- Email: [email protected]
Prospective use of the nitroblue tetrazolium dye test in febrile disorders
December, 1971 T h e ] o u r n a l o[ P E D I A T R I C S
943
Proq ective use of the nitroblue tetrazolium dye test in febrile disorders The reliability o[ the nitroblue tetrazolium dye test as an aid in the differential diagnosis o[ [ebrile disorders was evaluated in a prospective study of 168 febrile patients. A nomogram previously derived was used to predict correct patient classification and these results compared to classification on the basis of final diagnosis. The frequency o[ serious misclassification proved to be small. Similarity o[ present results to those of the retrospective study reported previously permitted pooling of the data and preparation of a revised nomogram. Equations which permit computation o[ specific probability of correct classification have been provided.
Ralph D. Feigin, M.D.,* Penelope G. Shackelford, M.D., and Sung C. Choi, Ph.D. ST. LOUI$~
MO.
T 1-I E w rI I T E blood cell count has been utilized frequently as an aid in the differential diagnosis of infectious diseases. Routine use of the total and differential white blood cell count has been, at best, a guide to correct diagnosis in some instances, of no value in others, and distinctly misleading in still others. A major step in differentiation of bacterial infection from those nonbacterial From the Department of Pediatrics and the Division o[ Biostatistics, Washington University School o[ Medicine, and the Division o[ In[ectious Diseases, St. Louis Children's Hospital. Supported in part by Public Health Service Training Grant No. AH00068-05. Presented in part at the American Academy o[ Pediatrics meeting, April 20, 1971, in St. Louis, Mo. Dr. Felgin is the recipient o[ United States PublicHealth Service Research Career Development Award No. lKO4AI46206 from the National Institute o] Allergy and InJeetious Diseases. *Reprint address: St. Louis Children's Hospital, 500 S. Kingshighway, St. Louis, Mo. 63110.
illnesses often confused with bacterial infection because of fever, leukocytosis, and other clinical symptoms has been made by Park and associates ~ using nitroblue tetrazolium (NBT) dye. The early observations of Park and associates1 have been confirmed and extended by Feigin and associates 2 in a carefully controlled but retrospective study which permitted the classification of all febrile patients into four groups solely on the basis of the per cent and absolute number of NBT-positive cells. A nomogram was developed to facilitate the classification of patients as follows: A = afebrile, control subjects; B = viral infection, partially but effectively treated bacterial infection, noninfectious fever; C = untreated bacterial infection; or D = ineffectively treated bacterial infection. Although the classification procedure was Vol. 79, No. 6, pp. 943-947
94 4
Feigin, ShackeI[ord, and Choi
shown to be efficient,~ the evaluation could be biased because of the retrospective nature of the analysis. Therefore, this study was undertaken to test the reliability of the NBT dye test on a prospective basis. MATERIAL
AND METHODS
Heparinized blood (1 to 2 ml.) was obtained from 168 febrile patients, between 3 months and 15 years of age, at time of admission to St. Louis Children's Hospital. Most of these patients were considered to be diagnostic problems in regard to the etiology of their fever. The NBT dye test was performed as reported by Park and associates ~ within 1 to 2 hours of the time blood was obtained. At the same time that blood was obtained for the NBT dye test, total white blood cell count and differential count were performed. The absolute number of neutrophils per cubic millimeter was calculated. The absolute number of NBT-positive neutrophils was determined from the absolute number of neutrophils and the percentage of NBT-positive cells. T h e values obtained for per cent and absolute number of NBT-positive ceils were used to classify the patients by nomogram into Groups A, B, C, or D. Placement of a patient into any group was made solely on the basis of the point of intersection of per cent and absolute number of NBT-positive cells on the nomogram, 2 a procedure which ignores the fact that the nomogram was constructed such that the probability of correct classification increases as the distance of the point from any dividing line on the nomogram increases. The patient's classification was recorded in the laboratory and reported to the physician caring for the patient. Following a detailed diagnostic evaluation, a definite diagnosis was made in 159 of the patients. Patients were classified (A, B, C, or D) on the basis of their final diagnosis and this classification was compared to the classification as determined by NBT nomogram. Statistical analysis of the data was perfonI~ed by the Division of Biostatistics, Washington University School of Medicine. The potential effect of total white blood cell
