Prognosis in Equine Colic Patients UsingMultivariable Analysis

Mathew J. Reeves, Charles R. Curtis, Mo D. Salman and Bryan J. Hilbert

ABSTRACT

Multiple logistic regression wasused to investigate prognosis in 308horses referred to the University ofMinnesota veterinary teaching hospi-tal with colic. Bivariate resultsidentified the following significantindividual parameters: absent orhypomotile abdominal sounds, medi-cal or surgical classification, perito-neal fluid total protein, anion gap,serum glucose, capillary refill time,blood pH, heart rate, packed cellvolume, base excess, serum chloride,plasma bicarbonate, serum urinarynitrogen and age. Two multivariableprognostic models were developedusing logistic regression. Model I(based on 257 cases with a mortalityrate of39%) included age, sex, medicalor surgical classification, capillaryrefill time, packed cell volume andheart rate. Model II (based on 138cases with a mortality rate of 48%)included age, sex, medical or surgicalclassification, capillary refill time,serum bicarbonate, serum chlorideand respiratory rate. Predictiveperformance of the models wasevaluated by treating the calculatedprobability of death for each horse as acontinuous test result. The influenceof varying the probability cutoff pointfor death on test characteristics(sensitivity, specificity and positiveand negative predictive values) wasdetermined. These models have not

been validated and thus their perfor-mance in a different population isuncertain.

RESUME

Les auteurs ont utilise la regressionlogistique multiple, pour analyser lepronostic relatif a 308 chevaux referesa l'hopital veterinaire d'enseignementde l'universite du Minnesota, a causede coliques. Des resultats a deuxvariables indentifierent les parametresindividuels significatifs suivants:bruits abdominaux absents ou ame-nuises, classification medicale ouchirurgicale, proteines totales duliquide abdominal, trou anionique,glucose serique, temps de remplissagedes capillaires, pH sanguin, frequencecardiaque, hematocrite, exces basi-que, chlorures seriques, bicarbonateplasmatique, azote ureique serique etage. Les auteurs developperent aussideux profils de pronostic a plusieursvariables, par la regression logistique.Le profil I se basait sur 257 cas quiafficherent un taux de mortalite de39%; il incluait l'age, le sexe, laclassification medicale ou chirurgi-cale, le temps de remplissage descapillaires, l'hematocrite et le rythmecardiaque. Le profil II se basait sur 138cas qui afficherent un taux demortalite de 48%; il incluait l'age, lesexe, la classification medicale ouchirurgicale, le temps de remplissage

des capillaires, le bicarbonate serique,les chlorures seriques et la frequencerespiratoire. L'evaluation de la perfor-mance de prediction des profils se fiten traitant la probabilite de mortcalculee pour chaque cheval commeun resultat de test continu. Les auteursdeterminerent aussi l'influence de lavariation du point limite de probabi-lite relatif a la mortalite, d'apres lescaracteristiques suivantes du test:sensibilite, specificite, valeurs deprediction positives et negatives.Comme ces profils n'ont pas etevalides, leur performance avec ungroupe different de chevaux demeureincertaine.

INTRODUCTION

Central to any discussion of equinecolic is the prognosis. Such informa-tion is important to the owner ortrainer as it often plays an integral rolewhen deciding between conservativeand surgical management of colicpatients. In an attempt to make morevalid prognostic assessments in coliccases, many authors (1-27) (Table I)have attempted to define individualparameters which are useful. Varia-bles which assess cardiovascularfunction are considered good prog-nostic guides (6), but serial estimatesof these parameters are important (4)and these individual parametersshould not be interpreted alone (28).

Department of Clinical Sciences (Reeves, Curtis), Department of Environmental Health (Curtis, Salman), College of Veterinary Medicine andBiomedical Sciences, Colorado State University, Fort Collins, Colorado 80523 and Department of Large Animal Clinical Sciences, Veterinary TeachingHospitals, 1365 Gortner Avenue, St. Paul, Minnesota 55108 (Hilbert). Present address of Dr. Hilbert: Epsom Equine Centre, 47 Epsom Avenue,Belmont, 6104 WA, Australia.This project was undertaken while the senior author was an intern and resident in the Department of Large Animal Clinical Sciences, College ofVeterinary Medicine, University of Minnesota.

Submitted March 22, 1988.

