Vox Sang. 31: 81-95 (1976)
Influence of Counting Statistics on Borderline Detection of Hepatitis B Antigen by a Solid-Phase Radioimmunoassay A. L.WAGNER, J. M. LEMAIRE and D. R.RICHARD Centre de Transfusion sanguine, Laboratoire des RadioClCments, Montpellier
Abstract. The detection of hepatitis B antigen by a solid-phase radioimmunoassay technique is by now well established, particularly where transfusions are concerned. However, it would appear that the use of systematic procedures leading to positive detection, such as the ‘cutoff‘ method (mean counts per minute of the negative controls multiplied by a coefficient of 2.1), are open to criticism if elementary precautions concerning the time span and the statistical accuracy of radioactivity counting are not taken. The method may even prove inaccurate in a certain number of borderline cases studied in relation to plasma and different sera, especially if subjected to a single screening process over a large number of samples analyzed by computer. These deficiencies can be avoided by correcting the positive coefficient in relation to the mean counts per minute of negative controls, the statistical accuracy (relative standard deviation) and the distribution of counting times.
Zntroduction The detection of hepatitis B antigen in serum by a solid-phase radioimmunoassay technique is by now well established [l, 3, 41. The purpose of this study is not to review any point of the procedure outlined further on, but to examine the influence of counting statistics on the criteria leading to positive detection. According to the prescriptions of the commercially available kit (Ausria 11, 125 Abbott Laboratories), the presence or absence of hepatitis B antigen is determined by comparing the net radioactivity (counts per minute; cpm) of unknown samples to a calculated ‘cutoff value’, which
Received: August 11, 1975; accepted: October 22, 1975.
88
WAGNER/LEMAIRE/RICHARD
results from the product of the net cpm mean of negative controls and a coefficient of 2.1. Only unknown samples whose net cpm are higher than the ‘cutoff value’ are to be considered positive with respect to hepatitis B antigen. The coefficient 2.1 has been determined by statistical analysis including a comparison with the variance and with the biologic distribution in a typically normal population; it represents a factor of 7 standard deviations from the mean cpm of negative controls [4]. However, the systematic application of this coefficient without taking into account the statistical accuracy of radioactivity counting would appear to be somewhat more open to criticism, particularly in screening blood donor populations or plasma pools in cases of borderline or doubtful detection of hepatitis B antigen. This paper reports a simple procedure approaching the general problem of the background, and one which permits a correction of criteria for positive detection by taking into account the mean error associated with radioactivity counting.
Method The principle of the test can be summarized as follows: unknown serum is added to plastic beads coated with guinea pig antibody, so that any hepatitis B antigen from the serum is fixed to the antibody. The serum is then aspirated and the beads rinsed twice with distilled water. When human hepatitis B antibody tagged with iodine-125 is added, it binds to any antigen on the bead, creating an antibody-antigen-antibody ‘sandwich‘. Within certain limits, the greater the amount of antigen in the serum, the higher is the final count rate. In random donnor populations, this test identifies approximately 0.41% of the specimens as positive with respect to hepatitis B antigen; the result for a similar population living in the south of France is 0.5% [2]. The commercial kit provides 7 negative controls which should be assayed with each run of unknown sera, with the same process and incubation time. The determination of criteria for positive detection involves the following two steps: Calculation of the cpm mean of negative controls. Three parameters are to be considered: counting time: tn (n =negative) net cpm (background substracted): Cn standard deviation: Sn =
1/Cn/tn
Individual values of the negative controls must fall inside the range 0.5-1.5 times the mean cpm; any value falling outside is discarded as aberrant (and a new mean cpm of negative controls is calculated).
Radioimmunoassay of Hepatitis B Antigen
89
Calculation of the positive threshold. The lower level of positive detection (or positive threshold) is obtained by multiplying the mean cpm (C,) of negative controls by the coefficient 2.1. This operation means that any control or serum should have a number of cpm equal to or higher than this 'cutoff value' to be considered as positive. We shall assign to any sample of this kind the following three parameters:
counting time: tp (p = positive) net cpm (threshold): Cp s C, x 2.1 standard deviation: S , = From a statistical point of view, the problem associated with radioactivity counting can be formulated as follows: given a total time t to count two known samples,
one negative and one at the positive threshold, how should tn and tp be distributed to obtain the lowest error on the difference: C, = CD- Cn, which means the minimum of its standard deviation: Se = Cn/tn + Cp/tp? To solve the problem, S , may be squared, the derivative arrived at and zeroed: (SeZ) reaches its minimum.
