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Personalized Medication Dosing Using Volatile Data Streams MM Ghassemi [1] , T Alhanai [1] , MB Westover [2] , RG Mark [1] , S Nemati [3] 1: Massachusetts Institute of Technology; 2: Massachusetts General Hospital,; 3: Emory University NIH Grants: T32EB001680, T90DA22759, K01ES025445, R01EB017205, R01GM104987

Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

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Page 1: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized Medication Dosing Using Volatile Data Streams

MMGhassemi[1],TAlhanai [1],MBWestover[2],RGMark[1],SNemati [3]1:MassachusettsInstituteofTechnology;2: MassachusettsGeneralHospital,;3:EmoryUniversity

NIHGrants:T32EB001680,T90DA22759,K01ES025445,R01EB017205,R01GM104987

Page 2: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Introduction

Page 3: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: A brief history

• 460BC: Personalized medicine was envisioned by Hippocrates

• 1990-2003: A surge of interest in personalized medicine following the human genome project

• 2017: FDA approves record number of personalized medicines

AllenFrances,MD,ProfessorofPsychiatry,DukeUniversity

“Itismoreimportanttoknowthepatientwhohasthediseasethanthediseasethepatienthas.”― Hippocrates

Page 4: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: A brief history

• 460BC: Personalized medicine was envisioned by Hippocrates

• 1990-2003: A surge of interest in personalized medicine following the human genome project

• 2017: FDA approves record number of personalized medicines

Page 5: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: A brief history

• 460BC: Personalized medicine was envisioned by Hippocrates

• 1990-2003: A surge of interest in personalized medicine following the human genome project

• 2017: FDA approves record number of personalized medicines

Page 6: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

But what is “personalization”

Page 7: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Static personalization is often performed at the level of demography (e.g. gender, weight)

• Dynamic personalization begins with demography, and becoming more patient-specific as better data and responses to treatment are collected (e.g. anesthesia control) EthambutolDosingSuggestions

Personalized medicine: Two approaches

Page 8: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: Two approaches

• Static personalization is often performed at the level of demography (e.g. gender, weight)

• Dynamic personalization begins with demography, and becoming more patient-specific as better data and responses to treatment are collected (e.g. anesthesia control)

Source:Medsteer, http://medsteer.com/

Page 9: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: Needs deployable approaches

• Patients and providers have been slow to adopt personalized medicines, or alter established behaviors

• Solutions must work under real-world, imperfect conditions

• Translational impact will require interpretable approaches that integrate with provider and patient workflows to address high-value problems

Page 10: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: Needs deployable approaches

• Patients and providers have been slow to adopt personalized medicines, or alter established behaviors

• Solutions must work under real-world, imperfect conditions

• Translational impact will require interpretable approaches that integrate with provider and patient workflows to address high-value problems

MissingData

Artifacts

Page 11: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Personalized medicine: Needs deployable approaches

• Patients and providers have been slow to adopt personalized medicines, or alter established behaviors

• Solutions must work under real-world, imperfect conditions

• Translational impact will require interpretable approaches that integrate with provider and patient workflows to address high-value problems

Solution

Problem

Page 12: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Medication dosing

• Errors are responsible for ~400,000 preventable hospital deaths each year

• Over- or under- dosing can• Extended hospital stay,• Require follow-up interventions,• Incur additional morbidity.

Personalized medicine: High value problem

Page 13: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Medication dosing

• Errors are responsible for ~400,000 preventable hospital deaths each year

• Over- or under- dosing can• Extended hospital stay,• Require follow-up interventions,• Incur additional morbidity.

Personalized medicine: High value problem

Page 14: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Medication dosing

• Errors are responsible for ~400,000 preventable hospital deaths each year

• Over- or under- dosing can• Extended hospital stay,• Require follow-up interventions,• Incur additional morbidity.

