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CRISMA CenterUPMC Critical CareUPMC Critical Care

Exemplary Care Cutting-edge Research World-class Educationwww.ccm.pitt.edu

Medical decision making and model-based reasoning

2010 Winter School in Mathematical &2010 Winter School in Mathematical & Computational Biology

U i it f Q l d B i b

Gilles Clermont, MD

University of Queensland, Brisbane

CRISMA CenterCenter for Inflammation and Regenerative ModelingCritical Care Medicine, Mathematics, and Industrial EngineeringUniversity of Pittsburgh

Exemplary Care Cutting-edge Research World-class Education

Objectives

Medical decision making

Constructing clinical knowledgeConstructing clinical knowledge

Model-based diagnostics

Global patterns and individual variability

Quantitative approaches to variability

Bedside translationBedside translation

Objectives

Case presentation72 yo to hospital by ambulance with vomiting, abdominal pain for 24 hours

Past medical historyDiabetes, on oral hypoglycemic agent

Vital signsTemperature 37.8 CBlood pressure very low 72/40Heart rate high 120

The essence of clinical medicine

TherapeuticsTherapeutics

DiagnosticsTesting gTesting

Exemplary Care Cutting-edge Research World-class EducationObservables States

Information gathering

Medical decision makingI f di i ( t t ) f i l t i f tiInfer diagnosis (state) from incomplete information (observations)

Inverse probleme se p ob e

Several diagnoses may be compatible with observations at handobservations at hand

Ill-posed

Diagnostic evaluation to narrow diagnosticDiagnostic evaluation to narrow diagnostic possibilities

Gathering of addition informationPerturbation challenges (experiment)

Therapeutic actionp

IterationState is typically evolving

State is typically evolvingTitration of care

Clinicians and the inverse problem

Exemplary Care Cutting-edge Research World-class EducationZenker, Rubin, Clermont, PLoS Comp Bio 2008

Objectives

The drug pipelineLead/candidate identification - $

Pre-clinical work - $I it

DifficultCandidate identificationClinical trial logisticsIn vitro

Animal

Phase 0 Phase I clinical $

Clinical trial logistics

InefficientHeuristicPhase 0, Phase I clinical - $

Toxicity/Safety

Phase II clinical RCT - $$

Heuristic

Expensive$BPhase II clinical RCT $$

Dose rangingEfficacy – proxy outcomes

Lengthy>12 years

Phase III clinical RCT - $$$EfficacyEffectiveness

>12 yearsFew exceptions

?RewardComparative outcomeRegistration

?RewardLimited exclusive rights

Phase IV –post marketing

The response to an inflammatory insult

Sepsis=i f ti i fl ti

Severe sepsis=i d f ti

Initiating EventInflammation

infection+inflammation sepsis+organ dysfunction

Initiating EventDamage/Dysfunction

Exemplary Care Cutting-edge Research World-class EducationAnti-inflammation

Hotchkiss and Karl NEJM 2003; 348:138-150

Clinical trials of immunomodulation

Acute Chronic

Sepsis

Acute pancreatitis

Inflammatory bowel disease

Acute pancreatitisAuto-immune diseases

Rhumatoid arthritisPsoriasis

Transplantation/rejectionTransplantation/rejection

Th h i thThe more chronic the process, the more successful we have been !

Clinical trials of immunomodulation in sepsis

>60 phase III clinical trials

>25,000 patients

>1.6 billion dollars

The strength of the Consensus – Then 2004

2553218

Quality {Strength {

The strength of the Consensus - 2008

2553218

Quality {Strength { 1. Strong –> do

2. Weak –> consider

{ ea co s de

Surviving sepsis - I

www.survivingsepsis.org

Surviving sepsis - II

Problems with RCTs in sepsis

Pre-clinical studies have high success but:Subjects have different degree of illness (30% vs 85%)

Studies in animal at low risk of deaths tell the same story as clinical trials (Eichacker et al. 2003)

Administration schedule is differentProblem of “attributable” mortality worse in humans

Phase II trials based on little dataPhase II trials based on little data

Design of Phase III trials is also poorly informed

More problems with sepsis trialsDoes the drug have the purported biological activity?

Is the burden of proof for efficacy relevant to the diseaseIs the burden of proof for efficacy relevant to the disease the drugs are intended to help?

Trials are limited by the nature of the study populationTrials are limited by the nature of the study populationHeterogeneousCo-morbidities

Redesigning clinical trials

Phase IIPlay the winner; drop the looser designsAdaptive seamless phase design

Use phase II patients as part of the phase II trialsTwo-stage designsTwo stage designs

Phase IIIG ti l d iGroup sequential design

Advanced adaptive schemespAdaptive randomizationSample-size reestimationBi k d tiBiomarker-adaptiveOthers

Treatment-switching

Treatment switchingHypothesis modification (superiority vs. non-inferiority)

But…

How does the result of an RCT apply to a particular patient?