The Journal o[ Pediatrics December 1971
Table I. Results of prospective analysis of 159 individuals Group as determined by final diagnosis (No. o[ individuals) A (41) B (73) C (31) D (14)
Group as predicted by NBT test
AIBIClD 40 i9 1 0
0 46 2 0
t 7 28 0
0 1 0 14
count and temperature on percentage of NBT-positive cells was studied by computing the correlation coefficient between total white blood cell count and percentage of NBT-positive celts, and temperature and NBT-positive cells for individuals in each group. Before analysis, total white blood cell count and temperatures were transformed by taking logarithms, and the angular transformation was employed on the percentage of NBT-positive cells to satisfy the statistical assumptions. RESULTS Results of the prospective classification procedure utiIizing tile nomogram were compared with results determined by clinical and other laboratory criteria as shown in Table I. The frequency of serious misclassification is small. It is clear that the main difficulty with the procedure is with individuals classified as Group B on the basis of criteria other than NBT test; 37 per cent of these patients were misclassified by NBT test to Group A (normal). Since Group B patients include individuals with viral infections, noninfectious fevers, or patients with bacterial infection receiving effective therapy, a Group A rather than B classification would not be serious. No antibiotic therapy would be indicated for patients with viral or noninfectious fevers and no change in therapy would be indicated for patients receiving antibiotics. The classification of 7 of 73 patients who were Group B by other criteria to Group C (untreated bacterial infection) by NBT dye test would have resulted in initiation of antibiotic therapy unnecessarily in these individuals if the results of the NBT test were
Volume 79 Number 6
Prospective use of N B T test
945
~qO00
8,O0O
T
i!l:i
6,000
I:
~ 4,00C :,v: iiiliiil /!i!:f/
• '.
I |
m
20 40 60 80 PERCENT NBT POSITIVE CELLS Fig. 1. Nomogram derived from dlscriminant analysis of the data. Percentage of NBT-positive cells is plotted on the abscissa and the absolute number of NBT-positive cells on the ordinate. For any given patient, the point of intersection of the two values permits visual categorization of the patient into 1 of the 4 following groups: Group A (control subjects), Group B (viral
infection, noninfectious febrile illnesses, partially treated bacterial infections), Group C (untreated bacterial infections), or Group D (ineffectively treated bacterial infections). The dotted lines within each zone denote the boundaries for 70 per cent confidence limits. utilized without regard to the patient's history, physical examination, or other laboratory criteria. Similarity of results of this prospective study to those obtained in the retrospective study reported previously, 2 permitted development of a new, improved, and refined classification procedure based on 356 patients (total classified in prospective and retrospective studies). Starting with 8 variables depending on the per cent and absolute number of NBT-positive cells, an optimal classification rule was determined by discriminant analysis and is detailed in the appendix. A new nomogram based on the discriminant functions was prepared (Fig. 1). Zones which permit visual categorization of N B T results with greater than 70 per cent reliability have been defined. The efficiency of the classification procedure when this nomogram is utilized for the 356 patients is shown in
Table II. Efficiency of classification procedures applied to 356 individuals Group as determined by final diaenosis (No. o[ individuals) A (61) B (203)
C (67) D (25)
Group as predicted by N B T test
AIBIcI
'
47 44
13 1t9
1 37
0 3
2 0
8 0
51 6
6 19
Table II. Although use of the nomogram permits rapid categorization of the patient, results of the N B T test can be utilized to achieve greater precision of predictability as detailed in the addendum. The correlation coefficients between percentage of NBT-positive ceils and either total white blood cell count or body temperature were small and not significant at the 5 per cent level based on appropriate degrees of freedom.
9 4 6 Feigin, ShackeI[ord, and Choi
DISCUSSION
A nomogram was presented previously z to facilitate application of the NBT dye test prospectively. T h e prospective study reported above was designed to eliminate the bias inherent in any retrospective study. Results obtained coupled with the simplicity of the N B T dye test confirm previous suggestions concerning the usefulness of this procedure.i, 2, 4 The similarity of these results to those reported in the retrospective study 2 permitted pooling of the data from both studies and preparation of a more detailed and refined nomogram. Formulas permitting assessment of probability of correct group placement have been provided. I t is important to stress that substitution of the values for per cent and absolute number of NBT-positive cells in the equations or use of the nomogram imbues the results of the N B T test with no more reliability than that defined by the probability analysis. Use of the NBT dye test for the differentiation of patients with febrile disorders must be limited to patients whose cellular and humoraI immunologic systems are intact. Although this may preclude the use of this test in patients with sickle cell disease, this need not invariably be the case. In sickle cell disease and other immunologically similar situations, it may be possible to ascertain the difference between false negative results due to dysfunction of the phagocytic system and true-negative results due to absence of systemic infection by use of the endotoxin stimulated NBT test. ~ T h e N B T dye test cannot be utilized at present as an aid in the diagnosis of neonatal infections. Increased metabolic activity of
The ]ournaI o[ Pediatrics December 1971
the leukocytes of the normal newborn infant 6, 7 results in falsely positive NBT dye test values in comparison to normal standards 1, 2 for children 3 months to 15 years of age. This test may be the most reliable, rapid, single laboratory test for distinguishing individuals with bacterial infection from those with nonbacteriaI febrile illnesses. T h e NBT dye test does not obviate the necessity for a detailed history, careful physical examination, and other laboratory tests to confirm the diagnostic leads provided by the dye test and to define more specifically the etiology and site of infection. The authors express their appreciation to Mrs. Hilary Thirkill and Dr. Ronald Keeney for technical assistance. They also express their appreciation to Dr. Philip R. Dodge for his helpful suggestions and critical appraisal of the manuscript. REFERENCES
1. Park, B. H., Fikrig, S. M., and Smithwick, E. M.: Infection and nitroblue-tetrazolium reduction by neutrophils, Lancet 2: 532, 1968. 2. Feigln, R. D., Shackelford, P. G., Choi, S. C., Flake, K. K., Franklin, F. A. Jr., and E/senberg, C. S.: Nitroblue tetrazolium dye test as an aid in the differential diagnosis of febrile disorders, J. PEDIATR. 78: 230, 1971. 3. Anderson, T. W.: An introduction to multivariate statistical analysis, New York, 1957, John Wiley & Sons, Inc., pp. 126-153. 4. Park, B. H.: The use and limitations of the nitroblue tetrazolium test as a diagnostic aid, J. PEDIATR.78: 376, 1971. 5. Park, B. H., and Good, R. A.: NBT test stimulated, Lancet 2: 616, 1970. 6. Humbert, J. R., Kurtz, M. D., and Hathaway, W. E.: Increased reduction of nitroblue tetrazolium by neutrophils of newborn infants, Pediatrics 45: 125, 1970. 7. Park, B. H., Holmes, B., and Good, R. A.: Metabolic activities in leukocytes of newborn infants, J. PEDIATR.76: 237, 1970.
