Method of determining calibration curve and apparatus using calibaration curve

A method of determining a calibration curve used in deciding the components of living organism by means of the least-squares method by using a plurality of measured data at different concentrations obtained by measuring reaction solutions of a plurality of standard substances having different concentrations. At least a single set of measured data Y(i) is weighted in a predetermined manner, the measured data Y(i) being obtained from the standard substance reaction solution at a specific concentration X(i) near a limit value used in deciding the living organism components. With the weighting, a calibration curve having a high precision at a portion near the limit value is realized resulting in a correct and highly reliable decision.

BACKGROUND OF THE INVENTION 
The present invention relates to a method of determining a calibration 
curve and an automatic analyzer using this calibration curve. More 
particularly, the invention relates to a method of determining a 
calibration curve suitable for precisely measuring a limit value (cutoff 
value) to be used as a decision criterion in analyzing the components of a 
living organism, and an automatic analyzer using this calibration curve. 
A conventional method of determining a calibration curve is known as 
disclosed in U.S. Pat. No. 3,998,591 and Japanese Patent Laid-open 
Publication JP-A-60-73436. 
Instead of a straight calibration line conventionally used by the enzyme 
immunoassay (EIA) for chemical inspections at clinics, a calibration curve 
is generally used in testing immunoreaction through EIA. In addition, the 
shape of a calibration curve is susceptible to change with the type of 
measuring systems and reaction conditions. EIA is an assay for micro 
substance so that it is often performed near a limit value of detection, 
thus posing a problem of a relatively large variation of measured data of 
standard substances for respective concentrations. The theoretical formula 
of a calibration curve of EIA can be obtained if the antigen-antibody 
reaction based on which the measurement is carried out can be 
quantitatively analyzed. The formula is generally a complicated non-linear 
function which is very difficult to be dealt with statistically so that an 
empirical formula is often used. In either case, it becomes necessary to 
prepare a regression model to regress the calibration curve and solve the 
concentration of an unknown sample substance. As a regression model, there 
are known logistic curves, For instance, the following model is known: 
##EQU1## 
where K=R.sub..infin. -R.sub.0, 
R.sub.0 : a response for a standard substance (sample) with 0 (zero) 
concentration 
R.sub..infin. : a response for a standard substance (sample) with infinite 
concentration 
a, b: parameter 
X(i): standard substance (sample) 
Y(i): measured data (e.g., absorptivity data) 
A conventional method of determining a calibration curve uses measured data 
per se of standard substances (samples). In other words, the conventional 
method determines a calibration curve without paying particular attention 
to the measured data near the cutoff value to be used in analyzing the 
components of living organism, in spite of the fact that the cutoff value 
plays an important role in diagnosing disease or pathology. Generally the 
average values of measured data of standard substances for respective 
concentrations are processed (through least-squares approach) to obtain 
the calibration curve. 
Recently, high sensitivity immunoassays have been developed and the 
operation of measuring data is highly automated. For instance, substances 
associated with infectious disease can now be automatically measured 
contrary to the conventional manual operation. Different from an ordinary 
quantitative measurement, immunoassays aim at a qualitative measurement 
through which it is decided if an object substance is present in a 
specimen. For instance, it is checked if there is an antibody of HIV 
(i.e., AIDS) to decide whether or not the patient is infected with AIDS. 
Taking as an example a cancer marker AFP (.alpha.-fetoprotein) commonly 
undergoing a quantitative measurement, for a screening test, to check the 
measured AFP value itself is not as important as to check if the measured 
AFP value falls within the range of values for a normal person or for a 
cancer patient. A limit value for such decision criterion is called a 
cutoff value. In order to reliably decide whether a person is infected 
with AIDS or cancer if the measured value of a specimen is higher than a 
cutoff value, and not infected if it is lower than the cutoff value, the 
data measured near the cutoff value are required to be more precise than 
the data for other concentrations. It is also necessary to use a 
calibration curve which well matches the concentrations at the 
concentration range near the cutoff value than at the other concentration 
ranges. 
The conventional method of determining a calibration curve, however, 
processes a plurality of measured data of standard substances without 
weighting the data in a particular concentration range, for example, the 
data near the cutoff value, to thus make the calibration curve well match 
measured data. The conventional method takes the necessary measures for 
reducing the adverse effects of data variation by increasing the number of 
measurements of a standard substance near the cutoff value and using the 
average value thereof. However, in determining the calibration curve, the 
average values of the measured data near the cutoff value are processed in 
the similar manner as the average values at the other concentrations, 
without taking into consideration weighting the data near the cutoff 
value. 
SUMMARY OF THE INVENTION 
It is therefore a first object of the present invention to provide a method 
of determining a calibration curve having a high precision at a portion 
where data within a particular concentration range of a standard substance 
are used. 
