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journa l homepage: www. int l .e lsev ierhea l th .com/ journa ls /cmpb

evelopment of a model-based clinical sepsisiomarker for critically ill patients

essica Lina,∗, Jacquelyn D. Parenteb, J. Geoffrey Chaseb, Geoffrey M. Shawa,my J. Blakemoreb, Aaron J. LeCompteb, Christopher Prettyb, Normy N. Razakb,ominic S. Leec, Christopher E. Hannb, Sheng-Hui Wanga

University of Otago Christchurch, Department of Medicine, Christchurch, New ZealandUniversity of Canterbury, Mechanical Engineering Department, Centre for Bioengineering, Christchurch, New ZealandUniversity of Canterbury, Mathematics and Statistics Department, Christchurch, New Zealand

r t i c l e i n f o

rticle history:

eceived 11 December 2009

eceived in revised form

April 2010

ccepted 7 April 2010

eywords:

epsis

nsulin sensitivity

iomarker

iagnosis

eceiver operator characteristic

lucose control

eal-time clinical application

a b s t r a c t

Sepsis occurs frequently in the intensive care unit (ICU) and is a leading cause of admission,

mortality, and cost. Treatment guidelines recommend early intervention, however posi-

tive blood culture results may take up to 48 h. Insulin sensitivity (SI) is known to decrease

with worsening condition and could thus be used to aid diagnosis. Some glycemic control

protocols are able to accurately identify insulin sensitivity in real-time.

Hourly model-based insulin sensitivity SI values were calculated from glycemic control

data of 36 patients with sepsis. The hourly SI is compared to the hourly sepsis score (ss)

for these patients (ss = 0–4 for increasing severity). A multivariate clinical biomarker was

also developed to maximize the discrimination between different ss groups. Receiver oper-

ator characteristic (ROC) curves for severe sepsis (ss ≥ 2) are created for both SI and the

multivariate clinical biomarker.

Insulin sensitivity as a sepsis biomarker for diagnosis of severe sepsis achieves a 50%

sensitivity, 76% specificity, 4.8% positive predictive value (PPV), and 98.3% negative predic-

tive value (NPV) at an SI cut-off value of 0.00013 L/mU/min. Multivariate clinical biomarker

combining SI, temperature, heart rate, respiratory rate, blood pressure, and their respective

hourly rates of change achieves 73% sensitivity, 80% specificity, 8.4% PPV, and 99.2% NPV.

Thus, the multivariate clinical biomarker provides an effective real-time negative predictive

diagnostic for severe sepsis. Examination of both inter- and intra-patient statistical distri-

bution of this biomarker and sepsis score shows potential avenues to improve the positive

predictive value.

1.5% projected annual incidence increase [1]. Sepsis treatment

. Introduction

epsis presents a serious medical problem in the adult inten-ive care unit (ICU) around the world, with a 11–15% incidencef severe sepsis, 30–60% mortality rate, $22,100 USD aver-

∗ Corresponding author. Tel.: +64 33786305.E-mail addresses: jessica.lin@otago.ac.nz, jesschlin@gmail.com (J. L

169-2607/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights resoi:10.1016/j.cmpb.2010.04.002

© 2010 Elsevier Ireland Ltd. All rights reserved.

age cost per case, $16.7 billion USD annual total cost, and

in).

guidelines and patient management protocols recommendearly goal-directed resuscitation of the septic patient duringthe first 6 h after infection recognition [2]. Currently, blood

erved.

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150 c o m p u t e r m e t h o d s a n d p r o g r a m

bacteria cultures are considered the gold standard for con-firmation of infection. However, only 51% of sepsis cases arepositively identified as cultured pathogens [3].

Early interventions have been documented to reduce mor-tality from 46.5% to 30.5% [4]. In addition, a landmarkclinical trial implementing a blood glucose control proto-col resulted in a reduction in the incidence of sepsis [5].Currently available biomarkers, such as procalcitonin (PCT),provide sepsis diagnostic test results in 2–3 h with commer-cially available kits, but to various levels of clinical accuracy[6].

