Data analysis system and computer program

Abstract

To provide materials for determining the reliability of a prediction formula for analysis conditions.SOLUTION: A data analysis system comprises: an analysis data storage unit 2 for storing actual values of multiple analysis results as analysis data in association with corresponding gradient conditions; a model expression storage unit 4 for storing a model expression serving as the basis for a prediction formula for calculating a prediction value of the analysis result from analysis conditions; and a data processing unit 6 for performing computational processing using the analysis data and the model expression. The data processing unit 6 includes a prediction formula creation unit 10 configured so as to create the prediction formula about a sample by applying the actual value of the analysis result stored in the analysis data storage unit 2 to the model expression stored in the model expression storage unit 4, and further includes a correlation data creation unit 12 configured to create correlation data that represent a correlation between each prediction value of the analysis result based on two or more analysis conditions calculated using the prediction formula created by the prediction formula creation unit 10 and the actual value of the analysis result.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a data analysis system and a computer program used for searching for an optimal gradient analysis of a sample. [Background technology]

[0002] When developing an analytical method for liquid chromatography analysis of a certain sample (a set of analytical conditions such as mobile phase flow rate, column temperature, gradient conditions, etc.), the user typically creates multiple analytical methods with different analytical conditions such as gradient conditions, analyzes the sample using each analytical method, and searches for an analytical method that best separates the peaks in the chromatogram obtained and quickly elutes each peak component.

[0003] On the other hand, there is also software that assists in the search for optimal analytical conditions for the analysis of a target sample. Such software creates a prediction equation that shows the correlation between the analytical conditions and the analytical results (retention time and peak width) for each component in the target sample from the chromatogram obtained by analyzing the target sample under multiple analytical conditions, and predicts the optimal analytical conditions for the analysis of the target sample based on the prediction equation created for each component and presents them to the user. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Weiqiang Hao, et.al.,Computer aided optimization of multilinear gradient elution in liquid chromatography,Journal of Chromatography A,Volume 1635,2021,461754,ISSN 0021-9673, [Non-Patent Document 2] PJ Schoenmakers, et.al., Gradient selection in reversed-phase liquid chromatography J. Chromatogr., 149 (C) (1978), pp. 519-537 [Non-Patent Document 3] MA Quarry, et.al., Prediction of precise isocratic retention data from two or more gradient elution runs. Analysis of some associated errors Anal. Chem., 58 (4) (1986), pp. 907-917 [Non-Patent Document 4] SR Gallant, et.al., Modeling gradient elution of proteins in ion-exchange chromatography AIChE J, 42 (9) (1996), pp. 2511-2520 [Non-Patent Document 5] JJ Baeza-Baeza, et.al., Approaches to model the retention and peak profile in linear gradient reversed-phase liquid chromatography J. Chromatogr. A, 1284 (2013), pp. 28-35 [Non-Patent Document 6] UD Neue, et.al., Peak compression in reversed-phase gradient elution J. Chromatogr. A, 1111 (2006), pp. 32-39 [Non-Patent Document 7] Weiqiang Hao, et.al., Influence of the pre-elution of solute in initial mobile phase on retention time and peak compression under linear gradient elution, Journal of Chromatography A,Volume 1618,2020,460858,ISSN 0021-9673, [Non-Patent Document 8] H. Poppe, et.al., Peak width in solvent-programmed chromatography I. General description of peak broadening in solvent-programmed elution J. Chromatogr., 204 (1981), pp. 77-84 Summary of the Invention [Problem to be solved by the invention]

[0005] In predicting optimal analytical conditions using the above software, depending on the analytical conditions and analysis results used to create the prediction formula, a highly reliable prediction formula may be created, or an unreliable prediction formula may be created. If optimal analytical conditions for the analysis of a target sample are predicted based on an inaccurate prediction formula with low reliability, analytical conditions that are actually inappropriate may be predicted as optimal analytical conditions, and even if the analysis is performed under the predicted analytical conditions, it is unlikely that the chromatogram expected by the user will be obtained. Conversely, if optimal analytical conditions for the analysis of a target sample are predicted based on an accurate prediction formula with high reliability, it is highly likely that the predicted analytical conditions are actually optimal, and even if the analysis is performed under the predicted analytical conditions, it is highly likely that the chromatogram expected by the user will be obtained.

