Statistical methods for quantifying the severity of clinical acute pancreatitis

JOURNAL

OF SURGICAL

Statistical JOHN H. C. RANSON. Dep.-rmen~~

22, 79-91

RESEARCH

of Surgery

Methods Clinical

(1977)

for Quantifying the Severity Acute Pancreatitis

B.M. B.Ch.,FACS, und Environmental 5.50 First Avenue, Suhmitted

AND BERNARD

Medicine. New York.

for publication

In acute pancreatitis, as in many other diseases, the spectrum of clinical illness varies widely. Some patients recover uneventfully with little or no treatment while in others the disease appears refractory to every therapy. A rational approach to the management of this type of disease and to the evaluation of proposed therapeutic measures requires the early identification of the severity of the illness by means of objective prognostic factors. In an earlier study [lo], 43 early measurements, or variables, were screened in 100patients with acute pancreatitis to determine which were of apparent prognostic value. Eleven early variables were found to be related to subsequent morbidity and mortality, as follows: on admission, age, white blood cell count, and blood glucose, serum lactic dehydrogenase, and serum glutamic oxaloacetic transaminase levels; and during the initial 48 hr, hematocrit decrease, blood urea nitrogen rise, lowest serum calcium, lowest arterial oxygen tension, highest base deficit, and estimated fluid sequestration. There was also an apparent relationship between initial serum amylase levels or a history of previous acute attacks and the severity of disease. In this report, the original series of 100 consecutive patients has been extended to 300, and the statistical approach for identifying high-risk patients has been considerably refined. MATERIALS

AND

METHODS

Patient Population A total of 300 consecutive patients with acute pancreatitis admitted to Bellevue

of

S. PASTERNACK,

New York University New York 10016

Medical

Ph.D.

Center,

August 2, 1976

Hospital and New York University Medical Center between January 1971and February 1975 has been evaluated. In 67 cases, the diagnosis was proved at laparotomy or autopsy, and, in 233, the diagnosis rested on the presence of upper abdominal pain, tenderness and guarding with vomiting, serum amylase levels which were elevated above 200 Somogyi units %, and an overall clinical course which was compatible with acute pancreatitis at discharge. There were 65 women and 235 men. Pancreatitis was associated with alcoholism in 207 patients and with biliary tract disease in 51. It occurred postoperatively in 17 patients. No previous known attack of acute pancreatitis had occurred in 193 patients, one such episode was documented in 50 patients, and more than one such episode was recorded in 57 paients. The management and morbidity in these patients have been previously described in detail [ 10, 1I]. Patients with elevated serum amylase levels postoperatively or with biliary tract disease but in whom no other clinical or operative evidence of pancreatitis was noted are not included. Patients who developed evidence of pancreatitis after abdominal trauma or direct surgical procedures on the pancreas were not studied. In the analysis of prognostic factors, values recorded after laparotomy have not been included, except in patients who developed pancreatitis postoperatively. Fluid sequestration was estimated by subtracting the volumes of nasogastric and urinary drainage from the volume of intravenous fluid administered. Blood sugar measurements in patients with known diabetes mel-

79 Copyright All rights

0 1977 by Academic Press. Inc. of tepoduction in any fuorm rrserved.

ISSN 0022-4804

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litus are excluded from analysis. In February 1974, the units in which serum lactic dehydrogenase levels were recorded by our clinical laboratories were changed. Formerly, the normal range was 200 to 450 units %. Currently the normal range is 100 to 225 International Units/liter, and in the present report all lactic dehydrogenase values are expressed in the current units. For purposes of analysis, the patients were divided into two groups on the basis of their overall clinical course. Group 1 included 244 patients who required 7 or less days of intensive care and recovered without major life-threatening complications. Group 2 consisted of 56 patients with severe pancreatitis; it included 22 patients who died and a further 34 who required more than 7 days of treatment in the intensive care unit. Statistical

Analysis

TABLE

1

EARLY

OBJECTIVE

ACUTE

PANCREATITIS

FEATURES

IN

At admission Age (years) Blood glucose (milligrams percent) White blood cell count (X 103 per cubic millimeter) Serum glutamic oxaloacetic transaminase (Sigma Frankel units percent) Serum amylase (Somogyi units percent) Previous episodes (number) Serum lactic dehydrogenase (international units per liter) Within 48 hr Hematocrit decrease (percentage) Blood urea nitrogen change (milligrams percent) Low serum calcium (milligrams percent) Low arterial oxygen tension (millimeters of mercury) High base deficit (milliequivalents per liter) Estimated fluid sequestration (milliliters)

1977

The analysis of the data proceeded in steps. First, each of the 13 variables was examined individually, ignoring the others, to determine its ability to distinguish between Group 1 patients and Group 2 patients. Then, that particular linear combination of variables which achieved optimal separation between the two groups was searched for by means of discriminant analysis. A linear function called z, the discriminant score, of the risk factors (variables x1, x2, . . . , x,), was looked for such that the mean values of z in the two groups were as far apart as possible relative to the variation of z within the two groups. Thus, given that z = blxl + bg2 + . . . + bgp, the values of the b’s are found such that the ratio 02 =

Seven risk factors, or variables, measured at the time of admission and six measured within 48 hr have been examined and are listed in Table 1.

THIRTEEN

VOL. 22, NO. 2, FEBRUARY

(21 - &?y variance of z within groups

is as large as possible, where ii denotes the mean of the discriminant scores for individuals in Group i (i = 1 of 2). The square root of the ratio D is called the generalized distance between the two groups. If D is greater than 3, this would correspond to the comparison of two univariate distributions whose means differ by more than 3 standard deviations, indicating little overlap between the two. The objective of maximizing the difference in discriminant scores between the two groups, while keeping each group as homogeneous as possible, need not necessarily involve the use of all available variables. Since some variables may not possess much discriminating power, either alone or in linear combinations with others, a stepwise selection procedure was used to identify those variables which contribute significantly to the separation of the two groups. These variables were selected by first identifying the single variable which showed the greatest differentiation between the two groups. The second variable to be selected was then determined by its

RANSON

AND

PASTERNACK:

SEVERITY

contribution to the differentiation as measured by the generalized distance statistic D. That is, each of the remaining variables was separately combined with the first, and the variable yielding the greatest increase in D was added to the discriminant analysis. Third, fourth, and additional variables were added in this manner. After the variables had been selected, a rule was required for discriminating between groups so that any new individual could be assigned to the more appropriate group. In our application, the correct diagnosis of severity of disease in acute pancreatitis becomes available only after a lapse of time. The need is to determine the severity at the earliest time after admission. Under the assumption that the variables in each group have a multivariate normal distribution, a rule was adopted which is based on the conversion of an individual’s discriminant score into a probability of group membership. Thus, the probability that an individual belonged to Group i (i = 1 or 2) could be determined, given the values of the variables entering into the discriminant score, and the individual could be assigned to the group for which he had the highest probability. Computer programs for performing the above operations are widely available. In this analysis, the subprogram DISCRIMINANT (version 6) in the Statistical Package for the Social Sciences was used. This program computed discriminant scores and classification probabilities (a priori probabilities were set at .50 for each group). It was thus possible to compute the number of individuals in each group who would have been wrongly classified by the allocation rule. By defining a “dummy” dependent variable y which takes the value 0 for each individual in Group 1 and 1 for each individual in Group 2, we could regress y onx,,x,, . . . , xI, for all individuals combined into one group. The simple linear regression equation y = a + bx could be used for estimating the risk of severe illness or death, where a is the regression

OF CLINICAL

ACUTE

PANCREATITIS

81

intercept, b the regression coefficient (both a and b being determined by the method of least squares), and x the value of the variable or risk factor being considered. The regression coefficient measures the absolute increase in the estimated risk of severe illness or death corresponding to a unit increase in the value of the risk factor. Dividing the regression coefficient by its standard error yields the usual t value. The multiple linear regression equation for estimating the risk of severe illness or death using p variables is: y = a + b,xl + b,x,

+ . . . + bpx,,

wherex,,x,, . . . , x, are the values of the p variables. The so-called partial regression coefficients bl, b2, . . . , b,, again estimated by the usual least-squares method, are measures of the association of each variable with risk of severe illness or death after adjusting for the effects of all the other variables included in the equation. The r values associated with these regression coefficients are called “adjusted” t values whereas the t values calculated for the univariate regression equation above are called “unadjusted” t values. Apart from a constant of proportionality, the estimated partial regression coefficients can be shown to be identical to the linear discriminant function coefficients obtained by discriminant analysis as described earlier. Thus, the t values for the partial regression coefficients, which may be considered the t values for the discriminant function coefficients, can be used to test the importance of particular variables in the discrimination. Furthermore, the multiple correlation coefficient, R, representing the correlation coefficient between the observed y of 0 or 1 and the estimated y value for each patient, can also be used as a measure of the degree to which a particular set of variables predicts the risk of death or severe illness. However, as described by Morrison [8], since the observed y for each patient is restricted to only two possible values, the largest possible

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value for R is less than 1. This qualification must be considered when one is tempted to interpret R2 x 100 as the percentage of the total variation in y “explained” by the regression. Also, it is to be noted that a simple mathematical relationship exists between the regression analysis statistic R2 and the discriminant analysis statistic D2; viz. D2 =

n(n - 2) v2

R2 I-

where y11 is the number of patients in Group 1, n2 is the number of patients in Group 2, and n = n, + n2. Either of these two statistics can be tested for statistical significance by a conventional F test for the significance of a multiple regression model by noting that F = (n - P -lkw2 pn(n - 2) = (n -P

D2

- 1)R2

p(1 - R2)

’

where p is the number of variables in the model and F is distributed as a variance ratio with p and n -p - 1 degrees of freedom. The data were also analyzed by the logistic regression model for estimating risk from p baseline variables. This model, which can be written in the form 1

VOL. 22, NO. 2, FEBRUARY

1977

such occurrences. Thus, for our application, the sum of the estimated y’s for all patients included in the analysis will equal the actual number of Group 2 patients included in the analysis. In order to evaluate how well the multiple logistic function predicts the risk of death or severe illness in patients presenting with acute pancreatitis, estimated risk scores were calculated for each patient having complete data on the variables included in the model. The patients were ranked according to their risk scores and were divided into 10 equal-sized groups or deciles. The “expected” number of patients with severe illness was then calculated for each decile by summing the estimated risks, y, for the individuals assigned to the decile, and this number was compared to the actual number of individuals with severe illnesses for these deciles. Three logistic models were used: (a) seven admission variables only, (b) six 48-hr variables only, and (c) nine variables (five at admission, four at 48 hr after admission) selected by the stepwise discriminant function analysis. RESULTS

Table 2 shows the means + 1 standard deviation for the seven admission variables and the six 48-hr variables, respectively, included in this study. Table 3 presents the results of the linear discriminant and linear regression analyses. Y= In the univariate analyses, all of the 13 1 + e-(a+b,xl+bzxa+...+bpxp) ’ variables except amylase had absolute adhas the advantage over the linear regres- justed t values greater than 2.00. This sion model that it will always yield analysis included only the 208 patients estimates of risk, y, which lie between 0 with complete admission data; the signifand 1, making them interpretable as probaicance of amylase was less than when all bilities. In this study we have used the 300 patients were included [ 111. Walker-Duncan maximum likelihood When the seven admission variables (weighted least squares) procedure [ 181 for alone were considered simultaneously, only estimating the regression coefficients bl, age and amylase lacked statistical signifib2, - f * , 6,. This procedure has a con- cance at the 0.05 level of probability; these straint which forces the total expected numtwo variables also ranked sixth and seventh, ber of occurrences of the event in ques- respectively, in the order of selection by tion (in this study, death or serious ill- the stepwise discriminant analysis program. ness) to equal the total observed number of The two variables most strongly related to

RANSON AND PASTERNACK:

SEVERITY

OF CLINICAL

TABLE PROGNOSTIC

Variable Admission Age

SIGNS

UPON

ACUTE PANCREATITIS

83

2

ADMISSION

Number of patients

AND

WITHIN

Mean

48

HOURS”

Standard deviation

Coefficient of variation (%)

Group I 244 Group 2 56

42.4 50.8

14.2 17.5

33.4 34.4

Blood glucose

Group 1 230 Group 2 56

144.8 216.2

50.2 108.1

34.7 50.0

White blood cell count

Group I 243 Group 2 54

IO.1 15.0

Serum glutamic oxaloacetic transaminase

Group 1 205 Group 2 44

136.4 234.0

Serum amylase

Group 1 244 Group 2 56

Previous episodes

Group 1 244 Group 2 56

Serum lactic dehydrogenase

Group 1 191 Group 2 35

48 hr Hematocrit decrease

959 1471 0.76 0.25 230.8 449.6

4.02 5.77 184.2 443.4 1306 1244 1.10 0.58 133.7 394.5

39.9 38.4 135.1 189.5 136.2 84.6 144.3 231.9 57.9 87.8

Group 1 223 Group 2 55

4.24 9.32

4.48 5.38

105.6 57.7

Blood urea nitrogen change

Group 1 224 Group 2 53

-4.78 3.32

5.88 20.0

122.9 603.0

Low serium calcium

Group I 230 Group 2 54

9.03 8.07

0.96 1.10

10.6 13.7

Low arterial oxygen tension

Group 1 207 Group 2 45

72.5 64.2

High base deficit

Group 1 208 Group 2 49

0.50 -2.43

Fluid sequestration

Group I 132 Group 2 38

3158 5276

11.7 12.1 3.94 5.71 1843 2143

16.1 18.9 722.8 235.1 58.4 40.6

o The number of patients, mean value, standard deviation, and coefficient of variation are shown for each variable by group. Group 1 includes patients who recovered without major life-threatening complications. Group 2 includes those who died and those who required more than I week of intensive care.

severity of disease were lactic dehydrogenase and blood sugar levels; these two also ranked first and second, but in reverse order, by the stepwise selection procedure. The seven admission variables yielded a multiple correlation coefficient of 0.64, and, thus, they accounted for 41.4% of the observed variance. These variables discriminated between Group I and Group 2 patients with a distance D = 2.29. The

mean risk scores, therefore, for Group 1 and Group 2 patients differed by 2.29 standard deviations. When the six 48-hr variables alone were considered simultaneously, only the base deficit had an absolute adjusted t value less than 2.00, although only nominally (t = 1.99). It also ranked sixth in the order of selection. The most significant discriminator in this set of six variables was

84

JOURNAL

OF SURGICAL

RESEARCH: TABLE

RESULTS

OF DISCRIMINANT (MULTIVARIATE)

VOL. 22, NO. 2, FEBRUARY

1977

3

ANALYSIS SHOWING THE UNADJUSTED (UNIVARIATE) AND ADJUSTED t VALUES AND RESULTS OF CLASSIFICATION PROCEDURE

Adjusted t valuesb Unadjusted Variable Admission 1. Age 2. Blood glucose 3. White blood cell count 4. Serum glutamic oxaloacetic transaminase 5. Serum amylase 6. Previous episodes 7. Serum lactic dehydrogenase 48

hr 8. 9. 10. 11. 12. 13.

Hematocrit decrease Blood urea nitrogen Low serum calcium Low arterial oxygen tension High base deficit Estimated fluid sequestration

Multiple correlation

t

values"

Seven variables

2.72 7.00 5.99

5.69 (1) 3.18 (4)

2.35 0.97 -2.98 6.36

Generalized

1.35 (6)c

-4.33 -0.30 -2.02 6.85

(R)

distance (D)

Classification result@ Group 1. Patients correctly classified: % Group 2. Patients correctly classified: %

Total. Patients correctly classified: %

Thirteen variables

1.34 2.89 0.94

(3) (7) (5) (2)

6.68 4.46 -5.59 -3.88 -3.61 5.62

R* x 100

Six variables

(9) (5)

(1) (5) (2) (4)

- 1.99 (6) 2.93 (3) 0.64 41.38 2.29

0.70 49.25

1581175 90.3

100/l 10

1.47 (9) 3.60 (5)

(10)

-3.17 (6) -0.43 (13) -2.32 (7) 4.64 (3) 4.72 2.24 -2.98 -3.18

Nine variables

3.44 (2) -0.55 (12) -3.41 (1) -1.94 (4) -0.44 (11) 1.35 (8)

-3.69

(6)

-2.53 (7) 5.16 (3)

3.85 (1) -3.88 -1.89

(2) (4)

- 1.64 (8)

0.81 64.91 3.40

0.81 65.38 3.43

90.9

87191 95.6

91194 %.8

27133 81.8

25/30 83.3

20122 90.9

21123 91.3

1851208 88.9

1251140 89.3

107/113 94.7

1121117 95.7

1.15

a Unadjusted t values are based on 208 cases with complete data on variables 1-7 and 140 cases with complete data on variables 8- 13; sign denotes whether Group 2 mean minus Group 1 mean is positive or negative. * Adjusted t value is the discriminant (regression) function coefficient divided by its standard error. c Numbers in parentheses denote order of selection of variables by stepwise discriminant analysis. d Group 1 includes patients who recovered without major life-threatening complications. Group 2 includes patients who died and those who required more than 1 week of intensive care.

The values of R and were 0.70 and 1.15, respectively. Note that in this instance 140 patients had complete data available on all six variables, whereas in the previous analysis using the seven admission variables there were 208 patients with complete data. When all 13 variables were included in the model, seven had absolute adjusted t values of less than 2.00. The poorest discriminators were amylase, blood urea nitrohematocrit

decrease.

D for this analysis

gen change, base deficit, and white blood cell count, each of which had absolute t values below 1.00, whereas the most statistically significant discriminators were serum lactic dehydrogenase, hematocrit decrease, serum calcium, and serum glutamic oxaloacetic transaminase, all of which had absolute t values above 3.00. By order of selection, calcium, hematocrit decrease, and serum lactic dehydrogenase ranked 1, 2, and 3, respectively. For this analysis

RANSON AND PASTERNACK:

SEVERITY

R = 0.81 and D = 3.40. There

were 113 patients with complete data on all 13 variables. The fourth model included nine variables, the four poorest discriminators identified above being dropped from the analysis. For this analysis, we noted that serum lactic dehydrogenase, calcium, hematocrit decrease, serum glutamic oxaloacetic transaminase, and blood sugar all had absolute t values exceeding 3.50. The values of R and D were almost identical to those resulting from use of the 13 variables. For the nine-variables analysis, 117 patients had complete data. The results of the discriminant analysis classification procedure showed that, in each of the four variable sets used, the proportion of patients correctly classified in Group 1 exceeded 90%. It was highest for the nine-variables model, being 96.8%. The percentage of patients correctly classified in Group 2 varied from 8 I .8 to 9 1.3%, again being highest for the nine-variables model. The overall number correctly classified by the nine-variables model was 112 of 117 or 95.7%. Estimated coefficients for the multiple TABLE MULTIPLE

LOGISTIC

FUNCTION

OF CLINICAL

logistic function are shown in Table 4 for three models: (a) seven admission variables; (b) six 48-hr variables; and (c) nine variables, five at admission and four at 48 hr after admission. These values are expressed in their natural units. In order to obtain unitfree comparisons, each variable can be expressed as a multiple of its own standard deviation, or, stated otherwise, each coefficient in natural units is multiplied by its own standard deviation to obtain a coefficient in standard units. Such coefficients are shown in Table 5. Measured in this way the most important, but not necessarily the statistically most significant, risk factors for death or serious illness are serum lactic dehydrogenase, serum glutamic oxaloacetic transaminase, and blood sugar levels when admission variables alone are considered; arterial oxygen tension, hematocrit decrease, and calcium when the 48-hr variables are considered; and serum lactic dehydrogenase, serum glutamic oxaloacetic transaminase, and calcium levels, number of previous episodes, and hematocrit decrease for the combined set of nine variables. The relative unimportance of arterial oxygen tension as a risk factor and the rela4

COEFFICIENTS

AND CONSTANT

Variable

Seven variables

Admission I. Age 2. Blood glucose 3. White blood cell count 4. Serum glutamic oxaloacetic transaminase 5. Serum amylase 6. Previous episodes 7. Serum lactic dehydrogenase

0.0223 0.0172 0.1666 -0.0046 -0.0001 -0.5951 0.0089

48 hr 8. 9. 10. I I. 12. 13.

Hematocrit decrease Blood urea nitrogen change Low serum calcium Low arterial oxygen tension High base deficit Estimated fluid sequestration

Constant n Values reported in natural units.

85

ACUTE PANCREATITIS

TERM”

Six variables

0.0628 0.0156 -0.0121 -3.5853 0.0154 0.2268 0.0551 -0.8484 -0.0972 -0.0666 0.0003

-9.4258

Nine variables

9.3197

0.3094 -1.7818 -0.0618 0.0002 6.7554

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MULTIPLE

LOGISTIC

VOL. 22, NO. 2, FEBRUARY 5

FUNCTION

COEFFICIENTS”

Variable

Seven variables

Admission I. Age 2. Blood glucose 3. White blood cell count 4. Serum glutamic oxaloacetic transaminase 5. Serum amylase 6. Previous episodes 7. Serum lactic dehydrogenase

0.3465 1.1055 0.7222 - 1.2056 -0.1319 -0.6203 1.7230

48 hr 8. 9. IO. I I. 12. 13.

1977

Hematocrit decrease Blood urea nitrogen change Low serum calcium Low arterial oxygen tension High base deficit Estimated fluid sequestration

Six variables

Nine variables 0.9620 0.8836 -3.5107 -3.3513 3.6092

1.0126 0.5194 -0.8792 -1.0419 -0.3056 0.6159

1.3882 - 1.7429 -0.6726 0.4213

” Values reported in standard units.

tive importance of previous episodes, when all other risk factors are included in the ninevariables model, is noteworthy. This can be explained by the interrelationships of these variables, which must constantly be borne in mind when interpreting the findings. Tables 6-8 present the results of the decile classification using the multiple logistic regression model with six, seven, and nine variables, respectively. Comparison of the expected numbers of deaths or serious illnesses with those actually obTABLE EXPECTED

AND

OBSERVED

NUMBERS ANALYSIS

served in each decile is in substantial agreement with the results of the discriminant analyses shown in Table 3. There is little difference in the use of the seven-variables model as contrasted to the use of the sixvariables model with regard to their abilities to predict death or severe illness, while the nine-variables model demonstrates the closest fit between expected and observed values. As can be seen, each of the three models provides a more than adequate description of the risk of death or serious 6

OF DEATHS OR SERIOUS WITH SEVEN VARIABLES

ILLNESSES: MULTIPLE AT ADMISSION

LOGISTIC

FUNCTION

Death or serious illness Decile of expected risk

Number of patients

Range of expected risk

I 2 3 4 5 6 7 8 9 10 All

21 21 20 21 21 21 21 20 21 21 208

0.001-0.005 0.006-0.010 0.010-0.015 0.016-0.021 0.022-0.034 0.035-0.064 0.066-o. 128 0.131-0.231 0.232-0.584 0.597- 1.oOO

Expected

Observed

0.07 0.16 0.25 0.38 0.56 1.00 2.12 3.50 7.43 17.53 33.00

0 0 0 I 0 0 2 4 IO 16 33

RANSON AND PASTERNACK:

SEVERITY TABLE

EXPECTED

AND

OBSERVED

NUMBERS FUNCTION

OF CLINICAL

87

ACUTE PANCREATITIS

7

OF DEATHS OR SERIOUS ILLNESSES: ANALYSIS WITH SIX VARIABLES”

MULTIPLE

LOGISTIC

Death or serious illness Decile of expected risk

Number of patients

Range of expected risk

1 2 3 4 5 6 7 8 9 10 All

14 14 14 14 14 14 14 14 14 14 1140

0.000-0.004 0.005-0.009 0.010-0.018 0.019-0.032 0.032-0.050 0.052-0.099 0.101-0.176 0.177-0.433 0.435-0.863 0.884-0.997

Expected

Observed

0.04 0.09 0.19 0.33 0.58 0.93 1.92 3.82 8.80 13.30 30.00

2 0 4 8 14 30

o Within 48 hr after admission.

illness as a function of their respective baseline variables. DISCUSSION

The spectrum of clinical illness associated with a specific disease frequently varies widely and the choice of treatment for individual patients must be determined on the basis of subjective assessment and past experience. An ineffective treatment may appear to be highly effective if applied to patients whose illness would have reTABLE EXPECTED

AND

OBSERVED

NUMBERS FUNCTION

solved sponaneously, and an effective treatment may appear worthless if administered to those with fulminant disease. Similarly, the morbidity of a specific mode of therapy may exceed its potential benefits when applied to patients with mild disease. The confusion which is produced by variation in severity of disease has been clearly illustrated by experience with acute pancreatitis. Many patients have mild or “edematous” pancreatitis and recover uneventfully following nasogastric suction and in8

OF DEATHS OR SERIOUS ILLNESSES: ANALYSIS WITH NINE VARIABLE@

MULTIPLE

LOGISTIC

Death or serious illness Decile of expected risk

Number of patients

1 2 3 4 5 6 7 8 9 10 All

12 11 12 12 12 11 12 12 11 12 117

Range of expected risk

Expected

Observed

0.00 0.00 0.00 0.01 0.03 0.06 0.21 1.87 8.86 11.96 23.00

0 0 0 0 0 0 1 1 9 12 23

0.000-0.000 0.000-0.000 0.000-0.000 0.000-0.001 0.001-0.003 0.004-0.008 0.009-0.032 0.032-0.455 0.472-0.974 0.988- 1.OOO

(1Five variables at admission, four variables within 48 hr after admission.

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travenous fluid administration. Others with or “necrotizing” severe, “hemorrhagic” pancreatitis develop serious or lethal respiratory, hypotensive, or septic complications. Treatment by early surgical drainage was initially recommended in 1925 by Moynihan [9] and in 1928 by Schmieden and Sebening [ 141. Following the report of Mikkelsen in 1934 [7], operative treatment fell into disfavor and, indeed, was thought to be harmful but recently has been recommended again in severe disease by Lawson et al. [6], Waterman et al. [ 191, Rosato et al. [13], and others. The list of other therapeutic measures which have been proposed for patients with pancreatitis includes thoracic duct drainage; pancreatic irradiation; the administration of 5-fluorouracil, acetazolamide, aprotinin, or steroids; surgical resection of the pancreas; peritoneal dialysis; and many other suggestions. In most cases, these measures have been recommended on the basis of nonhuman animal studies or clinical experience in which both patient selection and the efficacy of treatment were assessed largely by subjective criteria. In order to develop an objective system for quantifying the severity of disease, those particular variables or factors which have substantial prognostic value must be extracted from a large number of possible prognostic variables. Generally, a screening procedure is adopted which removes most of the variables from further consideration, leaving a relatively small number which can be studied more intensely. After the initial screening is completed, it is necessary to determine how the chosen variables can best be used for prognostic purposes. This may take the form of a rule for estimating the mean response or, for dichotomous variables, the probability of a positive response. The rule may be a predictive formula or it may be a scheme for classifying a patient into one of a number of categories. An expository paper which reviews the rationale for determining prognostic factors

VOL.

22, NO.

2, FEBRUARY

1977

and the statistical methods for finding and allowing for such factors in the design and analysis of clinical studies has recently been published by Armitage and Gehan (1). Methods which rely on the use of the range of normal values, or the mean plus or minus a multiple of the standard deviation, compared with the range of disease state values are commonly used for diagnostic purposes. Obvious extensions can be used in prognostic studies. Such techniques may be based on the use of one variable (univariate) or several variables (multivariate). Shoemaker and his associates [IS] used this type of approach to investigate the underlying physiologic problems of acutely ill postoperative patients by examining the frequency and type of variables which differentiate late survivors from nonsurvivors. In an earlier study, this method was used to screen the prognostic value of 43 objective measurements made during the initial 48 hr of treatment in 100 patients with acute pancreatitis. These variables were evaluated by comparing the mean values plus or minus 1 standard deviation in patients who were seriously ill or died with those in patients who recovered uneventfully [ 101. Eleven factors which correlated with subsequent morbidity and mortality were identified. For each of these factors, values beyond a level outside the mean plus or minus 1 standard deviation for those who recovered uneventfully were designated as a positive prognostic sign. It was found that the severity of illness in an individual patient could be related to the number of positive signs. In patients with three or more positive prognostic signs there was a high risk of serious illness or death, while this risk was small in those with less than three early signs. Eighty-eight out of the 100 patients were correctly classified according to severity of disease in this retrospective analysis. The prospective use of these 11 signs in 200 subsequent patients with acute pancreatitis correctly predicted the severity of disease in 185 patients or 92.5%

RANSON

AND

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of the cases [ 1 I]. The advantage of this earlier approach is that it provides a simple set of 11 signs which may be readily tabulated by the clinician at the bedside without special statistical measures. The disadvantages of this approach are that the patient cannot be accurately classified as to severity of disease until 48 hr after admission, so that the influence of treatment during that time remains unknown, and that a relatively large number of factors is required for classification. The present studies employing more sophisticated statistical methods were undertaken in an attempt to refine the early identification of seriously ill patients. The results of the discriminant analysis indicate that the severity of disease may be accurately identified in 88.9% of cases by the use of seven admission variables alone and in 95.7% of cases using nine variables which are available at the end of the initial 48 hr of treatment. Since the rules have been determined from these particular samples, this may be a better performance than would be expected with subsequent classification of new individuals. Nevertheless, it permits assessment of the discriminatory ability of the variables used, since, if a large proportion of cases were misclassified, it would suggest that the variables selected in the analysis are poor discriminators. Similarly, the multiple logistic regression model provides a highly accurate description of the risk of death or serious illness, even when admission variables only are considered. The probability that an individual is at high risk of death or severe disease can be determined by use of this model, and it results in a finer classification of risk than can be achieved by the previously described method based on the number of positive signs. The Walker- Duncan maximum likelihood estimation method that we have used has also been utilized by Armitage et al. [2] in analyzing data on women receiving treatments for advanced breast cancer and by the Coronary Drug Project Group [16] which has reported on factors

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influencing long-term prognosis after recovery from myocardial infarction. Halperin et al. [.5] have shown that the maximum likelihood approach is generally superior to the discriminant function approach originally proposed by Truett et al. [17], although it is more difficult computationally. Two editorials, by Gordon [3] and Gordon and Kannel [4], provide very useful comments on the implications and hazards involved in the use of the logistic function, especially with regard to cardiovascular epidemiology. A recent study by Romero et al. [12] has evaluated the predictive value of admission variables in 87 patients with acute pancreatitis using linear discriminant function analysis. This study was limited to patients with acute alcoholic pancreatitis and was designed to separate “complicated pancreatitis” with a 19% mortality from “uncomplicated pancreatitis.” A number of variables were included in that analysis which were not evaluated in the present study because they may depend, in some degree, on the subjective opinion of the observer. Such variables include abdominal distension, abdominal fullness, mass, and ascites. Nonetheless, retrospective analysis using seven admission variables was accurate in predicting the clinical course of 99% of cases within the definitions of the study. Significant admission parameters included hematocrit and blood-urea-nitrogen levels. In our study, admission hematocrits were 41.8 t 6.1% (SD) in Group 1 and 43.4 +- 6.9% (SD) in Group 2. The values were 42.0 ? 6.2% (SD) in patients who survived and 43.5 ? 6.9% (SD) in those who died. Neither of these differences was significant. Admission blood urea nitrogen levels did correlate with severity of disease in our patients but were not as accurate as 48-hr blood urea nitrogen change. These and other differences are probably related to patient selection and study definitions. It is, however, clear that the severity of acute pancreatitis can be estimated by early criteria, and further prospective

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studies are required to evaluate and refine the present methods. It is hoped that the data and methods described in this report may provide a basis for the objective identification of high-risk patients with acute pancreatitis, for specialized therapeutic measures, and also for the evaluation of the efficacy of treatment in reducing morbidity and mortality in this disease. Furthermore, there is a large number of other acute disease states in which the choice and relative efficacy of treatment remain highly controversial. It is possible that the techniques described in this report may be applied to such disease states and provide a basis for the early identification of subgroups of patients and the rational choice and evaluation of treatment. SUMMARY

AND CONCLUSIONS

Rational evaluation of the efficacy of treatment of acute pancreatitis requires objective measurement of the severity of disease. Univariate analyses of 13 early measurements in 300 patients with acute pancreatitis showed that the following 12 variables were associated with significantly increased risk of death or serious illness requiring more than seven days of intensive care treatment: at admission, age, blood sugar, white blood cell count, serum glutamic oxaloacetic transaminase, history of previous episodes, and serum lactic dehydrogenase, and, during the initial 48 hr, hematocrit fall, blood urea nitrogen change, lowest serum calcium, lowest arterial oxygen tension, highest base deficit, and estimated fluid sequestration. Simultaneous examination of sets of variables using multivariate linear discriminant analyses and multiple logistic regression analyses indicates that fewer variables are independently and additively associated with death or serious illness. Classification of patients with respect to risk by discriminant analysis and by the logistic model both yielded good results. The discriminant function approach using nine variables (at

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admission: age, blood sugar, serumglutamic oxaloacetic transaminase, number of previous episodes, and serum lactic dehydrogenase; during the initial 48 hr: hematocrit fall, lowest serum calcium, lowest arterial oxygen tension, and estimated fluid sequestration) led to the correct classification of 95.7% of the 117 patients included in this analysis. Grouping patients into deciles of estimated risk by the logistic function approach using the same nine variables resulted in a close correspondence of observed with expected deaths or serious illnesses in those deciles. The most predictive variable based on these analyses appears to be serum lactic dehydrogenase. Other variables of importance include serum glutamic oxaloacetic transaminase and blood sugar levels, when admission variables alone are considered simultaneously, and arterial oxygen tension, hematocrit decrease, and calcium, when the set of 48-hr variables are considered jointly. The interrelationship of the variables used must be borne in mind when interpreting these findings. Finally, although these analyses have shown that an accurate prediction of death or serious illness is possible using nine patient characteristics obtained at admission and within 48 hr after admission, further prospective studies on new patients presenting with acute pancreatitis are required to evaluate and refine current methods. REFERENCES 1. Armitage, P., and Gehan, E. A. Statistical methods for the identification and use of prognostic factors. Znt. J. Cancer 13: 16, 1974. 2. Armitage, P., McPherson, C. K., and Copas, J. C. Statistical studies of prognosis in advanced breast cancer. J. Chronic Dis 22: 343, 1969. 3. Gordon, T. Hazards in the use of the logistic function with special reference to data from prospective cardiovascular studies. J. Chronic Dis. 27: 97, 1974. 4. Gordon, T., and Kannel, W. B. Multiple contributors to coronary risk: Implications for screening and prevention. J. Chronic Dis. 25: 561, 1972. 5. Halperin, M., Blackwelder, W. C., and Verter,

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J. I. Estimation of the multivariate logistic risk function: A comparison of the discriminant function and maximum likelihood approaches. J. Chronic Dis. 24: 125, 1971. 6. Lawson, D. W., et a/. Surgical treatment of acute necrotizing pancreatitis.Ann. Surg. 172: 605, 1970. 7. Mikkelsen, 0. Pancreatitis acuta. Acta Chir. &and.

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II. Ranson, J. H. C., Rifkind, K. M., and Turner, J. W. Prognostic signs and non-operative peritoneal lavage in acute pancreatitis. Surg. Gynecol. Obstet.

143: 209, 1976.

12. Romero, C., et a/. Acute pancreatitis: A predictable disease. Surg. Forum 26: 446, 1975. 13. Rosato, E. F., Mullis, W. F., and Rosato, F. E. Peritoneal lavage therapy in hemorrhagic pancreatitis. Surge01 74: 106, 1973.

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14. Schmieden, V., and Sebening, W. Surgery of the pancreas. Surg. Gynecol. Obstrt. 46: 735, 1928. 15. Shoemaker, W. C., Elwyn, D. H., Levin, H., and Rosen, A. L. Use of nonparametric analysis of cardiorespiratory variables as early predictors of death and survival in postoperative patients.

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8. Morrison, D. G. Upper bounds for correlations between primary outcomes and probabilistic predictions. J. Amer. Sfat. Assoc. 67: 68, 1972. 9. Moynihan, B. Acute pancreatitis. Ann. Surg. 81: 132, 1925. 10. Ranson, J. H. C., ef al. Prognostic signs and the role of operative management in acute pancreatitis. Surg.

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16. The Coronary Drug Project Research Group. Factors influencing long-term prognosis after recovery from myocardial infarction. Three-year findings of the Coronary Drug Project. /. Chronic Dis. 27: 267, 1974.

17. Truett, J., Cornfield, J., and Kannel, W. A multivariate analysis of the risk of coronary heart disease in Framingham. J. Chronic Dis. 20: 51 I, 1967. 18. Walker, S. H., and Duncan, D. B. Estimation of the probability of an event as a function of several independent variables. Biometrika 54: 167, 1967. 19.

Waterman,N.C.,Walsky,R.,Kasdan,M.L.,and Abrams, B. L. The treatment of acute hemorrhagic pancreatitis by sump drainage. Sur,g. Gynecol.

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