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
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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
Control Systems Engineering LaboratoryCSEL Agenda
3
• Motivation, research goals & contributions!
• Self-regulation model development & estimation!
• Formulation of an adaptive smoking cessation intervention!
• Evaluation of nominal & robust performance!
• Extensions, summary, & conclusions
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)!
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
Control Systems Engineering LaboratoryCSEL Self-Regulation Models (cont.)
• 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
Control Systems Engineering LaboratoryCSEL Self-Regulation Models (cont.)
• Insights offered by a control engineering perspective!
- 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
Control Systems Engineering LaboratoryCSEL Self-Regulation Models (cont.)
• Insights offered by a control engineering perspective!
- 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!
- 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
Control Systems Engineering LaboratoryCSEL
• Insights offered by a control engineering perspective!
- 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!
- 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
Control Systems Engineering LaboratoryCSEL Self-Regulation Models (cont.)
• 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
Control Systems Engineering LaboratoryCSEL
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
Self-Regulation Models (cont.)
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%
Control Systems Engineering LaboratoryCSEL Agenda
22
• Motivation, research goals & contributions!
• Self-regulation model development & estimation!
• Formulation of an adaptive smoking cessation intervention!
• Evaluation of nominal & robust performance!
• Extensions, summary, & conclusions
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
Control Systems Engineering LaboratoryCSEL
• 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
Control Systems Engineering LaboratoryCSEL
• Connecting clinical concepts to control systems engineering!- Treatment goals ⇔ set points!
Control Systems Engineering LaboratoryCSEL HMPC Decision-Making
29
Specify intervention targets, components,
constraints
Supply dynamic models
Offline Online (done each review period)
Control Systems Engineering LaboratoryCSEL HMPC Decision-Making
29
Specify intervention targets, components,
constraints
Supply dynamic models
Offline
Obtain CPD, Craving, & Stress measurements
Online (done each review period)
Control Systems Engineering LaboratoryCSEL HMPC Decision-Making
29
Specify intervention targets, components,
constraints
Supply dynamic models
Offline
Obtain CPD, Craving, & Stress measurements
Predict how CPD & Craving will deviate from targets over the next p days using measurements,
models, and prior dose assignments
Online (done each review period)
Control Systems Engineering LaboratoryCSEL HMPC Decision-Making
29
Specify intervention targets, components,
constraints
Supply dynamic models
Offline
Obtain CPD, Craving, & Stress measurements
Predict how CPD & Craving will deviate from targets over the next p days using measurements,
models, and prior dose assignments
Determine the best set of ucouns, ubup, & uloz
adjustments for the following m days by minimizing an objective function subject to constraints
Online (done each review period)
Control Systems Engineering LaboratoryCSEL HMPC Decision-Making
29
Specify intervention targets, components,
constraints
Supply dynamic models
Offline
Obtain CPD, Craving, & Stress measurements
Predict how CPD & Craving will deviate from targets over the next p days using measurements,
models, and prior dose assignments
Determine the best set of ucouns, ubup, & uloz
adjustments for the following m days by minimizing an objective function subject to constraints
Online (done each review period)
Assign only the next set of dosage adjustments (moving horizon component)
Control Systems Engineering LaboratoryCSEL HMPC Decision-Making
29
Wait until the next review period
Specify intervention targets, components,
constraints
Supply dynamic models
Offline
Obtain CPD, Craving, & Stress measurements
Predict how CPD & Craving will deviate from targets over the next p days using measurements,
models, and prior dose assignments
Determine the best set of ucouns, ubup, & uloz
adjustments for the following m days by minimizing an objective function subject to constraints
Online (done each review period)
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
Control Systems Engineering LaboratoryCSEL
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
Control Systems Engineering LaboratoryCSEL
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
Control Systems Engineering LaboratoryCSEL Agenda
35
• Motivation, research goals & contributions!
• Self-regulation model development & estimation!
• Formulation of an adaptive smoking cessation intervention!
• Evaluation of nominal & robust performance!
• Extensions, summary, & conclusions
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!
• Baseline CPD = 9.3, Craving = 16.1
• Simulation time frame!
- Patient-reports of CPD, Craving, & Stress start on day 0 ➔ Dosage decisions made each day starting on day 0!
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). “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)!
from goal Craving levelWcrav ( )2Alterations to bupropion
dose over the next m daysWΔbup ( )2 + Alterations to lozenge dose over the next m daysWΔloz ( )2+
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
Control Systems Engineering LaboratoryCSEL
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
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:
- 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
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:
- 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