[0006] However, there was no information available to determine whether the prediction formula that had been created was highly reliable, making it difficult for users to determine whether the analytical conditions predicted to be optimal for the analysis of the target sample were actually optimal.

[0007] The present invention has been made in consideration of the above problems, and has an object to provide a user with information for judging the reliability of a prediction formula. [Means for solving the problem]

[0008] The data analysis system according to the present invention comprises: an analysis data storage unit that stores, as analysis data, actual values ​​of a plurality of analysis results obtained by performing analysis using a plurality of analysis conditions, in association with the corresponding analysis conditions; a model formula storage unit that stores a model formula that includes analysis conditions as variables and is the basis of a prediction formula for calculating a predicted value of an analysis result from the analysis conditions; a data processing unit that performs calculation processing using the analysis data stored in the analysis data storage unit and the model formula stored in the model formula storage unit, The data processing unit includes: a prediction formula generating unit configured to generate the prediction formula for the sample by applying actual values ​​of the plurality of analysis results stored in the analysis data storage unit together with the corresponding analysis conditions to the model formula stored in the model formula storage unit; and a correlation data generating unit configured to generate correlation data indicating a correlation between a predicted value of the analysis result for each of two or more analysis conditions calculated using the prediction formula generated by the prediction formula generating unit and an actual value of the analysis result. Effect of the Invention

[0009] According to the data analysis system of the present invention, correlation data is generated that indicates the correlation between the predicted values ​​of the analysis results for each analysis condition calculated using the prediction formula and the actual measured values ​​of the analysis results, and the generated correlation data can be used as material for determining the reliability of the prediction formula, thereby providing the user with material for determining the reliability of the prediction formula. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a block diagram showing an embodiment of a configuration of a data analysis system. [Diagram 2] FIG. 13 is a diagram illustrating an example of a screen displaying reliability information. [Diagram 3] 13 is a flowchart showing an example of a data analysis process performed in the embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] An embodiment of a data analysis system will be described below with reference to the drawings.

[0012] The data analysis system 1 is constructed by installing a computer program in a computer device, and comprises an analysis data storage unit 2, a model formula storage unit 4, a data processing unit 6, and a display 8.

[0013] The analysis data storage unit 2 is a storage area for storing a plurality of analysis results obtained by analyzing a sample using a plurality of different gradient conditions in the analysis device 100 in association with the gradient conditions as analysis data. The analysis results include chromatographic information related to the retention time of each component in the sample and the peak width of the peak of each component. The gradient conditions are conditions for how the ratio of the solvents constituting the mobile phase is changed over time. In this embodiment, gradient conditions are used as an example of analysis conditions, but the present invention is not limited to gradient conditions.

[0014] The model formula memory unit 4 stores, for each component in a sample, a model formula that is the basis of a retention time prediction formula that shows the relationship between gradient conditions and retention time, and a model formula that is the basis of a peak width prediction formula that shows the relationship between gradient conditions and peak width.

[0015] The analytical data storage unit 2 and the model formula storage unit 4 are realized by a partial area of ​​an information storage device such as a hard disk drive. The analysis device 100 is, for example, a liquid chromatograph.

[0016] The data processing unit 6 includes a prediction formula generating unit 10 and a correlation data generating unit 12. The data processing unit 6 is realized by a computer circuit equipped with a CPU (Central Processing Unit), and the prediction formula generating unit 10 and the correlation data generating unit 12 are functions obtained by executing a computer program in the data processing unit 6.