A clinically validated glucose–insulin model that is able tomodel insulin sensitivity (SI) in real-time has been used todevelop blood glucose protocols for critically ill patients [7,8].An integral-based parameter identification method has beenused to fit the data [9]. The model-based SI has been observedto indicate the severity of illness and metabolic status, as wellas being validated against euglycaemic clamp data [10]. Insulinsensitivity has also been previously documented as decreasingwith worsening condition [11], and increasing with improve-ment [12,13].

This study aims to evaluate the relationship of modelledinsulin sensitivity [7,14] and patient condition. In particular,this study examines using the modelled insulin sensitivity asa marker for real-time diagnosis and differentiation of Sys-temic Inflammatory Response Syndrome (SIRS) and sepsis in acohort of adult ICU patients. It extends the work of Blakemoreet al. [15] by increasing discrimination and utilizing additionalclinical measurements.

2. Methods

2.1. Physiological glucose–insulin model

The physiological glucose–insulin model for clinically illpatients has one compartment for plasma glucose, twocompartments for insulin kinetics, and a two-compartmentdextrose absorption model.

G = −pGG − SIGQ

1 + ˛GQ+ P(t) + EGPb − CNS

VG(1)

Q = −kQ + kI (2)

I = − nI

1 + ˛II+ uex(t)

VI+ e−kIuex(t)IB (3)

P1 = −d1P1 + D(t) (4)

P2 = −min(d2P2, Pmax) + d1P(1) (5)

P(t) = min(d2P2, Pmax) (6)

Eq. (1) represents the plasma glucose compartment whereG is the blood glucose level. Eq. (2) describes insulin actionin interstitial space where Q is the interstitial insulin level.

Eq. (3) describes the plasma insulin compartment where I isthe plasma insulin level. Eqs. (4)–(6) describe the absorptionof dextrose intake (D(t)) through stomach (compartment P1)and gut (compartment P2) and its appearance into plasma

b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 149–155

(P(t)). The transport of glucose from gut to the blood streamis saturable, and the maximum transport rate is Pmax.

Endogenous glucose production (EGP) for a healthy sub-ject varies throughout a day according to daily activities, foodintake and stress response etc. On a pharmacodynamics level,EGP is suppressed with increasing G and Q. Time-varying EGPis difficult to measure clinically and cannot be uniquely iden-tified in this study. Therefore this model uses a constant termEGPb in Eq. (1) to represent the basal endogenous glucose pro-duction for a patient under no presence of glucose or insulin.Insulin independent glucose removal (excluding central ner-vous system uptake CNS) and the suppression of EGP fromEGPb with respect to G are represented with pG. In contrast,insulin mediated glucose removal and the suppression of EGPfrom EGPb due to GLUT4 (which action is associated with thecompounding effect of receptor-binding insulin and blood glu-cose) is represented with SI. Insulin sensitivity (SI) is timevarying and reflects evolving patient condition.

In Eq. (3), the exogenous insulin administration into plasmainsulin is uex(t). Plasma insulin decay rate is n and VI is theplasma insulin distribution volume. Endogenous insulin pro-duction is expressed by e−kIuex(t)IB, where IB is the basal insulinproduction when no exogenous insulin is present. Endoge-nous insulin production is suppressed exponentially withexogenous insulin. Table 1 is a nomenclature for all the param-eters, symbols and abbreviation used in this article.

This model is an improvement from the model used in[15]. This model has an additional CNS for glucose uptakeas this uptake is found to be very consistent inter- andintra-individuals. Dextrose absorption model describes by Eqs.(4)–(6) is more physiological and universal compare to the sim-ple feed model in [15]. The simple feed model in [15] requiresthe enteral feeding be relatively constant (not changing morefrequently than every 2 h), whereas the dextrose absorptionmodel presented here is generic and applicable even for mod-elling meal intake. Finally, this model has an endogenousinsulin term e−kIuex(t)IB to ensure the entire differential equa-tions model in Eqs. (1)–(6) is not ill-conditioned when there isno exogenous insulin given over a significant period of time.

2.2. Sepsis score (ss) criteria and analysis

Sepsis is a systemic inflammatory response syndrome due toinfection [16]. In this study, sepsis is defined using the clinicalclassification score (ss) provided by the ACCP/SCCM guidelinedefinitions [17]. The criteria are defined in Tables 2–4, whichinclude SIRS and the Sepsis-related Organ Failure Assessment(SOFA) score [18].

Clinical data was gathered for n = 36 sepsis patients admit-ted to the medical ICU in Christchurch Hospital (Christchurch,New Zealand). Each patient was on the SPRINT blood glu-cose control protocol [13], providing 9208 total patient hoursof hourly modelled insulin sensitivity. The hourly SI was com-pared to SIRS and ss data. Note that each stay included periodsof sepsis and without sepsis (ss = 0). These periods are dif-ferentiated by positive blood culture and SIRS ≥ 2, and thus

ss ≥ 1.

Receiver Operator Characteristic (ROC) curves were usedto examine the performance of SI as a diagnostic markerfor sepsis. ROC curves effectively examine the ability of

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Table 1 – Nomenclature.

˛G Saturation parameter for insulin mediated glucose removal (L/mU)˛I Saturation parameter for insulin clearance from plasma (L/mU)CDF Cumulative distribution functionCNS Central nervous system glucose uptake (mmol/min)D(t) Dextrose intake (mmol/min)d1 Glucose absorption rate from stomach (min−1)d2 Glucose absorption rate from gut (min−1)EGP Endogenous glucose productionEGPb Basal endogenous glucose production rate (mmol/min)FN False negativeFP False positiveG Blood glucose level (mmol/L)GLUT Glucose transportersICU Intensive Care UnitI Plasma insulin level (mU/L)IB Basal endogenous insulin production rate (mU/min/L)k Interstitial insulin transport rate (min−1)k1 Exponential suppression of endogenous insulin production constantn Plasma insulin decay rate (min−1)NPV Negative predictive valueP(t) Glucose appearance in plasma from dextrose intake (mmol/min)P1 Glucose level in stomach (mmol)P2 Glucose level in gut (mmol)PCT procalcitoninPDF Probability density functionpG Insulin independent glucose removal (excluding central nervous system uptake) and

the suppression of EGP from EGPb with respect to G(min−1)

Pmax Maximal glucose flux from gut to plasma (mmol/min)PPV Positive predictive valueQ Interstitial insulin level (mU/L)ROC Receiver operator characteristicSI Insulin mediated glucose removal and the suppression of EGP from EGPb with respect to

G and Q(L/mU/min)

SIRS Systemic inflammatory response scoreSOFA Sepsis-related organ failure assessmentss Sepsis scoreTN True negativeTP True positiveuex(t) Exogenous insulin (mU/min)VI Plasma insulin distribution volume (L)VG Plasma glucose distribution volume (L)

Table 2 – SIRS criteria.

score Criteria

+1 Temperature <36 ◦C >38 ◦C+1 Heart rate >90/min+1 Respiratory rate or PaCO2 >20/min <32 mm Hg+1 White blood cell count <4 × 109/L or >12 × 109/L or presence of >10% immature granulocytes

Table 3 – SOFA criteria.

score System Criteria

+1 Cardiovascular MAPa or need for inotropes <60 mm Hg+1 Respiratory PaO2/FiO2 <250 mm Hg/mmHg<200 mm Hg/mmHg with pneumonia+1 Renal Urine output <0.5 mL/kg/h

tiptp

+1 Blood Platelets

a Mean arterial pressure.

he biomarker to differentiate between populations. Sensitiv-

ty, specificity, positive predictive value (PPV), and negativeredictive value (NPV) were also evaluated. ROC curves effec-ively examine the separation between normal and diseasedopulations in terms of probability density functions (PDF).

<80 × 109/L or 50% drop in 3 days

Variablility of ss score from 1 h to the next hour were also

examined.

Other clinical measurements were evaluated and com-bined with SI to create a biomarker that aims to maximizethe PDF separation or discrimination in normal and septic

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Table 4 – Sepsis score (ss) criteria.

Sepsis score SIRS > 2 Infectionduring stay

Organfailure > 1

Fluid resus-citation

Inotropepresent

Highinotropedosea

0 Normal1 Sepsis X X2 Severe sepsis X X X X3 Septic shock X X X X X

X X X X

Fig. 1 – Cumulative distribution function (CDF) of insulinsensitivity (SI), grouped by sepsis score (ss).

4 Refractory septic shock X X

a Adrenaline or noradrenaline >0.2 mg min−1 kg−1.

groups. The biomarker was created as an hourly changingfunction based on hourly SI and clinical measurements. Alinear recursive least square method was used to maximizethe discrimination between populations. Optimal weighingfunctions were chosen using the Optimization Toolbox inMatlabTM. The specific goal was to provide discriminationfor ss ≥ 2, where prior studies [15] only achieved it for ss ≥ 3.Achieving this goal for the lower ss = 2 value will provide amarker for a larger group of patients.

Ideally, cross validation or bootstrapping should be per-formed on the data to avoid overfitting. However, because thecurrent available data is very limited (36 patients), the samedata is used for both developing the biomarker and testing it.In particular, the low prevalence of high sepsis score hourslimits the ability to boot strap or cross validate effectively.Equally, it should be noted the work presented in this studyis more of a proof-of-concept study to justify a larger, morecostly comprehensive validation study, rather than a valida-tion study on its own. The method used in this work is novel inthe field of sepsis diagnosis, to the best of the authors’ knowl-edge. Finally, sepsis patient data used in this study is a subsetfrom a cohort representative of typical intensive care patients[13].

3. Results and discussion

Table 5 shows the total hours at each sepsis score. The majorityof the hours are at ss < 2.

3.1. Insulin sensitivity (SI) and sepsis score (ss)

Fig. 1 shows a cumulative distribution function (CDF) plot of SI,for each ss group. SI is generally lower for more severe sepsis.However, the distinction between the septic (ss ≥ 1) and non-septic (ss = 0) groups is not clear.

3.2. Insulin sensitivity SI as a biomarker

Fig. 2 shows the ROC curve for SI as a sepsis biomarker.There is minimal discrimination between no sepsis (ss = 0)

Fig. 2 – Receiver operator characteristic (ROC) curve for SI asa sepsis biomarker, grouped by sepsis score (ss), withcut-off points (x).

Table 5 – Patient hours by sepsis score (ss).

Sepsis score (ss) 0 1 2 3 4

Patient hours 4186 (45.1%) 4861 (52.3%) 91 (1.0%) 88 (0.9%) 60 (0.6%)

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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 149–155 153

Fig. 3 – Cumulative distribution function (CDF) of thec

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FcutTinS

tPwfbf

tdHi

Fig. 4 – Receiver operator characteristic (ROC) curve for themultivariate clinical biomarker, grouped by sepsis score(ss), with cut-off points (x).

linical biomarker, grouped by sepsis score (ss).

nd a sepsis score of ss = 1. For ss ≥ 2, an SI cut-off value of.00013 L/mU/min achieves a 50% sensitivity, 76% specificity,.8% PPV, and 98.3% NPV.

Even though SI is generally lower at higher ss values, theistribution of SI for each ss group overlaps too much with theon-septic group in Fig. 1. Therefore, using SI level itself is notcompletely effective sepsis biomarker.