It is a second object of the present invention to provide an automatic 
analyzer having means for partially weighting the data within a particular 
concentration range. 
The first object can be achieved by the method of forming a calibration 
curve using data of a plurality of reaction solutions having different 
concentrations of a standard substance, which method determines a 
calibration curve by processing through partial weighting of data within a 
particular concentration range. The second object can be achieved by the 
automatic analyzer having a sample feeding unit for installing a plurality 
of standard substances having different concentrations and a sampling unit 
for sampling the standard substances plural times, which automatic 
analyzer comprises first means for partially weighting the data within a 
particular concentration range of the data of reaction solutions of the 
standard substances, second means for processing the data weighted by 
first means, third means for determining a calibration curve based on the 
data processed by second means, and fourth means for displaying the 
determined calibration curve. 
Various methods are possible to weight the measured data. According to a 
first method, the number of data are increased by measuring a standard 
substance plural times at a specific concentration, and the data are 
separately and independently processed. Since the number of data at the 
specific concentration is large as compared with the data at the other 
concentrations, the specific concentration can be weighted. According to a 
second method, the number of data of a standard substance at a specific 
concentration is increased by n multiple by means of data processing to 
obtain a larger number of data than that at the other concentrations. The 
data are separately and independently processed to determine a calibration 
curve. According to a third method combining the first and second methods, 
the cutoff value used in analyzing the components of living organism can 
be measured with high precision. 
According to the automatic analyzer, the data of reaction solutions of 
standard substances within a particular concentration region are partially 
weighted and processed to determine a calibration curve. Therefore, the 
similar advantageous effects as above can be obtained.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The invention will be described in detail in connection with the 
embodiments shown in FIGS. 1 to 5. 
FIG. 1 is a flow chart illustrating multi-regression through the non-linear 
least-squares approach, the flow chart being used for explaining an 
embodiment of the calibration curve determining method of this invention. 
It is assumed that the measured data of a standard substance for a certain 
test item at concentrations X(0), X(b 1), X(2), X(3), X(4) and X(5) are 
Y(0), Y(1), Y(2), Y(3), Y(4) and Y(5), respectively. At step S1 shown in 
FIG. 1, the concentrations X(0) to X(5) for the certain test item are 
stored in a memory of a central processing unit 51 shown in FIG. 3. At 
step S2, the measured data Y(0) to Y(5) are stored in a predetermined 
memory. 
Using the stored concentrations and measured data, at step S3, the initial 
values of four parameters R.sub.0, K, a and b shown in the formula (1) are 
set as indicated by (1) to (3) in the block of step S3. 
It is further assumed that the concentration to be weighted is X(1). Then, 
data Y(1) are increased for use in data processing into Y(11), Y(12), 
Y(13), Y(14) and Y(15), where Y(11)=Y(12)=Y(13)=Y(14)=Y(15)=Y(1). These 
values Y(1), Y(11), Y(12), Y(13), Y(14) and Y(15) are independently used 
and subjected to multi-regression through the non-linear least-squares 
approach using the Gauss-Newton conversion method, to thereby determine 
four parameters .DELTA.R.sub.0, .DELTA.K, .DELTA.a and .DELTA.b (steps S4 
to S6). 
The multi-regression method will be detailed. Differences y(ij) between 
measured data Y(ij) for a certain test item and calculated values F(ij) 
obtained by substituting the determined parameters into the formula (1) 
are approximately given by: 
##EQU2## 
The relationship among measured data Y(ij), calculated values F(ij) and 
differences y(ij) is shown in FIG. 5. The parameters to be obtained take 
the values when the sum S of squares of the differences become minimum. 