[0017] The prediction formula generating unit 10 is configured to perform statistical analysis (fitting) by applying the chromatogram information of the sample read from the analysis data storage unit 2 to the model formula read from the model formula storage unit 4, thereby generating a retention time prediction formula and a peak width prediction formula for each component in the sample. Bayesian estimation or the like can be used as the statistical analysis algorithm.

[0018] Here, the model formula will be described.

[0019] First, an example of a model formula on which the retention coefficient prediction formula is based will be described.

[0020] The migration rate of a compound can be expressed as the inverse of the retention factor, and the retention time (t R The relationship between the retention coefficient k(t) at each time and the retention time can be expressed by the following formula 1 (see Non-Patent Document 1). [Formula 1] TIFF2025021597000002.tif18167, where t pis the dwell time (data acquisition time), and t0 is the hold-up time (the time from sample introduction to the appearance of the apex of the peak of the component not retained in the column). k(0) indicates the retention factor in the mobile phase composition before time 0. Here, it is assumed that the mobile phase composition is fixed and the retention factor does not change until the analysis begins.

[0021] It is also known that the relationship between the organic solvent concentration and the retention coefficient in reversed-phase analysis in liquid chromatography can be expressed by the following [Equation 2] (see Non-Patent Documents 1-5). [Formula 2] TIFF2025021597000003.tif18167Here, k(t) is the retention coefficient at each time, φ(t) is the organic solvent ratio of the mobile phase at each time, and k0 is the retention coefficient when the organic solvent ratio is 0. S1 and S2 are coefficients, and their values ​​change depending on the solute, stationary phase, and mobile phase.

[0022] The prediction formula generation unit 10 applies the chromatogram information and gradient information of the sample to the above model formulas [Formula 1] and [Formula 2] to perform fitting, thereby obtaining k0, S1, and S2 for each component in the sample, and thereby generating a retention time prediction formula for each component in the sample.

[0023] Next, an example of a model formula on which the peak width prediction formula is based will be described.

[0024] In reversed-phase gradient analysis, the peak width tends to decrease with the magnitude of the retention time, and this phenomenon is called peak compression. Peak compression can be expressed by the following [Equation 3] using the compression coefficient G (see Non-Patent Document 6). [Formula 3] TIFF2025021597000004.tif18167Where, W is the peak width, t0 is the hold-up time, k(t R ) is the retention factor during elution, and N is the theoretical plate number of the column.

[0025] The retention coefficient k(t) can be calculated using the same algorithm as that used to generate the retention coefficient prediction formula. However, the peak width varies more than the retention time, and may be overfitted to noise. Therefore, the prediction formula generating unit 10 applies chromatogram information and gradient information to the following [Formula 4], which ignores the quadratic term in the above [Formula 2], to perform fitting to calculate k0 and S1, and can calculate the peak width prediction formula for each component in the sample. [Formula 4] TIFF2025021597000005.tif18167

[0026] The compression coefficient G can be calculated using the following equation [5], which uses the retention coefficient (see Non-Patent Documents 7-8). [Formula 5] TIFF2025021597000006.tif18167

[0027] The correlation data generating unit 12 is configured to calculate the predicted retention time and peak width values ​​for each gradient condition for each component in the sample using a retention time prediction equation and a peak width prediction equation generated based on the above-mentioned model equation, and to generate correlation data showing the correlation between each of the calculated predicted values ​​and the actual measured values ​​(retention time values ​​and peak width values ​​in the analytical data) under the corresponding gradient conditions.

[0028] A display 8 is connected to the data processing unit 6, and the correlation data generated by the correlation data generating unit 12 is displayed on the display 8, for example, when desired by the user.

[0029] FIG. 2 shows an example of the correlation data displayed on the display 8.

[0030] The correlation data shown in Figure 2 is for one component (compound) specified by the user. The correlation data includes retention time (RT) prediction formula information and peak width prediction formula information for each component in the sample.