1/
Cn CP sea = +tn
tp
+ +
Now: tn tp = t = constant Then: dtp dtn = dt = 0, and: dtn = - dtp If we replace in formula (2) dtn by its value:
The condition for dSe = 0 is:
Cn
Cp
tna
tp'
-- - = 0
.= or: tpa - cp and ' tn' Cn tn The optimal distribution for tn and t, is thus:
t
90 and, if we establish: t tn = l + r
vz~
-= r
t.r tp = -
l+r
It should be observed that, in considering the positive threshold, the distribution
of tn and tp is only dependent on the value of r = VCp/Cn, which is none other than the square root of the coefficient 2.1 established from initial data. Replacing r by its value, we obtain the optimal distribution: tn = 0.408 x t and tp = 0.592 x t
(3)
At this optimum, the standard deviation Se may be expressed in terms of relative standard deviation: E = S,/C,, which results in:
E2=-.-
1
C,. t $2.ce.t=--
(r
+ 1)
(r - 1)
r + l r-1
a n d s i n c e : C e = Cn x 1.1: * Cn * t = 4.957
(4)
Within the limits of the standard error, the relative standard deviation E (%) describes the statistical accuracy of positive threshold determination with respect to the physical characters of radioactivity counting.
Results Some numerical examples will demonstrate the variations of E with different values of the mean cpm of the negative controls and various distributions of the counting times. Example 1 Cn = 200 cpm t = 20 min According to formula (3): tn = 8.16 min and tp = 11.54rnin.
From initial data: CP = Cn x 2.1 = 200 x 2.1 = 420 cpm Ce = Cp - Cn= 420 - 200 = 220 cpm
Radioimmunoassay of Hepatitis B Antigen
91
According to formula (4) the calculations give: &a=----
4.957
-
Cn-t E =
4.957
- 0,00124
200x20
1/ 0.00124 = 0.035 and
Se = &
*
Ce = 0.035 x 220 = 7.74 cpm
Within the limits of the 5% error (C, k 2 S,), the reliability limits for C , and the relative deviation (2 E ) are:
Cek 2 S ,
= 220 & 15.5 cpm
or (204.5-235.5 cpm)
2 E = 0.035 x 2 = 0.07 (7%)
Conclusion: for any sample positive at the lower level (420 cpm) and within the limits of the 5% error, there is a 95% chance that C, will fall inside the limits 204.5-235.5 cpm with a mean value of 220 cpm. One major consequence is that the threshold for positive samples (C,) must logically be lowered from 420 to (200 + 204.5) = 404.5 cpm, and the coefficient 2.1 corrected to 404.5/200 = 2.02. It should be noted that the usual procedure leads to considering as negative or doubtful any value below 420 cpm, though all values between 404.5 and 420 cpm are truly ‘statistically’positive (and all the more so between 420 and 435.5 cpm). On the other hand, it can be seen that the positive coefficient 2.02 and the positive threshold 404.5 cpm are very close to the theorical values, largely because of the long counting time and good distribution of t, and tp, which results in the low relative deviation of 7%. An equal distribution of 10 min for t, and t, does not greatly affect the statistical outcome and can be retained for practical purposes in cases where a small number of samples are to be counted or where there is a sufficiently prolonged period of time for counting. Example 2
Cn = 200 cprn t = 2 mn (with tn = 0.82 mn and tp = 1.18 mn or in practice: tn = tD = 1 mn) The same calculations as above give: 4.957
Ea=--
- 0.0124
200 x 2 &
=
y
m = 0.111 cpm = 220 f 49 cpm or (171-269 cpm)
S e = 0.111 x 220 = 24.5
Ce f 2 S e
2 & = 0.111 x 2 = 0.222 (22.2%)
WAGNER/LEMAIRE/RICHARD
92
Conclusion: within the limits of the 5% error, the short duration of counting means that C, will fall inside more extensive limits (171269 cpm) as compared to example 1. The positive threshold must be lowered to (200 + 171) = 371 cpm and the positive coefficient to 371/ 200 = 1.86. The relative deviation of 22.2% illustrates the poor conditions of radioactivity counting. In comparison with example 1, and additional range between 171 and 204.5 cpm must be considered as positive, at the risk of mixing true negative with ‘statistically’ positive samples, which appears more advisable than the contrary situation. Example 3
C, = 200 cpm t=4mn
In this example, we show the way we have chosen to associate counting times as short as possible, consistent with an acceptable accuracy: t, is adjusted to 1 min by an automatic rejection of samples below 300 cpm, and t, to 3 min by a preset time which only works for samples over 300 cpm (with a preset count of 3,000 cpm). In this case, the preceding calculations are not strictly valid since t, and t, are unlike the optimal distribution (from formula 3), but the approximation may be thought to be acceptable: 4.957
&2=--
- 0.0062
200 x 4
v
= 0.0062 = 0.079 Se = 0.079 x 220 = 17.3 cpm
E
C e f 2 Se = 220 f 34.6 cpm or (185.4-254.6 cpm) 2 E = 0.079 x 2 = 0.157 (15.7%)