The sum S is written as: 
##EQU3## 
Since the following equation stands, 
##EQU4## 
then the four formulas (3) to (6) are established: 
EQU .DELTA.R.sub.0 .SIGMA.x.sub.1.sup.2 +.DELTA.K.sub.0 .SIGMA.x.sub.1 x.sub.2 
+.DELTA.a.SIGMA.x.sub.1 x.sub.3 +.DELTA.b.SIGMA.x.sub.1 x.sub.4 
=.SIGMA.x.sub.1 y (3) 
EQU .DELTA.R.sub.0 .SIGMA.x.sub.1 x.sub.2 +.DELTA.K.sub.0 .SIGMA.x.sub.2.sup.2 
+.DELTA.a.SIGMA.x.sub.2 x.sub.3 +.DELTA.b.SIGMA.x.sub.2 x.sub.4 
=.SIGMA.x.sub.2 y (4) 
EQU .DELTA.R.sub.0 .SIGMA.x.sub.1 x.sub.3 +.DELTA.K.sub.0 .SIGMA.x.sub.2 
x.sub.3 +.DELTA.a.SIGMA.x.sub.3.sup.2 +.DELTA.b.SIGMA.x.sub.3 x.sub.4 
=.SIGMA.x.sub.3 y (5) 
EQU .DELTA.R.sub.0 .SIGMA.x.sub.1 x.sub.4 +.DELTA.K.sub.0 .SIGMA.x.sub.2 
x.sub.4 +.DELTA.a.SIGMA.x.sub.3 x.sub.4 +.DELTA.b.SIGMA.x.sub.4.sup.2 
=.SIGMA.x.sub.4 y (6) 
The increments .DELTA.R.sub.0, .DELTA.K.sub.0, .DELTA.a and .DELTA.b of the 
parameters satisfying the formulas (3) to (6) can be obtained by solving 
the following matrix equation (7): 
##EQU5## 
Using the obtained .DELTA.a, .DELTA.b, .DELTA.K.sub.0, and .DELTA.R.sub.0, 
and replacing the parameters with a=a+.DELTA.a, b=b+.DELTA.b, K.sub.0 
=K.sub.0 +.DELTA.K.sub.0, and R.sub.0 =R.sub.0 +.DELTA.R.sub.0, the 
parameters at the minimum sum S of squares are obtained through 
multi-regression. In the example shown in FIG. 1, the regression is 
repeated 20 times. The obtained parameters are substituted into the 
formula (1) to determine a calibration curve having a linear relation to 
the concentration (steps S7 to S10). 
The obtained calibration curve has been weighted for the data at a specific 
concentration X(1) so that the calibration curve determined with a portion 
near the specific concentration X(1) well matches the measured data Y(1), 
to thus allow a high precision of data near the specific concentration 
X(1). 
As appreciated from the foregoing description, in order to process the 
measured data while weighting the data at a concentration X(i), the number 
of measured data to be weighted at a concentration X(i) is increased by n 
multiple prior to the data processing to make the number larger than that 
at the other concentrations X(i'). Namely, the data are transformed into 
Y(i1), Y(i2), . . . , Y(in). The increased number of data as well as the 
other data are processed not as the averages but as independent data. For 
this purpose, obtained are the parameters satisfying the condition that 
the sum of squares of differences between independent data and calculated 
values F(ij) becomes minimum. 
The above-described weighting follows the first method. Specifically, n 
types of data Y(i1) to Y(in) are actually measured and these data are used 
in data processing. 
In applying the second weighting method, only a single set of data Y(i) are 
actually measured for weighting the concentration X(i). The data Y(i) are 
increased by n multiplier through data processing and thereafter, the 
parameters are calculated which satisfy, as described previously, the 
condition that the sum of squares of differences between respective data 
and calculated values F(ij) becomes minimum. 
In applying the third weighting method combining the first and second 
methods, data used for processing in weighting the concentration X(i) are 
Y(i).times.n1, Y(i+1).times.1, Y(i+2).times.n2, . . . , Y(i+n).times.n3, 
where n1, n2 and n3 are the values of multipliers described above. 
FIG. 2 is a flow chart illustrating a method of determining a calibration 
curve based on measured data (judging the usability of the calibration 
curve) and calculating the concentration of a specimen, the flow chart 
being used for explaining the embodiment of the calibration curve 
determining method of this invention. At step S21, measured data Y(0) to 
Y(11) are picked up. At step S22, it is checked if an object is a standard 
substance or a specimen. In case of a standard substance, a calibration 
curve is determined at step S23. At step S24, the determined calibration 
curve is checked if it is usable or not. If usable, the calibration curve 
is displayed at step S25. In case of a specimen at step S22, the 
concentration is calculated at step S26, and the specimen concentration is 
outputted at step S27. 
A calibration curve for a standard substance determined in accordance with 
the flow chart shown in FIG. 1 is used for calculating the components of 
an actual living organism in accordance with the flow chart shown in FIG. 
2. The calculated data may sometimes deviate greatly from the calibration 
curve obtained by the method shown in the flow chart of FIG. 1 (one of the 
reasons for this may be attributable to a degraded reagent). In such a 
case, the calibration curve is judged as not usable at corresponding flow 
step S24 without using such calibration curve, and a new calibration curve 
is again determined. 
Next, the automatic analyzer using the calibration curve determining method 
of this invention will be described. FIG. 3 shows the structure of an 
embodiment of the automatic analyzer according to this invention. 