Can J Vet Res 1989; 53: 87-94 87

TABLE I. Previously Reported IndividualParameters Determined to be PrognosticallyUseful in Equine Colic

Parameter Author

ClinicalHeart rate

Pulse amplitude

Blood pressure

Jugular filling

Oral mucousmembranecolor/capillary refilltime

Mental depression

Abdominal sounds

ClinicopathologicalPacked cell volume

Total anddifferentialleukocyte count

Lactate

Glucose

pHBUNTotal proteinAnion gap

S.I. intraluminalhydrostaticpressureHemostaticabnormalities

Peritoneal FluidTotal protein

Gross appearance

Cytology

Kalsbeek (1)White (2)Shideler (3)Svendson et al (4)Blood et al (5)Parry et al (6)Svendson et al(4)Greatorex (7)Parry et al (6)Gay et al (8)Parry et al (6)Parry et al (6)Svendson et al (4)

Svendson et al (4)Parry et al (6)Kalsbeek (I)Svendson et al (4)Parry et al (6)Coffman (9)Kalsbeek (1)Stashak (10)Svendson et al (4)Reeves et al (I 1)

Adams et al (12)Kalsbeek (1)Svendson et al (4)Parry et al (6)Pascoe et al ( 13)

Schalm et al (14)White (2)Hutchins (15)Moore et al (I 6)Donawick (17)Kalsbeek (1)Svendson et al (4)Parry et al (6)Kalsbeek (1)Svendson et al (4)Coffman (18)Reeves et al (I 1)Kalsbeek (1)Parry et al (6)Pascoe et al ( 13)Bristol ( 19)Gosset et al (20)

Allen et a! (21)

Byars et al (22)Johnstone et al (23)

Allen et al (21)Reeves et al (I 1)Swanwick et al (24)Brownlow (25)Coffman et al (26)Browlow (25)Adams et al (12)

The methods by which some ofthese parameters have been defined as";prognostically useful" are not alwaysclear. Some assessments seem to beprimarily based on clinical experience(7,26), while others have analyzedarbitrarily the distributions of thevariables between the two populationsof survivors and nonsurvivors (1,8).Other approaches have included thecalculation of survival rates for severaldifferent cutoff points within the rangeof values of a parameter (6,29), or thedemonstration of statistical signifi-cance of means between two popula-tions of survivors and nonsurvivors(17,21). However, the demonstrationof statistical significance between twogroups is not an axiom for predictiveability. In fact all of these methodsdescribed are often unreliable indetermining prognosis based on theassessment of one individual parame-ter, because no one individual parame-ter can reliably discriminate betweenthose cases which survive and thosethat do not (30).

Several authors have attempted tocompare the "prognostic merit" ofthese individual parameters. Theapproaches by which this has beendone have varied from subjectiveanalyses (4,8,17) to approaches basedon objective, multivariable statisticalmodelling (29,30) which are able tocontrol some of the inherent problemsassociated with the use of individualparameters in assessing prognosis(31). In particular, the effect of eachvariable can be adjusted for thepresence of all other variables in themodel and any interactions betweenthe independent variables can beincluded. A ranking order of thevariables' ability to discriminatebetween survivors and nonsurvivorscan also be obtained (30).The aims of this study were to use

multiple logistic regression to: 1)evaluate the usefulness of a wide rangeof individual clinical signs andclinicopathological parameters informulating prognosis for equine colicpatients and 2) formulate predictionmodels to evaluate prognosis in equinecolic cases using the individualvariables defined in the first stage ofthe study. Validation of these modelsis being undertaken in a separateprospective study.

MATERIALS AND METHODS

DATA COLLECTION

The medical case records for all thehorses suffering from acute abdominalpain of digestive origin (coded with a"6" as the first digit in the topographiccode in the computer-based recordingsystem, American Veterinary MedicalData Program (AVMDP, SouthCampus Courts, Bldg C, PurdueUniversity, West Lafayette, Indiana47907) presented to the veterinaryteaching hospital at the University ofMinnesota during a ten year period(July 1974 to June 1984) wereexamined. If the attending clinicianhad not noted in the case record thatcolic was a significant problem or ifthe medical, surgical or postmortemfindings were not consistent with colic,the case was eliminated from thestudy. Each colic admission to thehospital was regarded as a separatecase. Twelve cases which either wereeuthanized for economic reasons orwere dead on arrival at the hospitalwere excluded from the study.The following information recorded

at the time of initial examination wasretrieved from the case record:A) Signalment: age, sex and breed.B) History: duration in hours sincethe onset of colic was first observed bythe owner or trainer.C) Clinical signs: heart rate, respira-tion rate, rectal temperature and oralmucous membrane capillary refill time(CRT). Intestinal sounds were classi-fied into four categories according tothe description in the medical record:1) normal, 2) increased, 3) decreasedor 4) absent.D) Clinicopathological data included:

(i) Hematology: packed cell volume(PCV), total plasma protein (TPP)and total and differential leukocytecounts. The latter were used to classifythe differential leukocyte count ofeach sample into one of 11 groups,based on the system used by Parry et al(6).

(ii) Serum chemistry: sodium (Na+),potassium (K+), chloride (Cl-), glucoseand serum urea nitrogen (SUN).

(iii) Venous blood gases: pH, partialpressure of oxygen (PO2), partialpressure of carbon dioxide (pCO2),plasma bicarbonate (HCO3 ) and baseexcess.

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E) Peritoneal fluid analyses: descrip-tion of the gross appearance (includ-ing color, clarity, turbidity andpresence of bowel contents or purulentmaterial), total and differentialleukocyte count and total protein.When the serum Na+, Cl- and

HCO3 were measured and recorded,the anion gap (AG) was calculatedbased on the equation (AG = Na + - (Cr-+ HCO3)) used by Feldman andRosenburg (32).Two possible outcomes were

defined: alive at time of dischargefrom the hospital, or dead prior todischarge. Some horses in the lattergroup were euthanized to preventunnecessary suffering if the outcomewas considered hopeless. Horses weredischarged only after they had made asatisfactory recovery as indicated byvital signs and a return to normalintestinal function.

Cases were classified as eithermedical or surgical cases based on theclinician's final diagnosis and/ or thepostmortem findings. All the casesdefined as "medical" were treated withmedical therapy only, e.g. intestinallubricants, intravenous fluids, anal-gesics and controlled exercise. Allhorses operated upon were considered"surgical" cases. In addition horsesthat died or were euthanized prior tosurgical exploration that at postmor-tem had intestinal lesions which couldonly have been corrected at surgerywere also included in this group.

STATISTICAL ANALYSIS

An initial screening to reduce thenumber of independent variables wasdone by examining differences in thedistributions of the independentvariables between survivors andnonsurvivors. Student's t-tests wereused for continuous variables and chi-square analysis for categorical varia-bles. Only independent variables withp < 0.05 were considered further.The effect of single risk factors (only

those significant in the initial screen-ing) on death were examined furtherwith logistic regression. Logisticregression is the appropriate methodwhen the outcome is dichotomous(yes/ no) (31,33). Regression coeffi-cients for continuous variables repres-ent the change in log-odds of death fora one unit change in the independent

variable; the unit of measure will affectthe magnitude of the regressioncoefficient. Therefore standardizedregression coefficients (SRC; regres-sion coefficient multiplied by thestandard deviation of the independentvariable) (33) were calculated forcontinuous independent variables.The SRC are expressed in standarddeviation units, i.e. the change in thelog-odds of death for a change of onestandard deviation of the independentvariable. Thus a relative ranking ofcontribution to the probability ofdeath can be obtained by ranking theSRC (33). Significance of the regres-sion coefficients was assessed bycomparing the regression coefficientdivided by its standard error with a Zdistribution (31). Exponentiation ofthe regression coefficient for categori-cal variables yields an odds ratio (OR)which is a quantitative measure ofassociation between an outcome and apotential risk factor (31). Odds ratiosrange between 0 and infinity and thenull value (no association) is 1. Oddsratios > I are predisposing and implya direct association. Odds ratios < 1are preventive and imply an inverseassociation. Therefore, OR of 2 and0.5 have the same magnitude butimply a different association. Ninety-five percent confidence intervals forOR were calculated (31).The multivariable models were

constructed using a stepwise algo-rithm which assesses potential interac-tions and multicollinearity at each

step. The model-building algorithm issimilar to a forward-backward step-wise procedure (33), with the excep-tion of the assessment of possibleinteractions and multicollinearities ateach step. The assessment was basedon examining changes in the regres-sion coefficients of variables already inthe model when a new variable wasadded. When a regression coefficientchanged by more than one standarderror with the addition of the newvariable interaction or multicollinear-ity was suspected. At this point in thealgorithm an interaction term betweenthe variable whose regression coeffi-cient changed and the new variablewas tested. If there was no significant(p > 0.10) interaction the change inthe regression coefficient was consi-dered to have occurred because ofmulticollinearity (a complete descrip-tion of the algorithm is available uponrequest from Dr. Curtis). Thisapproach is called the "change inestimate criterion" (31). The algorithmwas simple, although time consuming,to implement because the computerprogram used (EGRET) is interactiveand allows inspection of the parameterestimates and attributes at each step ofthe modelling process (35). (Incontrast, most stepwise procedureseither examine all possible interac-tions or those specified initially.)The level of significance for a

variable to be entered or to beremoved from the model was p < 0.10and p > 0.10 respectively. This wasbased on the test for the regression

TABLE II. Bivariate Odds Ratios for Death from Colic for Categorical Variablesa

Variable Nb N that Died ORc 95% CI (OR)cAbdominal soundsNormal 36 5 1.0Hypermotile 41 7 1.3 0.4, 4.4Hypomotile 128 46 3.5* 1.3, 9.6Absent 67 45 12.7** 4.3, 37.1