Within the limits of the 5% error, the positive threshold must be lowered to (200 + 185.4) = 385.4 cpm and the positive coefficient corrected to 385.4/200 = 1.93; the relative deviation of 15.7% appears accurate. Note: the level of the mean cpm of negative controls plays a role in the value of the relative standard deviation E and the corrections to be applied to criteria for positive detection. For example, if C, = 100 cpm, t, and t, are adjusted as in example 1, the positive coefficient is: 1.99 and the 5% error relative deviation (2 F): 10%. The same results for C, = 300 cpm are: 2.04 and 5.7%.
Radioimmunoassay of Hepatitis B Antigen
93
Table 1. Comparison of positive results obtained in the detection of hepatitis B antigen by normal and corrected radioimmunoassay (counting characteristics were usually those of example 3) Source
Tested
Positive results normal method
corrected method total
Donors pools
Mean coefficients of positive resultsB recovered
statistically positive
recovered' n
%
7,082
144
151
7
4.64
1.896
1.758
13,117
92
101
9
8.91
1.893
1.807
3,699
199
204
5
2.45
1.886
1.778
(10 sera)
Plasma pools (10 units) Individual patients
Number of positive sera recovered with the corrected p r d u r e and considered negative with the normal procedure and corresponding percent of total positive. a Mean coefficient given by the first screening (recovered) and corresponding statistically positive mean coefficient.
Comments Comparative results for detection of hepatitis B antigen over a normal blood donor population, over plasma pools and over a series of patients are given in table I. The donor sera were put in groups of 10 and a single screening sample taken. Every positive result was checked the next day using a duplicate sample. If the initial result was confirmed, the sera making up each positive pool were individually tested. Finally, a usual neutralization technique was used to determine the specificity of each positive reaction to the hepatitis B antigen. It should be noted that the statistical correction of the coefficient 2.1 allowed 7 donors who were carriers of hepatitis B
94
WAGNERLEMAIRWRICHARD
antigen and who, from the initial testing, were theoretically negative to be detected. A parallel study to the one on blood donors was carried out on 2 liters plasma pools made up of 10 units of plasma. All these units had first been tested by counterelectrophoresis and found to be negative. As in the preceding case, a test was made on a single screening sample and followed up in the case of a positive result by a duplicate confirmation test then a neutralization test. The number of positive pools thus detected was particularly high (9 out of 101 positive pools or 8.9%). More interesting still are the results obtained with patients who were individually tested as possible carriers of hepatitis B antigen. The possible objection to the dilution of antigen because of the way the pools are made up, is not valid in this case. The same followup method was used as for the plasma pools. As can be seen from table I, 5 positive sera which would have been considered negative using normal procedures, were identified on initial testing. Moreover, 3 sera which were identified as positive under the same test conditions were not confirmed by the neutralization test. To date no satisfactory explanation has been found for this phenomenon. These results show the dangers associated with too rigorous an application of the 'cutoff' method, at least in borderline cases and without bearing in mind the statistical accuracy of radioactivity counting. These dangers become particularly marked when, as was the case for this study, a rigorous computer method is used to obtain optimal results. On the other hand, such a method is extremely useful when elementary precautions are taken with regard to counting times and associated statistics. Thus, formulae 3 and 4 allow for consistent statistical accuracy (or relative standard deviation) in testing and for counting times being established in relation to the mean cpm of negative controls. Naturally, the greater the accuracy required, the longer the necessary counting times. It will also be noted from table I that the mean coefficients obtained from the different positive samples identified through our corrective method are remarkably similar. This poses the problem of determining the positive threshold on the basis of a coefficient of 2.1, i.e. as we have seen, 7 standard deviations from the mean cpm of negative controls. It would seen preferable, especially when a single screening method without correction of the positive coefficient is used, and all the more if the counting times are short, to reduce the 'cutoff' value to 6 standard deviations or a coefficient of 1.8 relative to the mean value of the negative controls.
