Baseline Craving = 23.8


Alternate Patient B

51






Alternate Patient C, Sim 1





52


Alternate Patient C, Sim 2

53




- Baseline Craving = 17.2!

- fcpd = 1, fcrav = 0.2

Control Systems Engineering LaboratoryCSEL HMPC Objective Function

54

• Daily decision-making centered around:!

- Promoting cessation (meeting CPD and Craving targets)!

- Concern for intervention intensity!

• Dosage assignments calculated by minimizing an objective functionwhere !

!

!

min{[u(k+i)]m�1

i=0 ,[�(k+i)]p�1i=0 ,[z(k+i)]p�1

i=0 }J

J ,pX

i=1

||CPD(k + i)� CPDr

(k + i)||2Q

cpd

+pX

i=1

||Craving(k + i)� Cravingr

(k + i)||2Q

crav

+m�1X

i=0

||(uloz

(k + i)� uloz

r

)||2Q

loz

+m�1X

i=0

||(�uloz

(k + i))||2Q�loz

+ ...

Control Systems Engineering LaboratoryCSEL Objective Function (cont.)

55

J = Predicted daily deviation from goal CPDWcpd +( )2 Predicted daily deviation

from goal Craving levelWcrav ( )2Alterations to bupropion

dose over the next m daysWΔbup ( )2 + Alterations to lozenge dose over the next m daysWΔloz ( )2+


• Wcpd, Wcrav, WΔbup, and WΔloz penalties reflect a trade off between meeting intervention targets and dosing concerns

55





• Wcpd, Wcrav, WΔbup, and WΔloz penalties reflect a trade off between meeting intervention targets and dosing concerns

• Each day, optimized future intervention adjustments calculated by minimizing J!

- Subject to operational and clinical constraints!

- Optimization accomplished via well established, tractable computational routines that can be done within existing infrastructure

55




Control Systems Engineering LaboratoryCSEL Model Predictive Control!

Optimization Problem

56

subject to restrictions (i.e., constraints) on:

• manipulated variable range limits (i.e., intervention dosage limits)!!

• the rate of change of manipulated variables (i.e., dosage changes)!!

• controlled and associated variable limits (i.e., limits on measured primary and secondary outcomes)

Many operating and clinical requirements can be expressed as constraint equations for the Model Predictive Control optimization problem.

Take Controlled Variables to Goal Penalize Changes in the Manipulated Variables

J =

! "# $p

%

ℓ=1

Qe(ℓ)(y(t + ℓ|t) − r(t + ℓ))2 +

! "# $m

%

ℓ=1

Q∆u(ℓ)(∆u(t + ℓ − 1|t))2


57

Control Systems Engineering LaboratoryCSEL Control Systems Engineering

• The field that relies on engineering models to develop algorithmsfor adjusting system variables so that their behavior over time is transformed from undesirable to desirable.

58MANual AUTOmatic

• Control engineering plays an important part in many everyday life:!- Cruise control in automobiles!- Heating and cooling systems!- Homeostasis

Control Systems Engineering LaboratoryCSEL Model Predictive Control

• MPC - An algorithmic framework used for adjusting system variables in order to move a system from an undesirable to a desirable state.

• Steps for determining dosage adjustments:

59




- Predict how CPD and Craving will deviate from the desired levels over the next p days.

• Based on recent measurements, recent dose assignments, dynamic models of how CPD and Craving respond to dosage changes and initiation of a quit attempt.

- Determine the bupropion and lozenge dosages for the next m days that will best promote CPD = 0 and Craving = 0 each day during quit attempt.

• Calculated by minimizing an objective function - equation quantifying anticipated deviation from goals and intervention effort.

- Assign only the very next set of dose adjustments (moving horizon).

59




- Predict how CPD and Craving will deviate from the desired levels over the next p days.

• Based on recent measurements, recent dose assignments, dynamic models of how CPD and Craving respond to dosage changes and initiation of a quit attempt.

- Determine the bupropion and lozenge dosages for the next m days that will best promote CPD = 0 and Craving = 0 each day during quit attempt.

• Calculated by minimizing an objective function - equation quantifying anticipated deviation from goals and intervention effort.

- Assign only the very next set of dose adjustments (moving horizon).

- Repeat the next day with updated measurements.59

Control Systems Engineering LaboratoryCSEL Future Work

60

• Clinical & practical advantages of 3 Degree-of-Freedom HMPC (Nandola & Rivera, 2013) include:!

- Ability to tune for performance & plant-model mismatch (via αr, αd, fa: [0,1])!

- Objective function reduced to CPD and Craving goal-seeking!

- More “clinician-friendly” tuning

• Evaluate performance, robustness for patient-to-patient variability!

• Ultimately, novel clinical trials required


61

Control Systems Engineering LaboratoryCSEL OL Step & Impulse Responses

5 10 15 20 25 300

2

4

6

8Response of Craving to unit step in Quit on day 0

5 10 15 20 25 30

−8−6−4−2

0

Response of CPD to unit step in Quit on day 0

5 10 15 20 25 30

0.51

1.52

Response of Craving to unit impulse in Stress on day 0

5 10 15 20 25 30

0.20.40.60.8

1

Response of CPD to unit impulse in Stress on day 0

5 10 15 20 25 30

−3

−2

−1

0Response of Craving to unit impulse in Counseling on day 0

5 10 15 20 25 30−2

−1

0Response of CPD to unit impulse in Counseling on day 0

5 10 15 20 25 30

−4

−2

0Response of Craving to unit step in Bupropion on day 0

5 10 15 20 25 30

−3

−2

−1

0Response of CPD to unit step in Bupropion on day 0

5 10 15 20 25 30−0.6757

−0.3378

0

Day

Response of Craving to unit impulse in Lozenge on day 0

5 10 15 20 25 30−0.25−0.2−0.15−0.1−0.05

Day

Response of CPD to unit impulse in Lozenge on day 0

Control Systems Engineering LaboratoryCSEL Plant OL Transfer Functions

CPD

Craving

�=

Pcpdc

PcpdbPcpdl

Pcravc Pcravb Pcravl

�2

4uc

ub

ul

3

5+

PcpdQ

PcpdS

PcravQ PcravS

� Quit

Stress

�

Pcravc(s) =�50

3.752 s2 + 2 ⇤ 3.75 ⇤ 1.5 s+ 1

Pcravb(s) =�4.06 (2 s+ 1)