Treatment classificationMedical treatment 134 8 1.0Surgical treatment 174 110 27.1** 12.4, 59.0

SexMare 157 57 1.0Stallion 71 22 0.8 0.4, 1.4Gelding 80 39 1.7+ 1.0, 2.9

aN = 190 horses survived to discharge, n = 1 8 died or were euthanized prior to discharge. + p < 0.10;* p .0.05; ** p <0.01bN is the total number of horses in the specific category used to estimate the odds ratio. N that died isthe number of horses in the specific category that diedCOR = odds ratio. CI = confidence interval. The 95% Cl is calculated at eB ± 1.96*SE(B) from thelogistic regression equation. The comparison category is assigned OR = 1.0

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TABLE III. Bivariate Regression Coefficients for Death for Continuous Variables'

Variable N X± SDb INT B SE(B) SRC

PFTP- peritoneal fluidtotal protein (g/dL) 123 2.8 ± 1.5 -3.07 0.94** 0.19 1.41

ANION -anion gap (mEq/L) 175 16.4 ± 7.8 -2.86 0.17** 0.03 1.32GLC -glucose (mmol/L) 137 8.9 ± 4.1 -2.63 0.29** 0.06 1.19CRT -capillary refill

time (s) 296 1.9 ± 0.9 -2.79 1.17** 0.19 1.05pHc 216 7.3 ± 0.1 9.85 i0.007** 0.001 -0.92HR -heart rate(beats/ min) 303 66.7 ± 23.6 -2.98 0.036** 0.006 0.85PCV -packed cell volume (%) 292 41.4 ± 8.9 -4.48 0.096** 0.016 0.85BASE -base excess(mEq/L) 207 0.7 ± 6.1 -0.12 -0.13** 0.03 -0.79Cl - chloride (mEq/L) 189 96.4 ± 5.9 12.41 -0.13** 0.03 -0.77HC03- -bicarbonate (mEq/L) 215 25.9 ± 5.4 3.24 -0.13** 0.03 -0.70SUN -serum urea nitrogen(mmol/L) 138 8.6 ± 3.4 -1.41 0.14* 0.06 0.45AGE - age (years) 279 7.1 ± 4.9 -0.79 0.05* 0.03 0.35DURATION -duration ofclinical signs (h) 285 22.2 ± 28.2 -0.30 -0.008+ 0.005 -0.23RESP -respiration rate(breaths/ min) 298 28.5 ± 16.1 -0.95 0.014+ 0.007 0.23TOTNEUT - total neutrophils(109/L) 244 8359 ± 4392 -0.98 0.00005+ 0.00003 0.22

aBivariate logistic models; N = number of observations used to estimate the logistic regressioncoefficient; INT = intercept; B = logistic regression coefficient; SE(B) standard error of B;SRC = standardized regression coefficient = B*SD (variable); + p < 0.10; * p < 0.05; ** p < 0.01bMean and standard deviation of observations used in regressionCpH was transformed as ePH. X ± SD = 1530.8 ± 131.2

coefficient equal to 0 rather than thelikelihood ratio chi-square statisticbecause of the large number of missingvalues (3 1). Hosmer-Lemeshowgoodness-of-fit chi-square statistics(GOFCS) were calculated for the finalmodels (34). All logistic regressionswere done with the statistical softwareprogram EGRET for the personalcomputer (35).

Because of the large number ofmissing values a decision rule forconsideration of parameters for themultivariable models was formulated.Parameters for which there were > 50missing values were not considered forthe multivariable models. Model I wasconstructed from the complete dataset of 308 cases. The variables whichhad less than 50 missing observationswere: CRT, duration of colic signs,heart rate, PCV, respiration rate,intestinal sounds and medical orsurgical classification.

Since the collection of clinicopatho-logical data was scarce prior to 1978, asecond dataset consisting of the 210cases admitted during and after 1978was used to formulate a second model(Model II). The same missing valuecriterion was used. Variables whichhad less than 50 missing observations

were: CRT, PCV, heart rate, respira-tion rate, duration of colic signs,medical or surgical classification,intestinal sounds, total blood neutro-phil count, C1, HCO3 and pH. Ageand sex were included in models I and

II as potential confounding variablesregardless of significance.The predicted probability of death

(Pd) was calculated for each horseincluded in the models (31) as follows:

Pd = 11 + e(INT + Bk*Xk)

Where: INT = intercept; Bk = logisticregression coefficient for each variableX1, X2 ... Xk; X = value of eachvariable XI, X2 ... Xk. The Pd wasused as a continuous test by dichotom-izing the probability at a cutoff pointbetween 0 and 1. The success of themodels when used for predictingsurvival was evaluated by calculatingsensitivity, specificity and positive andnegative predictive values (36,37). Inthis case, sensitivity was defined as theproportion of cases that died whichhad Pd > cutoff point (positive testresult) for death. Specificity wasdefined as the proportion of cases thatlived which had Pd < cutoff point(negative test result).