Radioimmunoassay of Hepatitis B Antigen
95
Acknowledgements The authors wish to express their appreciation to Dr. L. R. OVERBY,Abbott Laboratories, North-Chicago, 111.) for helpful discussions concerning the methodology used in this study, and to Prof. W. A. OLIVER, University of Toronto, for reviewing the manuscript.
References 1 GINSBERG,A. L.; CONRAD,M. E.;BANCROFT,W. H.; LING,C. M., and OVERBY, L. R.: Antibody to Australia antigen: detection with a simple radioimmune assay, incidence on military populations, and role in the prevention of hepatitis B with gamma-globulin. J. Lab. clin. Med. 82: 317-325 (1973). 2 LEMAIRE,J. M. and CAZAL, P.: Personal commun. (1975). 3 LING, C. M. and OVERBY,L. R.: Prevalence of hepatitis B virus antigen as revealed by direct radioimmunoassay with 1W-antibody. J. Immun. 109: 834841 (1972). 4 OVERBY,L. R.; MILLER, J. P.; SMITH, I. D.; DECKER,R. H., and LING, C. M.: Radioimmunoassay of hepatitis B virus-associated (Australia) antigen employing IzKI-antibody. Vox Sang. 24: suppl., pp. 102-113 (1973).
Dr. A. WAGNER,Centre de Transfusion Sanguine, Laboratoire des RadioClCments, BP 1213, F-34000 Montpellier (France)
Influence of Counting Statistics on Borderline Detection of Hepatitis B Antigen by a Solid-Phase Radioimmunoassay A. L.WAGNER, J. M. LEMAIRE and D. R.RICHARD Centre de Transfusion sanguine, Laboratoire des RadioClCments, Montpellier
Abstract. The detection of hepatitis B antigen by a solid-phase radioimmunoassay technique is by now well established, particularly where transfusions are concerned. However, it would appear that the use of systematic procedures leading to positive detection, such as the ‘cutoff‘ method (mean counts per minute of the negative controls multiplied by a coefficient of 2.1), are open to criticism if elementary precautions concerning the time span and the statistical accuracy of radioactivity counting are not taken. The method may even prove inaccurate in a certain number of borderline cases studied in relation to plasma and different sera, especially if subjected to a single screening process over a large number of samples analyzed by computer. These deficiencies can be avoided by correcting the positive coefficient in relation to the mean counts per minute of negative controls, the statistical accuracy (relative standard deviation) and the distribution of counting times.
Zntroduction The detection of hepatitis B antigen in serum by a solid-phase radioimmunoassay technique is by now well established [l, 3, 41. The purpose of this study is not to review any point of the procedure outlined further on, but to examine the influence of counting statistics on the criteria leading to positive detection. According to the prescriptions of the commercially available kit (Ausria 11, 125 Abbott Laboratories), the presence or absence of hepatitis B antigen is determined by comparing the net radioactivity (counts per minute; cpm) of unknown samples to a calculated ‘cutoff value’, which
Received: August 11, 1975; accepted: October 22, 1975.
88
WAGNER/LEMAIRE/RICHARD
results from the product of the net cpm mean of negative controls and a coefficient of 2.1. Only unknown samples whose net cpm are higher than the ‘cutoff value’ are to be considered positive with respect to hepatitis B antigen. The coefficient 2.1 has been determined by statistical analysis including a comparison with the variance and with the biologic distribution in a typically normal population; it represents a factor of 7 standard deviations from the mean cpm of negative controls [4]. However, the systematic application of this coefficient without taking into account the statistical accuracy of radioactivity counting would appear to be somewhat more open to criticism, particularly in screening blood donor populations or plasma pools in cases of borderline or doubtful detection of hepatitis B antigen. This paper reports a simple procedure approaching the general problem of the background, and one which permits a correction of criteria for positive detection by taking into account the mean error associated with radioactivity counting.