Referring to FIG. 3, there is provided a sampling disk 10 on which a 
plurality of standard substances having different concentrations for 
respective test items can be mounted, with a plurality of standard 
substances for each test item being consecutively disposed one after 
another. A reaction disk 21, mounted rotatably, has at its outer 
circumferential portion a plurality of reaction vessels 22 serving also as 
measuring cells. A standard substance (sample) is carried out from a 
sample container 44 to a sampling probe 41 of a pipette 40. A reagent is 
dispensed with probes 38, 39 mounted at the end of dispensers 36, 37, the 
dispensers being movable in the direction indicated by a bi-directional 
arrow. A spectroscope 27 is constructed of a plurality of detectors for 
measuring a plurality of wavelengths at a same time. The spectroscope 27 
is mounted facing a light source lamp 25 so that a train of reaction 
vessels 22 passes through a light beam 26 from the light source lamp 25 
while the reaction disk 21 rotates counter clockwise. The light beam 26 is 
arranged to transmit thru the center of a reaction vessel, e.g., a 31st 
vessel 46 as counted clockwise from an ejection site 45 when the reaction 
disk 21 stops. A solution drain device and a cleaning device 24 are 
disposed between the light beam 26 site and ejection site 45. 
The overall arrangement of a controller is constructed of a multiplexer, 
logarithmic conversion amplifier 53, A/D converter 54, read-only memory 
ROM, random access memory RAM, printer 55, console panel 52, and 
mechanical component driver 35. The A/D converter 54 is connected further 
to a central processing unit CPU 51 via an interface 50. CPU 51 made of a 
microcomputer controls the whole apparatus including its mechanical 
system, and performs all data processing including such as determining a 
calibration curve through the above-described multi-regression, 
concentration calculation and the like. 
Reference numeral 56 represents a display device on which displayed is a 
calibration curve such as shown in FIG. 4 for measuring a cancer marker 
.alpha.-fetoprotein. Reference numeral 57 represents a dispenser for a 
reagent, and 58 a constant temperature oven. 
Next, the operation of the embodiment shown in FIG. 3 will be described. 
As a sample vessel 44 containing an object standard substance (sample) such 
as a cancer marker, substances associated with infectious disease and the 
like, is moved to the sampling site, the tip of the probe 41 of the 
pipette 40 is immersed into the sample vessel 44 to suck a predetermined 
amount of blood serum and hold it within the probe 41. Thereafter, the 
probe 41 is moved to the ejection site 45 of the reaction disk 21 to eject 
out the blood serum held in the probe 41 into the reaction vessel 22 at 
the ejection site 45. After the above sampling operation, the reaction 
disk 21 starts counter clockwise spontaneous rotation and continues it 
until the reaction vessels 22 larger in number by one than all of the 
reaction vessels 22 pass the ejection site. 
With the counter clockwise rotation of the reaction disk 21, the reaction 
vessel 22 containing the sample which was sampled by the above sampling 
operation now stops at a position one pitch of the reaction vessels in 
advance from the ejection site 45 in the counter clockwise direction. 
During rotation of the reaction disk 21, all the reaction vessels 22 on 
the disk 21 pass through the light beam 26. The spectroscope 27 thus 
measures absorptivity and outputs data signals to a multiplexer whereat a 
data signal having an object wavelength is selected and supplied via the 
A/D converter to CPU 51 and stored in RAM. 
Assuming that the time while the reaction disk 21 rotates and stops is 20 
seconds, for example, then the above operation is repeated cyclically for 
20 seconds at each cycle. As the cycles increase, the position of the 
reaction vessel 21 containing the sample advances one pitch after another 
in the counter clockwise direction when the disk 21 stops. A reagent is 
ejected out by the dispenser 36, 37 into the reaction vessel 22 containing 
the sample when it is stopped at the ejection site 46, 47 after having 
been rotated counter clockwise one pitch after another on the reaction 
disk 21. Thus, for a particular object sample, a first stage reaction 
starts upon application of a first reagent at the ejection site 47, and a 
second stage reaction starts upon application of a second reagent at the 
ejection site 46. Assuming that the stop time and rotation time of the 
reaction disk 21 during one cycle are 4.5 seconds and 15.5 seconds, 
respectively, the reaction processes of the object sample is measured 31 
times every 20 seconds, and the measured data for 10 minutes are stored in 
RAM. CPU 51 operates under control of the programs (refer to FIGS. 1 and 
2) stored in ROM to sample 31 measured data from RAM and process the data. 
Five or six standard substances, for example, required for each test item 
in determining a calibration curve are consecutively disposed on the 
sample disk 10 so that the plurality of standard substances having 
different concentrations for the test item are carried out to the reaction 
vessel 22 plural times (e.g., plural times corresponding to weighting) 
automatically and consecutively. In determining a calibration curve for a 
substance having no linear relation to the concentrations, it is essential 
to sample and measure standard substances having different concentrations 
plural times, which the present apparatus can realize. The reaction 
processes of the plurality of standard substances are measured for 10 
minutes as described above, and the measured data are stored for 
respective test items to be used for determining a calibration curve 
having a linear relation to concentrations. 
According to the present invention described above, it is possible to 
determine a calibration curve having a weighted portion within a 
particular concentration range. Therefore, the cutoff value to be used in 
the analysis of the components of living organisms can be measured with 
high precision.