Receiver operator characteristic(ROC) curves (36) were produced forboth models by plotting sensitivityagainst the false positive rate (100 -specificity). Positive and negativepredictive values were calculated forvarious cutoff points of Pd for eachmodel. Positive predictive value was

TABLE IV. Logistic Regression Models for Death from Colic'

Model lb

Y = -6.87 + 0.02 x AGE + -0.07 x SEXI + 0.64 x SEX2 + 3.28 x SURG +0.41 x CRT +0.04 x PCV +0.02 x HR.

(N = 257; GOFCSc = X28= 3.5, P - 0.90)

Model Ijb

Y -6.70+0.03 x AGE + -0.68 x SEXI +0.50x SEX2+ 2.86 xSURG +1.15 x CRT+ -0.12 x HC03-+ -0.09 x Cl- + 0.04 x RESP.

(N = 138; GOFCSc = X2 6.1, 0.5 <P < 0.75)where: SEXI = 0, SEX2 = 0 for mares

SEXI = 1, SEX2 =0 for stallionsSEXI = 0, SEX2 = 1 for geldingsSURG = 0 for medical classificationSURG = 1 for surgical classificationAGE = age in yearsCRT = capillary refill time (sec'1)HCO3 = plasma bicarbonate (mEq/ L)Cl- = chloride (mEq/L)RESP = respiration rate (min-')PCV = packed cell volume (%)HR = heart rate (min-')

ap (death) = I

le-ybAll coefficients in the models are unstandardizedcHosmer-Lemeshow goodness-of-fit chi-square statistic

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TABLE V. Adjusted Odds Ratios for Death from Colic for Categorical Variables in Models I and IIa

Model I (N = 257) Model I1 (N = 138)

Variable N OR 95% CI(OR) N OR 95% CI(OR)

SexMares 131 1.0 - 73 1.0Stallions 49 0.5 0.2, 1.2 24 0.5 0.9, 1.1Geldings 77 1.9 0.8, 4.4 41 0.7 0.1, 2.0

Treatment classificationMedical 111 1.0 - 41 1.0Surgical 146 26.7** 9.7, 73.4 97 17.5** 4.1, 74.6

al0l of the 257 horses used in model I died and 67 of the 138 horses used in model II died.N = number of horses in each category; OR = adjusted odds ratio; CI = confidence interval; 95% CIcalculated as B ± 1.96*SE(B) from logistic regression model. The comparison category is assignedOR = 1.0. ** p<0.01

the proportion of positive test cases(Pd > cutoff point) that died. Negativepredictive value was the proportion ofnegative test cases (Pd < cutoff point)that survived.

RESULTS

BIVARIATE ODDS RATIOSFOR CATEGORICAL VARIABLES

Bivariate OR for categorical varia-bles, significant in the initial screening,are presented in Table II. Horses withno intestinal sounds were 12.7 timesmore likely to die compared to thehorses with normal intestinal sounds,while reduced sounds were associatedwith a 3.5-fold increase in risk ofdeath. Horses classified as surgicalcases were 27 times more likely to diethan horses classified as medical cases.The OR for sex indicate that there wasno significant risk associated with anyparticular gender.

BIVARIATE REGRESSIONCOEFFICIENTS FORCONTINUOUS VARIABLES

Bivariate logistic and SRC forcontinuous variables, significant in theinitial screening, are presented inTable III. In rank of decreasingimportance (based on the magnitudeof the SRC) as prognostic variablesthese were: peritoneal fluid totalprotein (PFTP), AG, serum glucose,CRT, pH, heart rate, PCV, baseexcess, Cl1, HCO3 , SUN, age,respiratory rate and total bloodneutrophil count. All of these parame-ters were significantly (p < 0.05)related to death. As variables withpositive logistic regression coefficientsincrease, the risk of death increases.

Conversely, as variables with negativelogistic regression coefficientsincrease, the risk of death decreases.Respiratory rate, duration of colicsigns and total blood neutrophil countwere significant in the initial screeningbut did not show significant logisticregression coefficients.