APPENDIX
The motivation is to construct a rule which tends to separate groups as much as possible. Four discriminant functions were obtained as follows: fa = -57.3 -0.72 (% NBT) -0.018 (Abs. NBT) +52.8 (loglo Abs. NBT) +0.00023 (% NBT X Abs. NBT) fB = -69.4-0.69 (% NBT) -0.018 (Abs. NBT) +57.2 (log10 Abs. NBT) +0.00022 (% NBT X Abs. NBT)
Volume 79 Number 6
Prospective use o/ N B T test
fc = -71.1 -0.54 (% NBT) -0.017 (Abs. NBT) +55.8 (log10 Abs. NBT) +0.00020 (% NBT X Abs. NBT) fD = -80.6 -0.51 (% NBT) -0.019 (Abs. NBT) +57.8 (log10 Abs. NBT) +0.00026 (% NBT X Abs. NBT) Precise predictability can be obtained by substituting the per cent and absolute number of NBT positive cells obtained for any patient into each of the four equations above. Four f values will be obtained. Each of these f values can be used to derive probability utilizing the following equations. The probability that an individual is a member of any group is given by the (P) values. h e
P (A) =
fA e
fB +
fc
e
+
fD
e
+
e
+
e
fB e
P (B) ----
f*
fB
e
+
fa
e
+
f.
e
fo e
P (C) =
fA e
fB +
fc
e
+
e
fD +
e
+
e
fi, e
P (D) :
f~ e
f~ +
e
fc +
e
fD
As an example, suppose that following performance of an NBT dye test, white blood cell count, and differential cell count, a patient is found to have 14 per cent NBT-positive cells with an absolute number of NBT-positive cells of 1,160. One computes: fA = 75.75, fB = 78.10, fc = 75.50 and fD = 70.13. The individual can be best classified as a member of the group represented by the largest f value (fB). The probability that he might belong to Group A rather than Groups B, C, or D is obtained as follows: 75.75 e
75.75
78.10 e
+
75.50
e
+
2,35 l+e
e
+
-0.25 +e
1
1 + 10.49 + 1.28 + 0.00
70.13 e
-5s +e ~ 8 per cent
Similarly, the probability that he belongs to Groups B, C, or D would be: B, 86 per cent; C, 6 per cent; and D, 0 per cent. Therefore, he can be classified in Group B with 86 per cent confidence on the basis of probability computations or with greater than 70 per cent confidence utilizing visual categorization by nomogram.
947
943
Proq ective use of the nitroblue tetrazolium dye test in febrile disorders The reliability o[ the nitroblue tetrazolium dye test as an aid in the differential diagnosis o[ [ebrile disorders was evaluated in a prospective study of 168 febrile patients. A nomogram previously derived was used to predict correct patient classification and these results compared to classification on the basis of final diagnosis. The frequency o[ serious misclassification proved to be small. Similarity o[ present results to those of the retrospective study reported previously permitted pooling of the data and preparation of a revised nomogram. Equations which permit computation o[ specific probability of correct classification have been provided.
Ralph D. Feigin, M.D.,* Penelope G. Shackelford, M.D., and Sung C. Choi, Ph.D. ST. LOUI$~
MO.
T 1-I E w rI I T E blood cell count has been utilized frequently as an aid in the differential diagnosis of infectious diseases. Routine use of the total and differential white blood cell count has been, at best, a guide to correct diagnosis in some instances, of no value in others, and distinctly misleading in still others. A major step in differentiation of bacterial infection from those nonbacterial From the Department of Pediatrics and the Division o[ Biostatistics, Washington University School o[ Medicine, and the Division o[ In[ectious Diseases, St. Louis Children's Hospital. Supported in part by Public Health Service Training Grant No. AH00068-05. Presented in part at the American Academy o[ Pediatrics meeting, April 20, 1971, in St. Louis, Mo. Dr. Felgin is the recipient o[ United States PublicHealth Service Research Career Development Award No. lKO4AI46206 from the National Institute o] Allergy and InJeetious Diseases. *Reprint address: St. Louis Children's Hospital, 500 S. Kingshighway, St. Louis, Mo. 63110.
illnesses often confused with bacterial infection because of fever, leukocytosis, and other clinical symptoms has been made by Park and associates ~ using nitroblue tetrazolium (NBT) dye. The early observations of Park and associates1 have been confirmed and extended by Feigin and associates 2 in a carefully controlled but retrospective study which permitted the classification of all febrile patients into four groups solely on the basis of the per cent and absolute number of NBT-positive cells. A nomogram was developed to facilitate the classification of patients as follows: A = afebrile, control subjects; B = viral infection, partially but effectively treated bacterial infection, noninfectious fever; C = untreated bacterial infection; or D = ineffectively treated bacterial infection. Although the classification procedure was Vol. 79, No. 6, pp. 943-947
94 4
Feigin, ShackeI[ord, and Choi
shown to be efficient,~ the evaluation could be biased because of the retrospective nature of the analysis. Therefore, this study was undertaken to test the reliability of the NBT dye test on a prospective basis. MATERIAL
AND METHODS
Heparinized blood (1 to 2 ml.) was obtained from 168 febrile patients, between 3 months and 15 years of age, at time of admission to St. Louis Children's Hospital. Most of these patients were considered to be diagnostic problems in regard to the etiology of their fever. The NBT dye test was performed as reported by Park and associates ~ within 1 to 2 hours of the time blood was obtained. At the same time that blood was obtained for the NBT dye test, total white blood cell count and differential count were performed. The absolute number of neutrophils per cubic millimeter was calculated. The absolute number of NBT-positive neutrophils was determined from the absolute number of neutrophils and the percentage of NBT-positive cells. T h e values obtained for per cent and absolute number of NBT-positive ceils were used to classify the patients by nomogram into Groups A, B, C, or D. Placement of a patient into any group was made solely on the basis of the point of intersection of per cent and absolute number of NBT-positive cells on the nomogram, 2 a procedure which ignores the fact that the nomogram was constructed such that the probability of correct classification increases as the distance of the point from any dividing line on the nomogram increases. The patient's classification was recorded in the laboratory and reported to the physician caring for the patient. Following a detailed diagnostic evaluation, a definite diagnosis was made in 159 of the patients. Patients were classified (A, B, C, or D) on the basis of their final diagnosis and this classification was compared to the classification as determined by NBT nomogram. Statistical analysis of the data was perfonI~ed by the Division of Biostatistics, Washington University School of Medicine. The potential effect of total white blood cell
The Journal o[ Pediatrics December 1971
Table I. Results of prospective analysis of 159 individuals Group as determined by final diagnosis (No. o[ individuals) A (41) B (73) C (31) D (14)
Group as predicted by NBT test
AIBIClD 40 i9 1 0
0 46 2 0
t 7 28 0
0 1 0 14
count and temperature on percentage of NBT-positive cells was studied by computing the correlation coefficient between total white blood cell count and percentage of NBT-positive celts, and temperature and NBT-positive cells for individuals in each group. Before analysis, total white blood cell count and temperatures were transformed by taking logarithms, and the angular transformation was employed on the percentage of NBT-positive cells to satisfy the statistical assumptions. RESULTS Results of the prospective classification procedure utiIizing tile nomogram were compared with results determined by clinical and other laboratory criteria as shown in Table I. The frequency of serious misclassification is small. It is clear that the main difficulty with the procedure is with individuals classified as Group B on the basis of criteria other than NBT test; 37 per cent of these patients were misclassified by NBT test to Group A (normal). Since Group B patients include individuals with viral infections, noninfectious fevers, or patients with bacterial infection receiving effective therapy, a Group A rather than B classification would not be serious. No antibiotic therapy would be indicated for patients with viral or noninfectious fevers and no change in therapy would be indicated for patients receiving antibiotics. The classification of 7 of 73 patients who were Group B by other criteria to Group C (untreated bacterial infection) by NBT dye test would have resulted in initiation of antibiotic therapy unnecessarily in these individuals if the results of the NBT test were
Volume 79 Number 6
Prospective use of N B T test
945
~qO00
8,O0O
T
i!l:i
6,000
I:
~ 4,00C :,v: iiiliiil /!i!:f/
• '.