Personalized medicine: High value problem

Page 15: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• A personalized medication dosing policy for a common anticoagulant, heparin

• Provide an initial dose based on static demographics

• Provide subsequent doses based on real-time, noisy data stream

Personalized medicine: Our study goal

Page 16: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• A personalized medication dosing policy for a common anticoagulant, heparin

• Provide an initial dose based on static demographics

• Provide subsequent doses based on real-time, noisy data stream

Personalized medicine: Our study goal

Page 17: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• A personalized medication dosing policy for a common anticoagulant, heparin

• Provide an initial dose based on static demographics

• Provide subsequent doses based on real-time, noisy data stream

Personalized medicine: Our study goal

Page 18: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Methods

Page 19: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• We extracted 4,470 patients from MIMIC who received intravenous UFH infusions during their ICU stay

• MIMIC is a de-identified, publicly available EMR archive of 40,000+ unique ICU admissions between 2001 -2016.

The data

Page 20: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• We extracted 4,470 patients from MIMIC who received intravenous UFH infusions during their ICU stay

• MIMIC is a de-identified, publicly available EMR archive of 40,000+ unique ICU admissions between 2001 -2016

The data

Page 21: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Clinicians dose heparin, wait 6-12 hours, measure anticoagulation, then adjust dose as needed

• Goal is to obtain a therapeutic level of anticoagulation as quickly as possible, as indicated by aPTT

• aPTT may be categorized into one of three states: therapeutic, sub-therapeutic, and supra-therapeutic

The outcome

Page 22: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Clinicians dose heparin, wait 6-12 hours, measure anticoagulation, then adjust dose as needed

• Goal is to obtain a therapeutic level of anticoagulation as quickly as possible, as indicated by aPTT

• aPTT may be categorized into one of three states: therapeutic, sub-therapeutic, and supra-therapeutic

The outcome

Page 23: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Clinicians dose heparin, wait 6-12 hours, measure anticoagulation, then adjust dose as needed

• Goal is to obtain a therapeutic level of anticoagulation as quickly as possible, as indicated by aPTT

• aPTT may be categorized into one of three states: therapeutic, sub-therapeutic, and supra-therapeutic

The outcome

Page 24: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• We extracted all features that are believed to confound the relationship between UFH and aPTT

Clinical Features

Page 25: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Static features are single measures that don’t change over time

Clinical Features

Page 26: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Static features are single measures that don’t change over time

• Age, gender, etc.

Clinical Features

Page 27: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Static features are single measures that don’t change over time

• These features are routinely collected(no missing data)

Clinical Features

Page 28: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Continuously measured features change over time

Clinical Features

Page 29: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Continuously measured features change over time

• Heparindoseisoneofthesefeatures

Clinical Features

Page 30: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Continuously measured features change over time

• Amongseveral

Clinical Features

Page 31: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Continuously measured features change over time

• Thevalueofthesefeaturesareoccasionallymissing,orforsomepatientsunmeasured

Clinical Features

Page 32: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Multinomiallogisticregression(MNR)wheremodelfeaturesandparametersarere-estimatedforeachpatient,ateachaPTTdrawusingaweightedcombinationofthedatafrom• apopulationofexistingpatients,and

• theindividualpatient’sreal-timedatastream

Proposed Approach

Page 33: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Multinomiallogisticregression(MNR)wheremodelfeaturesandparametersarere-estimatedforeachpatient,ateachaPTTdrawusingaweightedcombinationofthedatafrom• apopulationofexistingpatients,and

• theindividualpatient’sreal-timedatastream

Proposed Approach

Page 34: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Multinomiallogisticregression(MNR)wheremodelfeaturesandparametersarere-estimatedforeachpatient,ateachaPTTdrawusingaweightedcombinationofthedatafrom• apopulationofexistingpatients,and

• theindividualpatient’sreal-timedatastream

Proposed Approach

Page 35: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Multinomiallogisticregression(MNR)wheremodelfeaturesandparametersarere-estimatedforeachpatient,ateachaPTTdrawusingaweightedcombinationofthedatafrom• apopulationofexistingpatients,and

• theindividualpatient’sreal-timedatastream

Proposed Approach

Page 36: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

IndividualState

Data

Interval

Features

Population

Samples Outcome

Parameters

MultinomialLogisticRegression,ateachinterval

Wherelikelihoodisaweightedcombinationofp andi data

Method, formally:

Populationversusindividualdataweightistime-dependent

weightinghyper-parameters

Datarow(i)Datarow(p)

Page 37: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

IndividualState

Data

Interval

Features

Population

Samples Outcome

Parameters

MultinomialLogisticRegression,ateachinterval

Wherelikelihoodisaweightedcombinationofp andi data

Method, formally:

Populationversusindividualdataweightistime-dependent

weightinghyper-parameters

Datarow(i)Datarow(p)

Page 38: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

IndividualState

Data

Interval

Features

Population

Samples Outcome

Parameters

MultinomialLogisticRegression,ateachinterval

Wherelikelihoodisaweightedcombinationofp andi data

Method, formally:

Populationversusindividualdataweightistime-dependent

weightinghyper-parameters

Datarow(i)Datarow(p)

Page 39: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

P(supra)increaseswrt dose;P(sub)decreaseswrt dose;P(ther)ismaximumwhen:

Yielding:

Heparinparameter

Non-heparinfeatureimpact

under

overWhere:

Method, formally:

Page 40: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

P(supra)increaseswrt dose;P(sub)decreaseswrt dose;P(ther)ismaximumwhen:

Yielding:

Heparinparameter

Non-heparinfeatureimpact

under

overWhere:

Method, formally:

Page 41: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Baseline 1: Multinomial logistic regression using static features, without personalization

• Baseline 2: Multinomial logistic regression using all features, without personalization and excluding subjects with missing data (23.6%) of all patients

• Baseline 3: Multilayer neural network. Densely connected, feed-forward, two hidden layers, softmax output, ReLUactivation, Xavier initialization, scaled conjugate gradient descent optimization, grid search topology selection.

• Baseline 4: Reinforcement learning via deterministic policy network. We defined the state, action, and rewards as follows: (1) State: aPTT and laboratory measures (2) Actions: maintain dose, increase dose, decrease dose. (4) Rewards: proportional to the aPTT error.

Non-personalizedbaseline methods

Page 42: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Baseline 1: Multinomial logistic regression using static features, without personalization

• Baseline 2: Multinomial logistic regression using all features, without personalization and excluding subjects with missing data (23.6%) of all patients

• Baseline 3: Multilayer neural network. Densely connected, feed-forward, two hidden layers, softmax output, ReLUactivation, Xavier initialization, scaled conjugate gradient descent optimization, grid search topology selection.

• Baseline 4: Reinforcement learning via deterministic policy network. We defined the state, action, and rewards as follows: (1) State: aPTT and laboratory measures (2) Actions: maintain dose, increase dose, decrease dose. (4) Rewards: proportional to the aPTT error.

Non-personalizedbaseline methods

Page 43: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Baseline 1: Multinomial logistic regression using static features, without personalization

• Baseline 2: Multinomial logistic regression using all features, without personalization and excluding subjects with missing data (23.6%) of all patients

• Baseline 3: Multilayer neural network. Densely connected, feed-forward, two hidden layers, softmax output, ReLUactivation, Xavier initialization, scaled conjugate gradient descent optimization, grid search topology selection.

• Baseline 4: Reinforcement learning via deterministic policy network. We defined the state, action, and rewards as follows: (1) State: aPTT and laboratory measures (2) Actions: maintain dose, increase dose, decrease dose. (4) Rewards: proportional to the aPTT error.

Non-personalizedbaseline methods

20

20

Input

Softmax

Page 44: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Baseline 1: Multinomial logistic regression using static features, without personalization

• Baseline 2: Multinomial logistic regression using all features, without personalization and excluding subjects with missing data (23.6%) of all patients

• Baseline 3: Multilayer neural network. Densely connected, feed-forward, two hidden layers, softmax output, ReLUactivation, Xavier initialization, scaled conjugate gradient descent optimization, grid search topology selection.