.3. Multivariate clinical biomarker utilising SI

ig. 3 shows the CDF of a biomarker combining SI and otherlinical factors, for each ss group. The clinical measurementssed in the biomarker include temperature, heart rate, respira-ory rate, blood pressure, and their respective rates of change.he multivariate biomarker generally decreases with increas-

ng sepsis severity. The discrimination between sepsis andon-septic groups is improved, as compared to Fig. 1 using

I only as a diagnostic test.Fig. 4 shows the ROC curve for this biomarker. For ss ≥ 2,

he biomarker achieves 73% sensitivity, 80% specificity, 8.4%PV, and 99.2% NPV. The addition of clinical measurementsith SI significantly improved the diagnostic test performance

or sepsis, as compared to using SI alone. In particular, theiomarker provides an effective negative predictive diagnosisor severe sepsis (ss = 2), which was not achieved previously.

It is also clear comparing Figs. 2 and 4 that the discrimina-ion between ss = 1 and ss ≥ 2 is now wider. Note that ss = 1 is

ifficult to discriminate from ss = 0 and simple, clinical SIRS.ence, as seen in Figs. 2 and 4, its discrimination from ss = 0

s still marginal.

Table 6 – Contingency table.

ss ≥ 2 226 h

Test positive 1967 h TP = 165 (1.8%)Test negative 7241 h FN = 61 (0.7%)Total 9208 h Sensitivity 73.0%

Table 6 is a contingency table showing the biomarker diag-nostic outcome for ss ≥ 2. There are 9208 total hours of patientdata. This data is classified into four categories using sepsisscore and biomarker test outcome: true positive (TP, n = 165),false positive (FP, n = 1802), false negative (FN, n = 61), and truenegative (TN, n = 7180). There are 8982 h when ss < 2 and 226 hwhen ss ≥ 2. Using the biomarker, 7241 h test negative and1967 h test positive.

Note that these ratios also indicate the relative incidenceand reflect clinical expectations where, by the hour, mostsepsis is not necessarily severe. This last point is critical asmost sepsis incidence is recorded by patients. By patient,the incidence of severe sepsis is 5–10% [1], which is reflectedin this cohort. However, with rapid, aggressive treatment itsincidence by hour is low. This low incidence is problem-atic in developing such a non-invasive and real-time clinicalbiomarker.

Fig. 5 provides a visual presentation of clinical sepsis scoreand the biomarker performance. Most of the patient hours aress < 2 (TN + FP). Even though the biomarker correctly identifiesthe severity of sepsis 73% of the time when ss ≥ 2 and 80% ofthe time when ss < 2, the PPV stays low because the ratio of TPto test positive is limited by the ratio between ss ≥ 2 and ss < 2.On contrast, NPV is inherently high because TN makes up themajority of test negative. Again, the mathematics indicate thatrelatively low incidence by hour, as seen in the 8982 h of ss < 2

and 4186 h of ss = 0, hinders good PPV despite good specificity.

ss < 2 8982 h

FP = 1802 (19.6%) PPV 8.4%TN = 7180 (78%) NPV 99.2%Specificity 79.9%

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154 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 149–155

Fig. 5 – Histogram of clinical biomarker data, grouped by

Fig. 6 – Scatter plot of clinical biomarker variation fromhour to hour with respect to sepsis score (ss) (axis

contingency results.

3.4. Sepsis time course

Fig. 6 effectively shows the probability of how ss changes from1 h to the next. The horizontal axis is the current hour ss andthe vertical axis is the ss for the next hour. The majority of thepatient data is when ss = 0 and ss = 1.

Patients at ss = 1 tend to stay at ss = 1, and patients hav-ing ss = 0 tend to stay at ss = 0. Interestingly, when ss ≥ 2, thehighest probability is moving to ss = 1 in the next hour. Thisset of results shows that if sepsis is detected at ss ≥ 2, currentrapid and aggressive ICU treatments are usually very effectivein reducing the severity of the inflammatory responses.