I |
m
20 40 60 80 PERCENT NBT POSITIVE CELLS Fig. 1. Nomogram derived from dlscriminant analysis of the data. Percentage of NBT-positive cells is plotted on the abscissa and the absolute number of NBT-positive cells on the ordinate. For any given patient, the point of intersection of the two values permits visual categorization of the patient into 1 of the 4 following groups: Group A (control subjects), Group B (viral
infection, noninfectious febrile illnesses, partially treated bacterial infections), Group C (untreated bacterial infections), or Group D (ineffectively treated bacterial infections). The dotted lines within each zone denote the boundaries for 70 per cent confidence limits. utilized without regard to the patient's history, physical examination, or other laboratory criteria. Similarity of results of this prospective study to those obtained in the retrospective study reported previously, 2 permitted development of a new, improved, and refined classification procedure based on 356 patients (total classified in prospective and retrospective studies). Starting with 8 variables depending on the per cent and absolute number of NBT-positive cells, an optimal classification rule was determined by discriminant analysis and is detailed in the appendix. A new nomogram based on the discriminant functions was prepared (Fig. 1). Zones which permit visual categorization of N B T results with greater than 70 per cent reliability have been defined. The efficiency of the classification procedure when this nomogram is utilized for the 356 patients is shown in
Table II. Efficiency of classification procedures applied to 356 individuals Group as determined by final diaenosis (No. o[ individuals) A (61) B (203)
C (67) D (25)
Group as predicted by N B T test
AIBIcI
'
47 44
13 1t9
1 37
0 3
2 0
8 0
51 6
6 19
Table II. Although use of the nomogram permits rapid categorization of the patient, results of the N B T test can be utilized to achieve greater precision of predictability as detailed in the addendum. The correlation coefficients between percentage of NBT-positive ceils and either total white blood cell count or body temperature were small and not significant at the 5 per cent level based on appropriate degrees of freedom.
9 4 6 Feigin, ShackeI[ord, and Choi
DISCUSSION
A nomogram was presented previously z to facilitate application of the NBT dye test prospectively. T h e prospective study reported above was designed to eliminate the bias inherent in any retrospective study. Results obtained coupled with the simplicity of the N B T dye test confirm previous suggestions concerning the usefulness of this procedure.i, 2, 4 The similarity of these results to those reported in the retrospective study 2 permitted pooling of the data from both studies and preparation of a more detailed and refined nomogram. Formulas permitting assessment of probability of correct group placement have been provided. I t is important to stress that substitution of the values for per cent and absolute number of NBT-positive cells in the equations or use of the nomogram imbues the results of the N B T test with no more reliability than that defined by the probability analysis. Use of the NBT dye test for the differentiation of patients with febrile disorders must be limited to patients whose cellular and humoraI immunologic systems are intact. Although this may preclude the use of this test in patients with sickle cell disease, this need not invariably be the case. In sickle cell disease and other immunologically similar situations, it may be possible to ascertain the difference between false negative results due to dysfunction of the phagocytic system and true-negative results due to absence of systemic infection by use of the endotoxin stimulated NBT test. ~ T h e N B T dye test cannot be utilized at present as an aid in the diagnosis of neonatal infections. Increased metabolic activity of