Most proposed modifications to the canonical dogma run against the principle of personalized medicine.against the principle of personalized medicine.

ThThus

Growing malaise with the use of RCTs are the soleGrowing malaise with the use of RCTs are the sole method in discovering clinical “truths”

M d l b d th d h l i d i iModel-based method can help in redesigning some aspects of clinical trials, not all

Medical Decision Making - Treatment

Resuscitate with fluids

Give antibioticsGive antibiotics

Take care of the underlying cause

Objectives

Model-based diagnostics and therapeutics

Back to our problem

Can a mathematical model help?

The response to an inflammatory insult

Severe sepsis=i d f ti

I f ti

Inflammationsepsis+organ dysfunction

InfectionDamage/Dysfunction

Exemplary Care Cutting-edge Research World-class EducationAnti-inflammation

A model of the inflammatory response

N* *N( )nau t+1 2

DP ( )cau t+

Several modes of death

Aseptic death Septic deathp p

Many asymptotic behaviors are possible

Predicting the response to treatment

Exemplary Care Cutting-edge Research World-class EducationOsuchowski, CCM 2009

Steroids

RationaleProfound anti-inflammatory effect

Decreases feverDecreases swellingPromotes apoptosis of immune cellsPromotes apoptosis of immune cells

Concept of relative adrenal insufficiency

Steroids (Ca) at high doses

Steroids at low dosesA handful of recent studies using smaller doses (200–300 mg/day hydrocortisone) for longer periods of time may have beneficial effectshave beneficial effects.

reversal of shocktrends toward decreased organ system dysfunctiondecreased mortality

Relative adrenal insufficiencyy

Yet, one large study (CORTICUS) failed to support this contentioncontention

A model-based intervention

Not good at all(N

Not good

Very good

No change

Very good

Objectives

An acute inflammatory perturbation

LPS 40ng/kg IVLPS (10ng/kg IV) LPS 40ng/kg IV

6000#1

LPS (10ng/kg IV)

5000 #9

00 1 2 3 4 5 6

Time (h)

00 1 2 3 4 5 6

Time (h)

Trajectories are consistent within individuals

“Shapes” are often consistent across individualsSuffredini et al. 1996

Genetic and Inflammatory Markersof Sepsis (GenIMS)of Sepsis (GenIMS)

NIGMS/NIH R01 2001 2005 (A K ll )NIGMS/NIH R01 y2001-2005 (Angus, Kellum)With additional support from GSK, OBI, DPC, Brahms

I ti h t t d f ti t ti t ED ith CAPInception cohort study of patients presenting to ED with CAPProposed N = 2,700 at 38 hospitals clustered in 4 regions

Pennsylvania (SW)y ( )ConnecticutMichigan (Detroit area)Tennessee (Memphis area)Tennessee (Memphis area)

Blood donor pools from same region(s) for population normsPowered for analyses in whites and blacks

All Inpatients with CAP (n = 1886)

354045

IL6IL10

202530

l IL10TNF

101520

1 2 3 4 5 6 71 2 3 4 5 6 7

Cytokines by Outcome (60 days)

120140 SSD

12 SSD

406080

100120

SSANSS

1 2 3 4 5 6 7

TNF SSDSSA

SSANSS

1 2 3 4 5 6 7

Day 1 cytokine levels in patients with and without severe sepsis

2.3h 95

1.9elin

<0 00011.9

Severe sepsis(n=715)

No SS(n=1073)

p<0.0001

No SS(n=1073)

p<0.0001

CI IL-10

2 40 w

p<0.0001

2.0Severe sepsis(n=715)

No SS(n=1073)

Day 1 cytokine levels in non-septic patients for prediction of severe sepsis

CI 2.1

3 6e an

ine 1.9

1.8p = 0.0087

p = 0.0009

No SS(n=1073)

3.2IL6

No SS(n=1073)

Analysis restricted to day 1 levels of those patients who do NOT have severe sepsis on first day

who do NOT have severe sepsis on first day

IL-6, IL-10 patterns v. Outcomes

HMLIL6/IL10

2 95 43 2H

3.813.735.6M

1.47.926.1LOverall %Frequency

2.95.43.2H

HMLIL6/IL10

72 261 447 5H

47.241.725.5M

26.927.518.7L% SevereSepsis

72.261.447.5H

84 693 696 4L

HMLIL6/IL1060 day %

56.174.390.0H

69.784.395.3M

84.693.696.4L60 day %Survival

Day 1 levels and survivalh

2.4 5.0

CI TNF IL-6

3 8elin

Dead(n=212)

Alive(n=1410)

1.8p<0.0001 3.8

3.4Dead(n=212)

Alive(n=1410)

Base p<0.0001

2 8% C

I IL-102.8

DeadAlive

p<0.0001

Dead(n=212)

Alive(n=1410)

Day 1 cytokine levels in patients who develop ARF and those that do not

7.5TNF

ARF = RIFLE-I or F5.5

l ±SD

ARFNo ARF

p<0.0001

(n=258)(n=1544)

IL-680IL-107.5

l ±SD

l ±SD 6

p<0.0001

p=0.0285

ARF(n=258)

No ARF(n=1544)

20ARF(n=258)

No ARF(n=1544)

The good news

Standard (although but no means elementary) statistical techniques identify “classes” of patients

PhysiologyOmics

Qualitative patterns, but not magnitude of response, often preserved across individuals

Within species

Objectives

Variability and personalized medicine

2010 Winter School in Mathematical &2010 Winter School in Mathematical & Computational Biology

University of Queensland Brisbane

Gilles Clermont, MD

University of Queensland, Brisbane

CRISMA CenterCenter for Inflammation and Regenerative ModelingCritical Care Medicine, Mathematics, and Industrial EngineeringUniversity of Pittsburgh

The big picture

Sources of variability

Between-subject variability

Measurement variability (between occasion)Measurement variability (between-occasion)

Residual uncertainty

Naïve pooling

All data points are assumed to arise from a single individual

A single function is fit to the combination of all individuals

Ignores intra-individual variability as well as correlation in time within individuals

Variant: fitting the average/median curve (generated before the fit))

Mixed models for ODE - pharmacokinetics

Naïve pooling Average fitp g Average fit

One model – many patients

Two-stage models

Standard TS

k k k kY X Eθ= +y

Iterative TS

g(x)( | , ) ( )( | )

k k k popk k k X Y mY X ρ ρ θθ

( | ) ( )( , | )( | , ) ( )

k k kk k k pop

Y XX Y m

ρ ρρ θρ ρ θ

Linear mixed-effects modelsOne model one patientOne model – one patient

MExemplary Care Cutting-edge Research World-class Education

Linear mixed-effects model

yi i i i i

i i i i i

Y m X b EY mX m X b b E= + += + + + +

The simplest viral model (v1.0)

Healthycell d

Virus Targetcell a - where active cell killingk

is implicit in this death rate

u - virus deathor shedding

Killercell

or shedding

Reaction formulation

∗ →x: target cellsy: infected cells

∗ →

v: virusr: killer cell

v x yβ

+ →x vx dxλ β•

= − −•

→ ∗ → ∗ →∗

y vx ay

v ky uv vx

y vx ay ryβ γ•

= − −

y r rγ

, ,x v y→ ∗ → ∗ →∗ v ky uv vxβ= − −

r c fr•

= −c

r∗ →

r → ∗Baccam et al, J Virol 2007

Mixed models for ODE

Exemplary Care Cutting-edge Research World-class EducationBaccam et al, J Virol 2007

Mixed-effects modelsOne model one patientOne model – one patient

Individual models vary in parameters? Alternative mathematical structures? Alternative mathematical structuresevaluated based on

Global error over the populationExemplary Care Cutting-edge Research World-class Education

Global error over the populationParsimony

Mixed-effects modelsMostly applied to

Generalized linear models“F i l ” ll d li bl“Fairly” well-posed non-linear problems

Frequent in population pharmacokinetics

Stochastic expression ofBetween subject variabilityj yRepeated measuresUnexplained residual error

Expressed as AlgebraicDiff ti l tiDifferential equations

NONMEMMonolix

What about the ill-posed problem?

The error model is important

Deviation between model predictions and data/heuristics

A few synonymsA few synonymsErrorObjective functionjCost function

Problem dependent functional formsProblem dependent functional forms Least squares - MLEMulti-objectivej

( ) ( ) 1 1( ) ( ) ( ( )) .....Td i i HE d m C d m b mθ θ θ= Γ − − +Γ − +∑( ) ( ) 1 1

( ) ( ) ( ( ))d i i Hs v t∑

Data Heuristics

Non-linear problem may be very messy

ErrorWell-posed Ill-posed

?Which is the correct minimum?

Parameter axis

minimum?

Parameter axis

This is what clinicians do all the time !