• Baseline 4: Reinforcement learning via deterministic policy network. We defined the state, action, and rewards as follows: (1) State: aPTT and laboratory measures (2) Actions: maintain dose, increase dose, decrease dose. (4) Rewards: proportional to the aPTT error.

Non-personalizedbaseline methods

20

20

Input

Softmax

reinforce

Page 45: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Results

Page 46: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• UFHmisdoingisconsistentlyerror-proneevenaftermultipleaPTTdraws(andconsequentopportunitiesfordoseadjustment).

• 80%ofoursamplestoppedreceivingaPTTdrawsaftertheirfifthadjustment

• 5%ofthe3,883patientwithrecordedaPTTvalueshadasixthdoseadjustment.

Data characteristics

2/3ofpatientsmis-dosed

Page 47: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• UFHmisdoingisconsistentlyerror-proneevenaftermultipleaPTTdraws(andconsequentopportunitiesfordoseadjustment).

• 80%ofoursamplestoppedreceivingaPTTdrawsaftertheirfifthadjustment

• 5%ofthe3,883patientwithrecordedaPTTvalueshadasixthdoseadjustment.

Data characteristics

Page 48: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• UFHmisdoingisconsistentlyerror-proneevenaftermultipleaPTTdraws(andconsequentopportunitiesfordoseadjustment).

• 80%ofoursamplestoppedreceivingaPTTdrawsaftertheirfifthadjustment

• 5%ofthe3,883patientwithrecordedaPTTvalueshadasixthdoseadjustment.

Data characteristics

Page 49: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• UFHmisdoingisconsistentlyerror-proneevenaftermultipleaPTTdraws(andconsequentopportunitiesfordoseadjustment).

• 80%ofoursamplestoppedreceivingaPTTdrawsaftertheirfifthadjustment

• 5%ofthe3,883patientwithrecordedaPTTvalueshadasixthdoseadjustment.

Data characteristics

Page 50: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• UFHmisdoingisconsistentlyerror-proneevenaftermultipleaPTTdraws(andconsequentopportunitiesfordoseadjustment).

• 80%ofoursamplestoppedreceivingaPTTdrawsaftertheirfifthadjustment

• 5%ofthe3,883patientwithrecordedaPTTvalueshadasixthdoseadjustment.

Data characteristics

Page 51: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• UFHmisdoingisconsistentlyerror-proneevenaftermultipleaPTTdraws(andconsequentopportunitiesfordoseadjustment).

• 80%ofoursamplestoppedreceivingaPTTdrawsaftertheirfifthadjustment

• 5%ofthe3,883patientwithrecordedaPTTvalueshadasixthdoseadjustment.

Data characteristics

Page 52: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Highest overall accuracy (60%)

• Highest overall VUS (0.46), a 0.02 improvement over the RL approach

• 7.3% more likely to detect supra-therapeutic doses than the population model that didn’t exclude patients

Overall performance of personalized approach

Page 53: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Highest overall accuracy (60%)

• Highest overall VUS (0.46), a 0.02 improvement over the RL approach

• 7.3% more likely to detect supra-therapeutic doses than the population model that didn’t exclude patients

Overall performance of personalized approach

Page 54: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

• Highest overall accuracy (60%)

• Highest overall VUS (0.46), a 0.02 improvement over the RL approach

• 7.3% more likely to detect supra-therapeutic doses than the population model that didn’t exclude patients

Overall performance of personalized approach

Page 55: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Temporal performance of personalized approach

Our approach consistently outperformed the best comparable baseline across time

Page 56: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Temporal performance of personalized approach

Time(Hours)

Our approach might reduce errors, and bring patients to therapeutic aPTT, faster.

Page 57: Personalized Medication Dosing Using Volatile Data Streams · •460BC: Personalized medicine was envisioned by Hippocrates •1990-2003: A surge of interest in personalized medicine

Conclusion and Future Direction• Heparindosingguidelinesarebasedonpopulationmodels

• Patient-specificmodelinghasthepotentialtoimproveperformance

• WeareworkingtodeploythisalgorithmwithintheBIDMCforreal-worldimpact

http://ghassemi.xyz

QuestionsandCollaborations: