Timms - Defense Slides - A novel engineering approach to modeling and optimizing smoking cessation interventions

Control Systems Engineering Laboratory
CSEL
 
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

CSEL 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

CSEL Agenda
3

CSEL 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

CSEL 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

CSEL 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

CSEL 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

CSEL 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

CSEL Agenda
7

CSEL 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

CSEL 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

CSEL 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

CSEL McCarthy et al., 2008 (cont.)
10
AC group average
PNc group average
AC single subject ex
PNc single subject ex
0 5 10 15 20 25 30 35
0
5
10
15
CPD
0 5 10 15 20 25 30 35
5
15
25
35
Craving
0 5 10 15 20 25 30 35
0
1
Day
Quit
TQD
TQD
TQD
#CigarettesPoints

• Data sets 
 
• Target Quit Date = TQD
• Quit represents initiation of
a quit attempt
• Our focus: 36 days  
(7 pre-TQD, 28 post-TQD)
10
AC group average
PNc group average
0 5 10 15 20 25 30 35
0
5
10
15
CPD
0 5 10 15 20 25 30 35
5
15
25
35
Craving
0 5 10 15 20 25 30 35
0
1
Day
Quit
TQD
TQD
TQD
#CigarettesPoints

• 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
AC group average
PNc group average
0 5 10 15 20 25 30 35
0
5
10
15
CPD
0 5 10 15 20 25 30 35
5
15
25
35
Craving
0 5 10 15 20 25 30 35
0
1
Day
Quit
TQD
TQD
TQD
#CigarettesPoints

CSEL 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

CSEL 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-
Regulator
e
+
+
Pr
Disturbances  
e.g., intervention,
emotional/cognitive  
state, smoking cues
Biological or
psychological
outcome 
e.g., blood nicotine,
urge level 
Cigarette
smoking
• Hypothesized set points (r): blood nicotine, affect, urge levels!
• Disturbances: Interventions, emotional/cognitive states,  
context cues

CSEL 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

CSEL 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 plausibility
13
Fit [%] = 100 ⇤
✓
1
||y(t) ˜y(t)||2
||y(t) ¯y||2
◆
Pd(s)
+
-
C(s)
e
+
+
P(s)rcrav
Quit
CPD Craving

CSEL 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 model
P(s) =
K1(⌧as + 1)
⌧1s + 1
Pd(s) = Kd
C(s) =
Kc
⌧cs + 1

CSEL 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 into 
the 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 35
0
5
10
15
CPD
0 5 10 15 20 25 30 35
15
20
25
30
Craving
0 5 10 15 20 25 30 35
0
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

CSEL
- 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

CSEL
0 5 10 15 20 25 30 35
0
5
10
15
20
CPD
0 5 10 15 20 25 30 35
0
10
20
30
40
Craving
0 5 10 15 20 25 30 35
0
1
Day
Quit
21
AC subject data
AC 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%

CSEL Agenda
22

CSEL Adaptive Intervention Structure
23
Treatment
Goals
Treatment 
Dosages Measured
Outcomes
Measured
Disturbances
Decision
Rules
Behavior
Change
Mechanisms
• Connecting clinical concepts to control systems engineering

CSEL
• 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
Treatment 
Dosages Measured
Outcomes
Measured
Disturbances
Behavior
Change
Mechanisms

CSEL
- 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
Treatment 
Dosages Behavior
Change
Mechanisms

CSEL
- 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

- 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
4
uc
ub
ul
3
5 +

PcpdQ
(s) PcpdS
(s)
PcravQ
(s) PcravS
(s)

Quit
Stress

• 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

CSEL HMPC Decision-Making
29
Specify intervention
targets, components,
constraints
Supply dynamic
models
Ofﬂine Online (done each review period)

29
constraints
Supply dynamic
models
Ofﬂine
Obtain CPD, Craving, & Stress measurements
Online (done each review period)

29
constraints
Supply dynamic
models
Ofﬂine
Predict how CPD & Craving will deviate from
targets over the next p days using measurements,
models, and prior dose assignments

29
constraints
Supply dynamic
models
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
Supply dynamic
models
Ofﬂine
Assign only the next set of dosage
adjustments (moving horizon component)

29
Wait until the next review period
constraints
Supply dynamic
models
Ofﬂine
Assign only the next set of dosage
adjustments (moving horizon component)

CSEL 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 50
0
5
10
CPD
0 5 10 15 20 25 30 35 40 45 50
0
10
20
30
Craving
0 5 10 15 20 25 30 35 40 45 50
0
1
Quit
Day
0
0
Baseline CPD
Baseline Craving
Representative patient model

CSEL 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) + d0
(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.!
!

CSEL 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

CSEL
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, and 
Qu, 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 1
i=0 ,[z(k+i)]p 1
i=0 }
J ,
pX
i=1
||y(k + i) yr(k + i)||2
Qy
+
m 1X
i=0
|| u(k + i)||2
Q u
+
m 1X
i=0
||u(k + i) ur||2
Qu
+
p 1X
i=0
|| (k + i) r||2
Q
+
p 1X
i=0
||z(k + i) zr||2
Qz

CSEL
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, and 
Qu, 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 1
i=0 ,[z(k+i)]p 1
i=0 }
J ,
pX
i=1
||y(k + i) yr(k + i)||2
Qy
+
m 1X
i=0
|| u(k + i)||2
Q u
+
m 1X
i=0
||u(k + i) ur||2
Qu
+
p 1X
i=0
|| (k + i) r||2
Q
+
p 1X
i=0
||z(k + i) zr||2
Qz
• Basing dosing decisions in a quantified optimality criterion represents
a significant departure from current treatment methods!

CSEL 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

CSEL Agenda
35

CSEL 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

CSEL 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 days
36

CSEL
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 50
0
10
20
Craving
0 5 10 15 20 25 30 35 40 45 50
0
1
2
Bupropion Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
Counseling Dose
0 5 10 15 20 25 30 35 40 45 50
0
10
20
Lozenge Dose
0 5 10 15 20 25 30 35 40 45 50
0
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
Craving
Responses w/ intervention
Response, no intervention
Target level

CSEL
0 5 10 15 20 25 30 35 40 45 50
0
5
10
0 5 10 15 20 25 30 35 40 45 50
0
10
20
0 5 10 15 20 25 30 35 40 45 50
0
1
2
Bupropion Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
Counseling Dose
0 5 10 15 20 25 30 35 40 45 50
0
10
20
Lozenge Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
Disturbance Signal(s)
0 5 10 15 20 25 30 35 40 45 50
−2
0
2
Nominal Performance, Simulation 2
• Able to promote
- 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
Craving
Responses w/ intervention
Target level

CSEL 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 50
0
5
10
CPD
0 5 10 15 20 25 30 35 40 45 50
0
10
20
30
Craving
Nominal (representative) patient model
Alternate patient model
Day
TQD
TQD

Alternate Patient, Simulation 1
• Able to promote
- 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 50
0
5
10
0 5 10 15 20 25 30 35 40 45 50
0
10
20
30
0 5 10 15 20 25 30 35 40 45 50
0
1
2
Bupropion Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
Counseling Dose
0 5 10 15 20 25 30 35 40 45 50
0
10
20
Lozenge Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
0 5 10 15 20 25 30 35 40 45 50
−1
0
1
Day
Quit
Stress
CPD
Craving Responses w/ intervention
Target level

Alternate Patient, Simulation 2
• Able to promote
- CPD=0, t ⩾ day 17!
- Steady-state uloz: 4 loz/day!
• Trade-off between Craving
offset and steady-state 
uloz assignment
41
0 5 10 15 20 25 30 35 40 45 50
0
5
10
0 5 10 15 20 25 30 35 40 45 50
0
10
20
30
0 5 10 15 20 25 30 35 40 45 50
0
1
2
Bupropion Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
Counseling Dose
0 5 10 15 20 25 30 35 40 45 50
0
10
20
Lozenge Dose
0 5 10 15 20 25 30 35 40 45 50
0
1
0 5 10 15 20 25 30 35 40 45 50
−1
0
1
Day
Quit
Stress
CPD
Craving Responses w/ intervention
Target level

CSEL Agenda
42

CSEL 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

CSEL 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

CSEL 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

CSEL 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

CSEL 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

CSEL
Thank you!
!
www.kevintimms.com!
!
http://csel.asu.edu/?q=AdaptiveIntervention
48

CSEL 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

CSEL 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 function 
 
 
where !
!
!
min
{[u(k+i)]m 1
i=0 ,[ (k+i)]p 1
i=0 ,[z(k+i)]p 1
i=0 }
J
J ,
pX
i=1
||CPD(k + i) CPDr(k + i)||2
Qcpd
+
pX
i=1
||Craving(k + i) Cravingr(k + i)||2
Qcrav
+
m 1X
i=0
||(uloz(k + i) ulozr )||2
Qloz
+
m 1X
i=0
||( uloz(k + i))||2
Q loz
+ ...

CSEL Objective Function (cont.)
55
J =
Predicted daily deviation
from goal CPDWcpd +( )2 Predicted daily deviation
from goal Craving levelWcrav ( )2
Alterations 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
J =

• 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
J =

CSEL 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)(ˆy(t + ℓ|t) − r(t + ℓ))2
+
m
ℓ=1
Q∆u(ℓ)(∆u(t + ℓ − 1|t))2

CSEL
57

CSEL Control Systems Engineering
• The ﬁeld that relies on engineering models to develop algorithms 
for adjusting system variables so that their behavior over time is
transformed from undesirable to desirable.
58
MANual AUTOmatic
• Control engineering plays an important part in many everyday life:!
- Cruise control in automobiles!
- Heating and cooling systems!
- Homeostasis

CSEL 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

CSEL 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

CSEL
61

CSEL OL Step & Impulse Responses
5 10 15 20 25 30
0
2
4
6
8
Response 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
0.5
1
1.5
2
Response of Craving to unit impulse in Stress on day 0
5 10 15 20 25 30
0.2
0.4
0.6
0.8
1
Response of CPD to unit impulse in Stress on day 0
5 10 15 20 25 30
−3
−2
−1
0
Response of Craving to unit impulse in Counseling on day 0
5 10 15 20 25 30
−2
−1
0
Response of CPD to unit impulse in Counseling on day 0
5 10 15 20 25 30
−4
−2
0
Response of Craving to unit step in Bupropion on day 0
5 10 15 20 25 30
−3
−2
−1
0
Response 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

CSEL Plant OL Transfer Functions

CPD
Craving
=

Pcpdc
Pcpdb
Pcpdl
Pcravc
Pcravb
Pcravl
2
4
uc
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 + 1
e( 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 + 1
e( 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

CSEL
Optimized Adaptive
Smoking Cessation
Intervention
ILD / EMA
Dynamical Systems
Modeling
Control Algorithms
(e.g., Model Predictive Control)
Intervention Performance Objectives
& Clinical Constraints
ExperimentationComputing Technology
Optimized 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

CSEL Self-Reg. Parameter Estimates
65

CSEL Effects of Parameter Uncertainty
66

CSEL 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 + c0
X + e2
(1)
(2)

CSEL 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

CSEL
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)

CSEL Mediation Model Estimates
72

CSEL
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

CSEL
74
0 5 10 15 20 25 30 35 40
0
5
10
15
20
Cigsmked
Active Drug, Counseling − Data
Active Drug, Counseling − Self−Regulation Model
Placebo Drug, No Counseling − Data
Placebo Drug, No Counseling − Self−Regulation Model
0 5 10 15 20 25 30 35 40
15
20
25
30
Craving
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

CSEL
75
0 5 10 15 20 25 30 35 40
0
5
10
15
20
Cigsmked
Active Drug, Counseling − Data
Active Drug, Counseling − Self−Regulation Model
Placebo Drug, No Counseling − Data
Placebo Drug, No Counseling − Self−Regulation Model
0 5 10 15 20 25 30 35 40
15
20
25
30
Craving
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

CSEL

CSEL 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

CSEL
78
Y. Dong, Dissertation

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