3.5. Biomarker comparison

The clinical informative values a biomarker may providein sepsis are: detection of infection; diagnosis of SIRSseverity and infection progression; and patient treatmentguidance, responsiveness, and prognosis. One such investi-gated biomarker is procalcitonin (PCT), which was first foundelevated in sepsis in 1993 [19]. PCT is a precursor of thehormone calcitonin, synthesized by thyroid C cells, but in sep-sis has an extra-tyroidal origin. Upon intravenous injectionof endotoxin from E. coli in healthy volunteers, serum PCTbecomes detectable after 4 h, maintaining a plateau through8–24 h, following an increase of proinflammatory cytokines[20].

PCT can be measured from serum plasma by commerciallyavailable immunoluminometric assay kits such as LUMItestPCT (Brahms, Berlin, Germany) and Kryptor PCT (Brahms, Hen-nigsdorf, Germany). The use of PCT has been approved by theFDA “in conjunction with other laboratory findings and clin-ical assessments to aid in the risk assessment of critically illpatients on their first day of ICU admission for progression tosevere sepsis and septic shock”.

The reported diagnostic power of PCT from 25 studies

using PCT (2966 patients) as a diagnostic marker of sep-sis, severe sepsis, or septic shock in the adult ICU or aftersurgery or multiple trauma, compared with nonseptic SIRShas sensitivity ranging from 42% to 97% or even 100%, and

numbers = ss + biomarker/1000).

specificity ranging from 48% to 100% [21]. Optimal cut-off val-ues for PCT, determined from ROC curves, ranged from 0.6 to5 ng/mL.

PCT is generally only assessed once a day and thus can-not provide real-time detection. In contrast, the biomarkerpresented in this study is a real-time marker. In addition,all of these studies had some form of extensive clinical pre-screening for sepsis and/or SIRS, biasing the sensitivity orspecificity. The overall results reported are no better, and oftenworse, than those reported here.

Traditionally, diagnostic test results are based on a cut-off point. This method effectively treats all patients as asingle, generic person with one clear cut-off point that dis-tinguishes between normal and abnormal states. However,recent medical treatments have been moving towards patientcustomisation—tailoring treatments to patient needs [22].Although this study has so far provided a sepsis biomarkerthat has a cut-off value which can differentiate ss ≥ 2 fromss < 2 most of the time, this biomarker is also a time-varyingvalue. As with most clinical measurements, this biomarkerwould have both inter- and intra-patient statistical distribu-tion.

3.6. Future work

It is therefore of interest to further investigate how thisbiomarker changes through time for patients, and how muchvariability there is between patients. A means of normal-izing patients and likely changes using stochastic modelswould improve biomarker performance. An observationalstudy and follow-up of a biomarker for sepsis diagnosis inthe ICU would provide the data needed for that analysis.Finally, the statistical model of a biomarker, like the one

developed in this paper, may be more useful clinically byproviding a probability analysis of disease progression in real-time.

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. Conclusions

nsulin sensitivity as a sepsis biomarker for diagnosis of severeepsis achieves a 50% sensitivity, 76% specificity, 4.8% PPV, and8.3% NPV at an SI cut-off value of 0.00013 L/mU/min. A dis-riminating threshold was not found between the ss = 0 ands = 1 cohorts due to a high degree of population overlap. Alinical biomarker combining SI, temperature, heart rate, res-iratory rate, blood pressure, and the respective rate of changechieves 73% sensitivity, 80% specificity, 8.4% PPV, and 99.2%PV, and thus can act as an effective negative predictive diag-osis for severe sepsis.

PPV performance is poor because the ratio of true posi-ive to test positive is limited by the ratio of hours wheres ≥ 2 to ss < 2. The majority of patient hours had ss < 2.owever, the multivariate clinical biomarker may provideatient-specific diagnosis, and effectively show the proba-ility of sepsis time course from hour to hour. Real-timeesults may aid in the treatment and management of sep-is in the ICU. Future work includes an observational studynd follow-up of a biomarker for sepsis diagnosis in theCU.

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