Method The principle of the test can be summarized as follows: unknown serum is added to plastic beads coated with guinea pig antibody, so that any hepatitis B antigen from the serum is fixed to the antibody. The serum is then aspirated and the beads rinsed twice with distilled water. When human hepatitis B antibody tagged with iodine-125 is added, it binds to any antigen on the bead, creating an antibody-antigen-antibody ‘sandwich‘. Within certain limits, the greater the amount of antigen in the serum, the higher is the final count rate. In random donnor populations, this test identifies approximately 0.41% of the specimens as positive with respect to hepatitis B antigen; the result for a similar population living in the south of France is 0.5% [2]. The commercial kit provides 7 negative controls which should be assayed with each run of unknown sera, with the same process and incubation time. The determination of criteria for positive detection involves the following two steps: Calculation of the cpm mean of negative controls. Three parameters are to be considered: counting time: tn (n =negative) net cpm (background substracted): Cn standard deviation: Sn =
1/Cn/tn
Individual values of the negative controls must fall inside the range 0.5-1.5 times the mean cpm; any value falling outside is discarded as aberrant (and a new mean cpm of negative controls is calculated).
Radioimmunoassay of Hepatitis B Antigen
89
Calculation of the positive threshold. The lower level of positive detection (or positive threshold) is obtained by multiplying the mean cpm (C,) of negative controls by the coefficient 2.1. This operation means that any control or serum should have a number of cpm equal to or higher than this 'cutoff value' to be considered as positive. We shall assign to any sample of this kind the following three parameters:
counting time: tp (p = positive) net cpm (threshold): Cp s C, x 2.1 standard deviation: S , = From a statistical point of view, the problem associated with radioactivity counting can be formulated as follows: given a total time t to count two known samples,
one negative and one at the positive threshold, how should tn and tp be distributed to obtain the lowest error on the difference: C, = CD- Cn, which means the minimum of its standard deviation: Se = Cn/tn + Cp/tp? To solve the problem, S , may be squared, the derivative arrived at and zeroed: (SeZ) reaches its minimum.
1/
Cn CP sea = +tn
tp
+ +
Now: tn tp = t = constant Then: dtp dtn = dt = 0, and: dtn = - dtp If we replace in formula (2) dtn by its value:
The condition for dSe = 0 is:
Cn
Cp
tna
tp'
-- - = 0
.= or: tpa - cp and ' tn' Cn tn The optimal distribution for tn and t, is thus:
t
90 and, if we establish: t tn = l + r
vz~
-= r
t.r tp = -
l+r
It should be observed that, in considering the positive threshold, the distribution
of tn and tp is only dependent on the value of r = VCp/Cn, which is none other than the square root of the coefficient 2.1 established from initial data. Replacing r by its value, we obtain the optimal distribution: tn = 0.408 x t and tp = 0.592 x t
(3)
At this optimum, the standard deviation Se may be expressed in terms of relative standard deviation: E = S,/C,, which results in:
E2=-.-
1
C,. t $2.ce.t=--
(r
+ 1)
(r - 1)
r + l r-1
a n d s i n c e : C e = Cn x 1.1: * Cn * t = 4.957
(4)
Within the limits of the standard error, the relative standard deviation E (%) describes the statistical accuracy of positive threshold determination with respect to the physical characters of radioactivity counting.
Results Some numerical examples will demonstrate the variations of E with different values of the mean cpm of the negative controls and various distributions of the counting times. Example 1 Cn = 200 cpm t = 20 min According to formula (3): tn = 8.16 min and tp = 11.54rnin.
From initial data: CP = Cn x 2.1 = 200 x 2.1 = 420 cpm Ce = Cp - Cn= 420 - 200 = 220 cpm
Radioimmunoassay of Hepatitis B Antigen
91
According to formula (4) the calculations give: &a=----
4.957
-
Cn-t E =
4.957
- 0,00124
200x20
1/ 0.00124 = 0.035 and
Se = &
*
Ce = 0.035 x 220 = 7.74 cpm
Within the limits of the 5% error (C, k 2 S,), the reliability limits for C , and the relative deviation (2 E ) are:
Cek 2 S ,
= 220 & 15.5 cpm
or (204.5-235.5 cpm)
2 E = 0.035 x 2 = 0.07 (7%)
Conclusion: for any sample positive at the lower level (420 cpm) and within the limits of the 5% error, there is a 95% chance that C, will fall inside the limits 204.5-235.5 cpm with a mean value of 220 cpm. One major consequence is that the threshold for positive samples (C,) must logically be lowered from 420 to (200 + 204.5) = 404.5 cpm, and the coefficient 2.1 corrected to 404.5/200 = 2.02. It should be noted that the usual procedure leads to considering as negative or doubtful any value below 420 cpm, though all values between 404.5 and 420 cpm are truly ‘statistically’positive (and all the more so between 420 and 435.5 cpm). On the other hand, it can be seen that the positive coefficient 2.02 and the positive threshold 404.5 cpm are very close to the theorical values, largely because of the long counting time and good distribution of t, and tp, which results in the low relative deviation of 7%. An equal distribution of 10 min for t, and t, does not greatly affect the statistical outcome and can be retained for practical purposes in cases where a small number of samples are to be counted or where there is a sufficiently prolonged period of time for counting. Example 2
Cn = 200 cprn t = 2 mn (with tn = 0.82 mn and tp = 1.18 mn or in practice: tn = tD = 1 mn) The same calculations as above give: 4.957
Ea=--
- 0.0124
200 x 2 &
=
y
m = 0.111 cpm = 220 f 49 cpm or (171-269 cpm)
S e = 0.111 x 220 = 24.5
Ce f 2 S e
2 & = 0.111 x 2 = 0.222 (22.2%)
WAGNER/LEMAIRE/RICHARD
92
Conclusion: within the limits of the 5% error, the short duration of counting means that C, will fall inside more extensive limits (171269 cpm) as compared to example 1. The positive threshold must be lowered to (200 + 171) = 371 cpm and the positive coefficient to 371/ 200 = 1.86. The relative deviation of 22.2% illustrates the poor conditions of radioactivity counting. In comparison with example 1, and additional range between 171 and 204.5 cpm must be considered as positive, at the risk of mixing true negative with ‘statistically’ positive samples, which appears more advisable than the contrary situation. Example 3
C, = 200 cpm t=4mn
In this example, we show the way we have chosen to associate counting times as short as possible, consistent with an acceptable accuracy: t, is adjusted to 1 min by an automatic rejection of samples below 300 cpm, and t, to 3 min by a preset time which only works for samples over 300 cpm (with a preset count of 3,000 cpm). In this case, the preceding calculations are not strictly valid since t, and t, are unlike the optimal distribution (from formula 3), but the approximation may be thought to be acceptable: 4.957
&2=--
- 0.0062
200 x 4
v
= 0.0062 = 0.079 Se = 0.079 x 220 = 17.3 cpm
E
C e f 2 Se = 220 f 34.6 cpm or (185.4-254.6 cpm) 2 E = 0.079 x 2 = 0.157 (15.7%)
Within the limits of the 5% error, the positive threshold must be lowered to (200 + 185.4) = 385.4 cpm and the positive coefficient corrected to 385.4/200 = 1.93; the relative deviation of 15.7% appears accurate. Note: the level of the mean cpm of negative controls plays a role in the value of the relative standard deviation E and the corrections to be applied to criteria for positive detection. For example, if C, = 100 cpm, t, and t, are adjusted as in example 1, the positive coefficient is: 1.99 and the 5% error relative deviation (2 F): 10%. The same results for C, = 300 cpm are: 2.04 and 5.7%.
Radioimmunoassay of Hepatitis B Antigen
93
Table 1. Comparison of positive results obtained in the detection of hepatitis B antigen by normal and corrected radioimmunoassay (counting characteristics were usually those of example 3) Source
Tested
Positive results normal method
corrected method total
Donors pools
Mean coefficients of positive resultsB recovered
statistically positive
recovered' n
%
7,082
144
151
7
4.64
1.896
1.758
13,117
92
101
9
8.91
1.893
1.807
3,699
199
204
5
2.45
1.886
1.778
(10 sera)
Plasma pools (10 units) Individual patients
Number of positive sera recovered with the corrected p r d u r e and considered negative with the normal procedure and corresponding percent of total positive. a Mean coefficient given by the first screening (recovered) and corresponding statistically positive mean coefficient.
Comments Comparative results for detection of hepatitis B antigen over a normal blood donor population, over plasma pools and over a series of patients are given in table I. The donor sera were put in groups of 10 and a single screening sample taken. Every positive result was checked the next day using a duplicate sample. If the initial result was confirmed, the sera making up each positive pool were individually tested. Finally, a usual neutralization technique was used to determine the specificity of each positive reaction to the hepatitis B antigen. It should be noted that the statistical correction of the coefficient 2.1 allowed 7 donors who were carriers of hepatitis B
94
WAGNERLEMAIRWRICHARD
antigen and who, from the initial testing, were theoretically negative to be detected. A parallel study to the one on blood donors was carried out on 2 liters plasma pools made up of 10 units of plasma. All these units had first been tested by counterelectrophoresis and found to be negative. As in the preceding case, a test was made on a single screening sample and followed up in the case of a positive result by a duplicate confirmation test then a neutralization test. The number of positive pools thus detected was particularly high (9 out of 101 positive pools or 8.9%). More interesting still are the results obtained with patients who were individually tested as possible carriers of hepatitis B antigen. The possible objection to the dilution of antigen because of the way the pools are made up, is not valid in this case. The same followup method was used as for the plasma pools. As can be seen from table I, 5 positive sera which would have been considered negative using normal procedures, were identified on initial testing. Moreover, 3 sera which were identified as positive under the same test conditions were not confirmed by the neutralization test. To date no satisfactory explanation has been found for this phenomenon. These results show the dangers associated with too rigorous an application of the 'cutoff' method, at least in borderline cases and without bearing in mind the statistical accuracy of radioactivity counting. These dangers become particularly marked when, as was the case for this study, a rigorous computer method is used to obtain optimal results. On the other hand, such a method is extremely useful when elementary precautions are taken with regard to counting times and associated statistics. Thus, formulae 3 and 4 allow for consistent statistical accuracy (or relative standard deviation) in testing and for counting times being established in relation to the mean cpm of negative controls. Naturally, the greater the accuracy required, the longer the necessary counting times. It will also be noted from table I that the mean coefficients obtained from the different positive samples identified through our corrective method are remarkably similar. This poses the problem of determining the positive threshold on the basis of a coefficient of 2.1, i.e. as we have seen, 7 standard deviations from the mean cpm of negative controls. It would seen preferable, especially when a single screening method without correction of the positive coefficient is used, and all the more if the counting times are short, to reduce the 'cutoff' value to 6 standard deviations or a coefficient of 1.8 relative to the mean value of the negative controls.
Radioimmunoassay of Hepatitis B Antigen
95
Acknowledgements The authors wish to express their appreciation to Dr. L. R. OVERBY,Abbott Laboratories, North-Chicago, 111.) for helpful discussions concerning the methodology used in this study, and to Prof. W. A. OLIVER, University of Toronto, for reviewing the manuscript.
References 1 GINSBERG,A. L.; CONRAD,M. E.;BANCROFT,W. H.; LING,C. M., and OVERBY, L. R.: Antibody to Australia antigen: detection with a simple radioimmune assay, incidence on military populations, and role in the prevention of hepatitis B with gamma-globulin. J. Lab. clin. Med. 82: 317-325 (1973). 2 LEMAIRE,J. M. and CAZAL, P.: Personal commun. (1975). 3 LING, C. M. and OVERBY,L. R.: Prevalence of hepatitis B virus antigen as revealed by direct radioimmunoassay with 1W-antibody. J. Immun. 109: 834841 (1972). 4 OVERBY,L. R.; MILLER, J. P.; SMITH, I. D.; DECKER,R. H., and LING, C. M.: Radioimmunoassay of hepatitis B virus-associated (Australia) antigen employing IzKI-antibody. Vox Sang. 24: suppl., pp. 102-113 (1973).
Dr. A. WAGNER,Centre de Transfusion Sanguine, Laboratoire des RadioClCments, BP 1213, F-34000 Montpellier (France)