MULTIVARIABLE MODELS

The final models were summarizedin Table IV. Model I consisted of 257cases, of which 101 died (61% survivalrate), while model II consisted of 138cases, of which 67 died (52% survivalrate). Odds ratios for the categoricalvariables in both models are presentedin Table V. Intestinal sounds failed toenter either model. Classification as asurgical case was strongly associatedwith an increased risk of death. Sexand age were included in both modelsas potential confounders, howevernone of their OR was significant.The logistic and SRC of death for

continuous variables for both modelsare shown in Table VI. The value of

the regression coefficient for anyparticular variable is adjusted for allthe other variables in the model.Standardized regression coefficientsfor model I indicate that heart rate,PCV and CRT were of approximatelyequal importance in the model andthat the contribution of age was muchless than these three parameters.Standardized regression coefficientsfor model II demonstrated that CRThad the greatest contribution to themodel while HCO3, respiration rateand chloride were of similar andintermediate importance. The relativeimportance of age again was small.The GOFCS statistics for models I

and II are summarized in Table IV.Both models fit the data well asindicated by the large p-values. TheGOFCS statistics for model II was lessthan model I indicating that model IIdid not fit the data as well. However, itmay purely be a function of the smallerdata set used in model II (n = 138)compared to model I (n = 237).

EVALUATION OFBOTH MODELS AS TESTS

The test characteristics of models Iand II for different cutoff points in thePd are shown in Table VII. The rela-tionship between sensitivity andspecificity is demonstrated by thereceiver operator characteristic(ROC) curves for models I and II inFig. 1. Both models show a similarcurve with neither model showing anyobvious advantage.The predictive value of positive and

negative test results of the two modelswith various cutoff points are demon-strated in Fig. 2. The predictive value

TABLE VI. Logistic and Standardized Regression Coefficients for Continuous Variables in ModelsI and II'

Model I (N 257) Model II (N = 138)Variable X ± SD B SE(B) SRC X ± SD B SE(B) SRC

Intercept -6.87** 1.11 6.69** 5.18AGE 7.3 ± 4.9 0.02 0.03 0.10 7.4 ± 4.9 -0.03 0.05 -0.15CRT 1.9 ± 0.9 0.42+ 0.26 0.38 2.0 ± 0.9 1.15** 0.40 1.04PCV 42.0 ± 8.9 0.04+ 0.02 0.35 - - -

HR 64.4 ± 22.0 0.02* 0.01 0.44 - - -

HCO3- - - - 26.2 ± 5.0 -0.12* 0.05 -0.60C1- - 96.3 ± 5.9 -0.09* 0.05 -0.53RESP - 27.8 ± 14.4 0.04* 0.02 0.58

al0I of the 257 horses used in model I died and 67 of the 138 horses used in model II died. X ± SD isthe mean and standard deviation for the independent variables; B = logistic regression coefficient;SE(B) = standard error for logistic regression coefficient; SRC = standardized regressioncoefficient = B*SD (variable); + p < 0.10; * p < 0.05; ** p < 0.01

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TABLE VII. Test Characteristics of Models I and II for Different Cutoff Points in the PredictedProbability of Death'

Model I (N = 257) Model II (N= 138)

Cutofft Se Sp PV+ PV- Se Sp PV+ PV-

0.10 96 62 62 96 99 54 67 970.20 96 67 66 96 94 59 69 910.30 95 71 68 96 91 63 70 880.40 89 77 71 92 88 72 75 860.50 82 82 75 88 82 82 81 830.60 70 89 80 82 70 89 86 760.70 59 93 85 78 64 94 92 740.80 32 96 82 68 52 96 92 680.90 17 99 94 65 33 99 96 610.95 8 99 89 62 19 100 100 57

aSee Table IV for definition of the two models. Se= sensitivity; Sp= specificity; PV + positivepredictive value; P- = negative predictive valuebTest cutoff point for predicted probability of death from models I and II.

P(death) > cutoff point is test positiveP(death) < cutoff point is test negative

adjusts the Pd based on the sensitivityand specificity of the model at a givencutoff point.

Figure 2 illustrates that for anygiven cutoff point model I had a highernegative predictive value while modelII had a higher positive predictivevalue. Thus model I was better inpredicting those horses that survivedwhile model II was better in predictingthose horses that died with this groupof horses.

DISCUSSION

In this retrospective study therewere some major deficiencies in thenature and consistency of parametersrecorded in the medical records. Thiswas partly due to the emergency

100 MModel I

90 o ModeI31

70

60

'-50 -

en) 40II

False positive rote ( 100- specificity )

Fig. 1. Receiver operator characteristic curvesfor models I and II.

situation often associated with coliccases which tends to limit the numberand extent of the diagnostic testsperformed. The extent of the missingdata in this study played havoc withthe multivariable logistic regressionanalyses. It was necessary to discardseveral parameters which were incon-sistently recorded. These includedblood leukocyte differential category,peritoneal fluid gross appearance,peritoneal fluid total and differentialleukocyte counts, nature and amountof nasogastric reflux and rectalpalpation findings. These discardedparameters may be important prog-nostic factors. Other parameterswhich were never recorded in thisstudy but have been defined asprognostically useful such as bloodlactate (16,17) could have beenimportant contributors in the finalmodels. Thus the models defined fromthe final data set are not representativeof all the parameters which may beprognostically useful; this was espe-cially true for the clinicopathologicaldata.

There are obvious biases in thisstudy. It is likely that the amount ofdata recorded on each case varied withthe clinician, disposition of the horse,severity of disease and the emergencyof the situation. Cases that were notexhibiting signs of colic when theyarrived were less likely to have the fullrange of diagnostic tests performed.Also, cases which died soon afterarrival are also likely to have a paucityof diagnostic test results recorded. Ingeneral, however, it was concluded

that with increasing severity of colicsigns that more diagnostic data wouldbe recorded. There is, therefore, aninherent bias in the cases that met thecriteria for model selection. Such abias is likely to spuriously increase thecalculated OR and regression coeffi-cients thus indicating stronger associa-tions of risk than probably exist.

Economic factors may influence themanagement and outcome of somecolic cases, which obviously affects theprognosis outcome variable. Caseswhich were euthanized for economicreasons were eliminated from the study(n = 5). However, there may have beenother cases in which the influence ofeconomic factors on the outcome wasnot adequately recorded in the medicalrecord. Duration of disease, as well asprevious treatments may producedifferences in the clinical and labora-tory data between cases. These influen-ces would also be active in future colicpopulations on which these modelscould be used. Hence, the finalaccuracy of these models is unlikely tobe adversely affected. The inclusion of acase into either a surgical or medicalgroup based on retrospective informa-tion sometimes relied on subjectivecriteria and opinion. All cases thatunderwent surgical exploration wereregarded as "surgical", yet it isundoubtedly true that a small propor-tion of cases were "medical" casesincorrectly taken to surgery.

Additionally, it must be noted thatthese models were evaluated using the

Predicted probability of death cutoff

Fig. 2. Relationship of predictive values ofmodels I and II to the cutoff point of predictedprobability of death.PV+ = positive predictive value.PV- = negative predictive value.

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same data used to construct them. Thustheir performance was better thanwould be expected in practice. Until themodels have been evaluated withindependent data their "true" perfor-mance is uncertain, although the testcharacteristics presented are probablythe "best case" scenario.

Despite the limitations of onlyassessing one parameter the bivariateOR for categorical variables and SRCfor continuous variables can be usefulin approximating the relative impor-tance of each parameter's influence onthe risk of mortality of colic patients.The bivariate logistic regressioncoefficients for continuous variables(Table III) represent the increase in thelog-odds of death for a unit change in avariable. Their magnitude is thereforeinfluenced by the unit of measure of thevariables. For example, the logisticregression coefficient for capillary refilltime (CRT) is large compared to thelogistic regression coefficient for heartrate because the normal range of CRTvalues is much smaller than that forheart rate. However, the relativemagnitude of variables' effects can becompared to each other if SRC areused. The relative ranking of thebivariate SRC for the continuousvariables (Table III) is only approxi-mate and should not be over inter-preted. This is because the SRCdepends on the standard deviation ofthe variable which can vary dramati-cally and thereby give an inaccuratemeasure of a variables effect (38).

Using the logistic equation (seeMaterials and Methods) and theparameter estimates in Table III, theprobability of death can be calculatedfor any particular value of an individualparameter. This may be useful as anestimate of the prognosis of a case,providing one is cognizant of thelimitations discussed previously whenusing individual parameters to deter-mine prognosis.The importance of surgical classifica-

tion on mortality was demonstrated bya large OR of 26.7 in model I (Table V)which was very similar to the bivariateresult (Table II). Surgery was includedin the model because it was a veryimportant confounding variable (it wasassociated with most of the risk factorsof interest [data not presented here] aswell as strongly associated withprognosis). However, its inclusioncould prevent other more biologically

important predictors of prognosis fromentering the model. There were nointeractions found between surgicalclassification and the other variableswhich indicates that the risk factors forprognosis within the surgical andmedical classifies cases were the same(i.e. surgical classification was not aneffect modifer) (33). This in our opinionjustifies the inclusion of surgery in themodels as an important confounderand risk factor for prognosis. However,the presence of interactions in themodel cannot be completely ruled outdue to the small sample size. Analternative would be to create twoseparate models, one for surgical casesand one for medical cases. Unfortu-nately, dividing the population into twogroups would result in an insufficientnumber of cases in each model forsophisticated analyses. Of the sevenother variables considered in theanalysis of model I, duration of colicsigns, intestinal sounds and respirationrate failed to enter the model. The SRCindicate that heart rate, PCV and CRTwere of approximate equal importancein the model (Table VI). These resultsconfirm the importance of cardiovascu-lar parameters in determining progno-sis. The bivariate results (Table III)indicated that PFTP, AG and serumglucose were also valuable parametersin determining prognosis. Unfortu-nately, none of these parameters couldbe included in the multivariableanalysis, so it is unknown whether thesewould have replaced some of thesecardiovascular parameters in the finalmodel.