[0031] Each of the retention time prediction formula information and the peak width prediction formula information includes a two-dimensional graph with two mutually perpendicular axes, one of which represents the actual values ​​for each gradient condition and the other axis representing the predicted values ​​for each gradient condition, a table showing the predicted values ​​and actual values ​​for each gradient condition, and a coefficient of determination for each prediction formula.

[0032] Each plot on the two-dimensional graph shows the intersection of the predicted value and the actual value under each gradient condition. If the prediction formula fits under all gradient conditions (the predicted value is close to the actual value = valid), the plot of the actual value will be located on the line x = y with a slope of 1 in the two-dimensional graph. On the other hand, if there are gradient conditions for which the prediction formula does not fit (is not valid), the plot of the actual value will deviate from the line x = y in the two-dimensional graph. In this way, by looking at the two-dimensional graph, it is clear at a glance under which gradient conditions the prediction formula is highly reliable and under which gradient conditions it is less reliable, making it easy for users to recognize the reliability of the prediction formula. Furthermore, by simultaneously showing a table of the predicted values ​​and the actual values ​​for each gradient condition, users can easily confirm how far the predicted values ​​deviate from the actual values.

[0033] In addition, the "coefficient of determination" shown in each of the retention time prediction formula information and the peak width prediction formula information is a statistic for evaluating whether the prediction formula is valid. The Rhat statistic is known as such a statistic. If the estimation of the prediction formula is valid, the Rhat statistic is approximately 1. If the Rhat statistic exceeds 1.1, it is generally evaluated that the estimation was performed but was not valid. Rhat is a value obtained when Bayesian estimation is used as the statistical analysis algorithm for fitting used to generate the prediction formula. This statistic is 1 if the fluctuation of the actual measurement value can be completely explained by the predicted value obtained by the prediction formula, and the more the fluctuation that cannot be explained (the worse the prediction performance of the prediction formula), the smaller the value becomes. By referring to such values, the user can check the reliability of each prediction formula.

[0034] Next, the data analysis process executed by the data processing unit 6 will be described with reference to the flowchart of FIG.

[0035] The prediction formula generation unit 10 of the data processing unit 6 reads out the analytical data of the sample to be analyzed from the analytical data storage unit 2 (step 101), and further reads out the model formula used to generate the prediction formula from the model formula storage unit 4 (step 102). Thereafter, the data processing unit 6 applies the analytical data to the model formula and performs fitting using a predetermined statistical analysis algorithm to determine each coefficient of the model formula, and generates a retention time prediction formula and a peak width prediction formula (step 103).

[0036] When the retention time prediction formula and the peak width prediction formula are generated, the prediction values ​​of the retention time and the peak width for each gradient condition are calculated using each generated prediction formula, and the calculated prediction values ​​and the actual measured values ​​are used to generate correlation data as shown in Fig. 2 (step 104). The correlation data generated here is displayed on the display 8, for example, when the user desires.

[0037] The above-described embodiment is merely one example of the embodiment of the present invention. Although the correlation data for each gradient condition has been described as the analysis condition, the present invention is not limited thereto, and can be similarly applied to other analysis conditions (column oven temperature, flow rate, etc.). The embodiment of the data analysis system and computer program according to the present invention is as follows.

[0038] In one embodiment of the data analysis system according to the present invention, an analysis data storage unit stores actual values ​​of a plurality of analysis results obtained by performing analysis using a plurality of analysis conditions, in association with the corresponding analysis conditions, as analysis data; a model formula storage unit that stores a model formula that includes analysis conditions as variables and is the basis of a prediction formula for calculating a predicted value of an analysis result from the analysis conditions; a data processing unit that performs calculation processing using the analysis data stored in the analysis data storage unit and the model formula stored in the model formula storage unit, The data processing unit includes: a prediction formula generating unit configured to generate the prediction formula for the sample by applying actual values ​​of the plurality of analysis results stored in the analysis data storage unit together with the corresponding analysis conditions to the model formula stored in the model formula storage unit; and a correlation data generating unit configured to generate correlation data indicating a correlation between a predicted value of the analysis result for each of two or more analysis conditions calculated using the prediction formula generated by the prediction formula generating unit and an actual value of the analysis result.