The Ill-posed problemModel ensemble as a collection of “good” models

ErrorError

Probability(density)

Exemplary Care Cutting-edge Research World-class EducationParameter axis

Patient specific models and ill-posednessThe one-step processThe one step process

E(Mn)( n)

E(M ) ≡ P ti t ifi blE(Mn) ≡ Patient-specific ensemble

Naïve pooling and ill-posedness

E(Mn)( n)

E(M ) ≡ M t d l E blE(Mn) ≡ Metamodel or EnsembleMany many more models than individuals

Many many more models than individuals

Influenza virus biology

VHVSAVIdtdV

VVVHVAV

1+−−−−= αγγγ

dH FHbVHRaRHDbdtdH

HFHVRHD −−++= γ)(

IaEIbVHdtdI

IIEHV −−= γ

FaHFbIcMbdtdF

FFHFF −−+=

MaMVbDbdt

dMMMVMD −−+= )1)((

RaFHbdtdR

RHF −=

)1( EaIEbMEbdtdE

EEIEM −+−=dt EEIEM

)1( PaMPbdtdP

PPM −+=

AaSAVPbdA−−= γ AaSAVPb

dt AAVA −−= γ

)1( SrPdtdS

Hancioglu, Swigon ,Clermont, JTB 2008

Ensemble modelParallel computation environment

Known how to distribute chainschainsAdaptive load balance

6 “meta-chains”6 meta-chainsValidity unknown

e7 samplese7 samples

Several “clusters” of behavior compatible with datacompatible with data

Standard behaviorRelapsing behavior“S d ”“Superspreaders”

Parameter distributions

Probabilistic course of disease

Also compatible with the data

Treatment predictions

Not intuitive

Probabilistic ensembles for individuals

E(M)E(M)

pop iθ θ θ= +As a mixed-effect modelAs a mixed effect model,

Remains an open-problem

θ θi

Probabilistic ensembles – for subpopulations

E(M)E(M)

Sparsity -> pooling “similar” patients may be good enoughThe clinician does thisThe clinician does this

ConclusionsWe live in the ill-posed world

There are methods (early) of approachThere are methods (early) of approachLimited by paucity of data in any single individualLimited by incongruence between time of observation and di d idisease dynamics

Bayesian-methods may indicate a systematic approach to this problem

Computationally intensive for real-time acute care p yapplications

Objectives

Biomarker-guided therapy using model-predictive control

First attempts at applying engineering concept to guide treatment

Diabetes (Parker)Anti-coagulationDepth of anesthesia (Haddad Bailey)Depth of anesthesia (Haddad, Bailey)

Currently NO point-of-care measurements of biomarkers would allow the implementation of such techniques for acute inflammation

Not quite true!Not quite true!

Targeted Therapy - Model Predictive Control

“Base” SystemBase System• Real patient• Patient metamodelINPUT

•Actual dataOUTPUT•Actual dataActual data Actual data•Predicted data

Sensor• Error betweenActuator

Th d i d i “h l h”

Error betweenactual/desired

Actuator

Controller

• The desired output is “health” • The MPC method uses actual data and model simulations

to estimate output: the discrepancy is estimated (Sensor)

• The MPC method suggest an optimal intention strategy which is time dependent (Actuator)

Model Predictive ControlObjective: find the control strategy which minimizes the difference between the predicted trajectory and a reference goal over a finite horizon. (D=0, P=0)

g ( , )Predictions are calculated using a model of the process.

statespace o o

predicted trajectory

current stateoo

reference trajectory

di ti h i

TK TK+1 TK+P

current stateoo

TK+P+1

prediction horizon

control

TK+C+1

control strategydose

control variable

control window

The model

minnau

na( )nau t+

maxnau dp ( )cau t+

mincau max

cauDay, Rubin, Clermont, Math Biosc 2010

Titrated therapy (MPC)

Simulated clinical trial of a balanced treatmentControls vs. Static vs. Standard vs. Targeted therapy

Insult is Sepsis1000 patients are sim lated1000 patients are simulatedTreatment initiated based on levels of activated phagocytic cellsBoth anti and pro-inflammatory effectors are allowed to be either administered or removed

Static therapy: fixed dose of anti-inflammatory

Standard Therapy: titrated based on baseline data and an existing (meta) model

Targeted Therapy: is allowed to react to observations (biomarker data) which are different from model

predictions

Population heterogeneity creates mismatch

Targeted therapy is better, more forgiving

Titrated therapy – population variationsSuccess Failure

How complex should useful models be?It depends on the intent

DescriptionPredictionPrediction

Measureable read-outs

Compartmentalized

Design of a device to selectively g yadsorb septic blood

Knowledge and successful translation

EmpiricalEpicycles

Kepler/Newton Ellipses

GR - EinsteinPrecessing ellipses

QG - ??Black hole physicsEpicycles

- to XVII centuryEllipses Precessing ellipses Black hole physics

First interactionbetween a physical

Discrepancy betweenpredictions and

Discrepancy betweengravity and otherbetween a physical

law and empiricobservation

predictions and empiric observation

gravity and otherforces of nature

Exemplary Care Cutting-edge Research World-class EducationDepth of knowledge

CRISMA Center UPMC Critical CareUPMC Critical...

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