1.12 s2 + 2 ⇤ 1.1 ⇤ 1 s+ 1e(�3 s)

Pcravl(s) =�0.70 (0.44 s+ 1)

0.5 s+ 1

PcravQ(s) =7.30 s2 + 2.20 s+ 0.02

s2 + 0.23 s+ 0.04

PcravS (s) =3 (0.6 s+ 1)

0.8 s+ 1

Pcpdc(s) =

�30

42 s2 + 2 ⇤ 4 ⇤ 1.5 s+ 1

Pcpdb(s) =

�3.08 (2.5 s+ 1)

1.52 s2 + 2 ⇤ 1.5 ⇤ 1 s+ 1e(�3 s)

Pcpdl(s) =

�0.13 (s+ 2.25)

0.5 s+ 1

PcpdQ(s) =

�9.25 s2 � 0.96 s+ 0.01

s2 + 0.23 s+ 0.04

PcpdS(s) =

1.65 (0.5 s+ 1)

0.8 s+ 1


Optimized Adaptive Smoking Cessation

Intervention

ILD / EMA

Dynamical SystemsModeling

Control Algorithms(e.g., Model Predictive Control)

Intervention Performance Objectives& Clinical Constraints

ExperimentationComputing TechnologyOptimized Smoking

Cessation Intervention

Long-Term Goal

Long-term goal: Design a personalized smoking intervention where treatments are adjusted over time based on changing needs of a patient.

64

Control Systems Engineering LaboratoryCSEL Self-Reg. Parameter Estimates

65

Control Systems Engineering LaboratoryCSEL Effects of Parameter Uncertainty

66

Control Systems Engineering LaboratoryCSEL Dynamic Mediation Modeling

• Classical statistical mediation: Causal chain described by Baron & Kenney (1986), MacKinnon (2008)

• Traditionally described with static structural equation models: where a, b, c’ correspond to steady-state gains

67

M = �01 + aX + e1

Y = �02 + bM + c0X + e2

(1)

(2)

Control Systems Engineering LaboratoryCSEL Dynamic Mediation Modeling (cont.)

• Casting mediated behavior change as a dynamical system: temporal emphasis (Collins et al., 1998)

• Structural equation models (1) and (2) correspond to steady-state process models!

- Basis for a fluid analogy akin to production-inventory systems in supply chains (Navarro-Barrientos et al., 2011; Schwartz et al., 2006)

68


69

Dynamic Mediation Model

Develop dynamic models to describe the process of behavior change according to a mediational mechanism

• Fluid analogy: Basis for differential equation model development

I20

M(t)

Y(t)Pipe

Valve

X(t)

c' X(t)

a X(t)

b M(t)

Y(t)


70


• Dynamical systems representation of behavior change as a meditational process ➔ Parallel-cascade system

71

M(s) = Pa(s)X(s) + d1(s)

Y (s) = Pc0(s)M(s) + Pb(s)M(s) + d2(s)

(3)

(4)

Control Systems Engineering LaboratoryCSEL Mediation Model Estimates

72


73

Towards Adaptive Intervention Design

• Have a model for failed quit attempt that can act as basis for design of a closed-loop intervention (dashed green below).!

• Proposed an open-loop drug mechanism that can promote cessation (solid blue below).

CPD

Current Craving

Quit Attempt & Intervention


74

0 5 10 15 20 25 30 35 400

5

10

15

20Cigsmked

Active Drug, Counseling − DataActive Drug, Counseling − Self−Regulation ModelPlacebo Drug, No Counseling − DataPlacebo Drug, No Counseling − Self−Regulation Model

0 5 10 15 20 25 30 35 4015

20

25

30Craving

0 5 10 15 20 25 30 35 40

0

1

Day

Independent Variable (Quit Attempt=1, Yes; Quit=0, No)

Current Craving

CPD


Craving Self-Regulator’s gain is smaller and time constant is larger for AC group: smaller and

slower resumption in CPD for AC group

• Model estimates suggest:!

- Initial reduction in CPD larger in AC group!

- Active treatment may diminish self-regulatory-nature of cessation


75


0 5 10 15 20 25 30 35 400

5

10

15

20Cigsmked

Active Drug, Counseling − DataActive Drug, Counseling − Self−Regulation ModelPlacebo Drug, No Counseling − DataPlacebo Drug, No Counseling − Self−Regulation Model

0 5 10 15 20 25 30 35 4015

20

25

30Craving

0 5 10 15 20 25 30 35 40

0

1

Day

Independent Variable (Quit Attempt=1, Yes; Quit=0, No)

CPD

Current Craving

• Model estimates suggest:!

- Initial reduction in CPD larger in AC group!

- Active treatment may diminish self-regulatory-nature of cessation!

- Craving Generation Process: Equation structure suggests two underlying subprocesses in competition

Control Systems Engineering LaboratoryCSEL Behavioral Interventions as

Dynamical Systems

• From Glass, G.V., Wilson, V.L. and J.M. Gottman, “Design and Analysis of Time-Series Experiments,” Colorado Associated University Press, 1975.

77


78

Y. Dong, Dissertation