[0039] In aspect [1] of the above embodiment, the correlation data includes a two-dimensional graph in which one of two intersecting axes represents the actual value of the analysis result for each of the analytical conditions, and the other axis represents the predicted value of the analysis result for each of the analytical conditions.

[0040] In the aspect [2] of the above embodiment, the correlation data includes reliability information of the prediction formula taking into account the degree of discrepancy between the actual values ​​of the analysis results and the predicted values ​​of the analysis results for the plurality of analysis conditions. This aspect [2] can be combined with the aspect [1] above.

[0041] In the above embodiment, the analytical result includes a retention time of each component contained in the sample. This embodiment can be combined with the above embodiment.

[0042] In the above embodiment, in aspect [4], the analytical result includes a peak width of each component contained in the sample. This aspect [4] can be combined with the above aspects [1], [2], and / or [3].

[0043] In aspect [5] of the above embodiment, the apparatus further includes a display (8), and the data processing unit (6) is configured to display the correlation data generated by the correlation data generating unit (12) on the display (8). This aspect [5] can be combined with the above aspects [1], [2], [3], and / or [4].

[0044] In the aspect [6] of the above embodiment, the two or more analytical conditions may include analytical conditions other than the plurality of analytical conditions. With this aspect, it is possible to confirm whether the prediction of the analytical result under analytical conditions other than the analytical conditions used to generate the prediction formula is appropriate. This aspect [6] can be combined with the above aspects [1], [2], [3], [4], and / or [5].

[0045] One embodiment of the computer program according to the present invention is configured to configure the above-mentioned data analysis system by being installed in a computer. [Explanation of symbols]

[0046] 1. Data analysis system 2 Data storage section 4 Data Processing Section 6. Information input device 8. Display

Claims

1. an analysis data storage unit that stores, as analysis data, actual values ​​of a plurality of analysis results obtained by performing analysis using a plurality of analysis conditions, in association with the corresponding analysis conditions; a model formula storage unit that stores a model formula that includes analysis conditions as variables and is the basis of a prediction formula for calculating a predicted value of an analysis result from the analysis conditions; a data processing unit that performs calculation processing using the analysis data stored in the analysis data storage unit and the model formula stored in the model formula storage unit, The data processing unit includes: a prediction formula generating unit configured to generate the prediction formula for the sample by applying actual values ​​of the plurality of analysis results stored in the analysis data storage unit together with the corresponding analysis conditions to the model formula stored in the model formula storage unit; and a correlation data generating unit configured to generate correlation data indicating a correlation between a predicted value of the analysis result for each of two or more analytical conditions calculated using the prediction formula generated by the prediction formula generating unit and an actual value of the analysis result.

2. 2. The data analysis system according to claim 1, wherein the correlation data includes a two-dimensional graph in which one of two intersecting axes represents the actual value of the analysis result for each of the analysis conditions and the other represents the predicted value of the analysis result for each of the analysis conditions.

3. 2. The data analysis system according to claim 1, wherein the correlation data includes reliability information of the prediction formula taking into account a degree of discrepancy between an actual value of the analysis result and a predicted value of the analysis result for the plurality of analysis conditions.

4. The data analysis system according to claim 1 , wherein the analysis result includes a retention time of each component contained in the sample.

5. The data analysis system according to claim 1 , wherein the analysis result includes a peak width of each component contained in the sample.

6. Further equipped with a display, The data analysis system according to claim 1 , wherein the data processing unit is configured to display the correlation data generated by the correlation data generating unit on the display.

7. The data analysis system according to claim 1 , wherein the two or more analysis conditions include an analysis condition other than the plurality of analysis conditions.

8. A computer program configured to construct the data analysis system according to any one of claims 1 to 7 when introduced into a computer.

Images