Again surgical classification wasassociated with a very high risk ofmortality (OR = 17.5) in model II,while CRT remained in the model PCVand heart rate dropped out. Theentrance of HCO3-, C1- and respiratoryrate into the model may be an exampleof multicollinearity, in that these threeparameters may be explaining similarinformation to that explained by heartrate and PCV. The SRC of CRT ismuch larger in model II (1.04)compared to model I (0.38). This isprobably due to the absence of heartrate and PCV; there was no interactionwith these two parameters, thus thelogistic regression coefficient (B) andSRC are much larger. The fact thatCRT remained in the model while theother two cardiovascular parametersdropped out may indicate that CRT is

the strongest predictor of cardiovascu-lar function.

Respiration rate became an impor-tant contributor to model II. Interest-ingly, this parameter showed only slightstatistical significance in the bivariateanalysis and failed to enter model I.Thus its importance may be conditionalon the presence of other parameters inthe model. Although hypochloremiahas been documented in colic cases(4,39), the prognostic merit of serumC1- has not been previously identified.The SRC of the bivariate analysis(Table II) and its incorporation intomodel II indicates its importance.Intestinal sounds, duration of colicsigns, total blood neutrophil count andpH all failed to enter model II,indicating their lack of importancewhen several parameters are assessedsimultaneously.

Multivariable models can also beutilized in clinical prediction; in thisstudy they were used to predictprognosis of equine colic cases.Previous multivariable models formu-lated for use in equine prognosis (29,30)have had limited usefulness in predict-ing the outcome of colic cases becauseno evaluation of the performance ofthese models when used as a continuoustest has been undertaken. The predic-tive probability of death (Pd), calcu-lated from the logistic regressionequation, can be used as a test forsurvival or death in the same way as anyother clinical test can be used.Intuitively, horses which have acalculated Pd < 0.5 would be regardedas more likely to live. This is called anegative test result. Hence, using this Pdestimate, the negative predictive value(the probability of survival given anegative test result) would be obtainedfrom Fig. 2. Those horses with Pd> 0.5would be considered more likely to die.This is a positive test result. Theprobability ofdeath given a positive testresult (the positive predictive value) isthen obtained from Fig. 2 in a similarfashion. One should be clear about theinterpretation of the results. A positivepredictive value of 75% means thatgiven 100 horses that had the same Pdresult, 75 of them would die and 25would live. The odds of mortality forsuch cases would be 3 to 1.The predictive value of a test is not

only a property of the test's sensitivityand specificity but also the prevalenceof the condition in the population being

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tested (36). In this study, the prevalencerepresents the proportion of caseswhich die. In general, as the prevalenceincreases the positive predictive valueincreases, while the negative predictivevalue decreases (37). The prevalence ofcases which died is relatively high in thisstudy, because of the referral nature ofthe caseload (the mortality rates of thehorses used in models I and II were 39%and 48%, respectively). The perfor-mance of these models, in particular thepositive predictive value, when used ona general population of horses withcolic will probably be lower thanpresented in this study, due to the lowerprevalence of mortality in such cases.The difference in prevalence of deathbetween the two models may explainwhy model II had a higher positivepredictive value and a lower negativepredictive value than model I (Fig. 2).Hence, the interpretation of the positiveand negative predictive values will varyfrom setting to setting, according to theprevalence in the population beingtested. Predictive values can becalculated for a given prevalence usingthe sensitivity and specificity of the test(37).

Finally, before these models can berelied upon to predict the outcome offuture colic cases they need to bevalidated on a separate colic popula-tion. The evaluation of the models as acontinuous test is presented only todemonstrate how such models can beused in the clinical setting oncevalidation has occurred and theusefulness of such models has been fullyevaluated. Such validation is presentlybeing undertaken.

ACKNOWLEDGMENTS

The first author is indebted to Drs.R.S. Morris and J. Gay for theirassistance in the initiation of this study.The authors are grateful to Drs. N.Ducharme, H.N. Erb, T.S. Stashak andJ. Traub-Dargatz for reviewing themanuscript.

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