The ]ournaI o[ Pediatrics December 1971
the leukocytes of the normal newborn infant 6, 7 results in falsely positive NBT dye test values in comparison to normal standards 1, 2 for children 3 months to 15 years of age. This test may be the most reliable, rapid, single laboratory test for distinguishing individuals with bacterial infection from those with nonbacteriaI febrile illnesses. T h e NBT dye test does not obviate the necessity for a detailed history, careful physical examination, and other laboratory tests to confirm the diagnostic leads provided by the dye test and to define more specifically the etiology and site of infection. The authors express their appreciation to Mrs. Hilary Thirkill and Dr. Ronald Keeney for technical assistance. They also express their appreciation to Dr. Philip R. Dodge for his helpful suggestions and critical appraisal of the manuscript. REFERENCES
1. Park, B. H., Fikrig, S. M., and Smithwick, E. M.: Infection and nitroblue-tetrazolium reduction by neutrophils, Lancet 2: 532, 1968. 2. Feigln, R. D., Shackelford, P. G., Choi, S. C., Flake, K. K., Franklin, F. A. Jr., and E/senberg, C. S.: Nitroblue tetrazolium dye test as an aid in the differential diagnosis of febrile disorders, J. PEDIATR. 78: 230, 1971. 3. Anderson, T. W.: An introduction to multivariate statistical analysis, New York, 1957, John Wiley & Sons, Inc., pp. 126-153. 4. Park, B. H.: The use and limitations of the nitroblue tetrazolium test as a diagnostic aid, J. PEDIATR.78: 376, 1971. 5. Park, B. H., and Good, R. A.: NBT test stimulated, Lancet 2: 616, 1970. 6. Humbert, J. R., Kurtz, M. D., and Hathaway, W. E.: Increased reduction of nitroblue tetrazolium by neutrophils of newborn infants, Pediatrics 45: 125, 1970. 7. Park, B. H., Holmes, B., and Good, R. A.: Metabolic activities in leukocytes of newborn infants, J. PEDIATR.76: 237, 1970.
APPENDIX
The motivation is to construct a rule which tends to separate groups as much as possible. Four discriminant functions were obtained as follows: fa = -57.3 -0.72 (% NBT) -0.018 (Abs. NBT) +52.8 (loglo Abs. NBT) +0.00023 (% NBT X Abs. NBT) fB = -69.4-0.69 (% NBT) -0.018 (Abs. NBT) +57.2 (log10 Abs. NBT) +0.00022 (% NBT X Abs. NBT)
Volume 79 Number 6
Prospective use o/ N B T test
fc = -71.1 -0.54 (% NBT) -0.017 (Abs. NBT) +55.8 (log10 Abs. NBT) +0.00020 (% NBT X Abs. NBT) fD = -80.6 -0.51 (% NBT) -0.019 (Abs. NBT) +57.8 (log10 Abs. NBT) +0.00026 (% NBT X Abs. NBT) Precise predictability can be obtained by substituting the per cent and absolute number of NBT positive cells obtained for any patient into each of the four equations above. Four f values will be obtained. Each of these f values can be used to derive probability utilizing the following equations. The probability that an individual is a member of any group is given by the (P) values. h e
P (A) =
fA e
fB +
fc
e
+
fD
e
+
e
+
e
fB e
P (B) ----
f*
fB
e
+
fa
e
+
f.
e
fo e
P (C) =
fA e
fB +
fc
e
+
e
fD +
e
+
e
fi, e
P (D) :
f~ e
f~ +
e
fc +
e
fD
As an example, suppose that following performance of an NBT dye test, white blood cell count, and differential cell count, a patient is found to have 14 per cent NBT-positive cells with an absolute number of NBT-positive cells of 1,160. One computes: fA = 75.75, fB = 78.10, fc = 75.50 and fD = 70.13. The individual can be best classified as a member of the group represented by the largest f value (fB). The probability that he might belong to Group A rather than Groups B, C, or D is obtained as follows: 75.75 e
75.75
78.10 e
+
75.50
e
+
2,35 l+e
e
+
-0.25 +e
1
1 + 10.49 + 1.28 + 0.00
70.13 e
-5s +e ~ 8 per cent
Similarly, the probability that he belongs to Groups B, C, or D would be: B, 86 per cent; C, 6 per cent; and D, 0 per cent. Therefore, he can be classified in Group B with 86 per cent confidence on the basis of probability computations or with greater than 70 per cent confidence utilizing visual categorization by nomogram.
947