Data analysis system, data analysis method and computer program

Abstract

To increase a degree of freedom in constructing a model expression that is a basis of regression analysis and to increase accuracy of an approximate expression to be derived.SOLUTION: A data analysis system includes: a data storage part that stores responses, which are a plurality of analysis results obtained by a plurality of analyses executed under a plurality of analysis conditions, and factors, which are a plurality of parameters included in the analysis conditions, in a manner that the responses and the factors are associated with each other; a data processing unit configured to use at least one of the factors as a variable and to create an approximate expression indicating a relationship between the variable and the responses; and an information input device for a user to input information to the data processing unit. The data processing unit is configured to execute: a variable setting step of setting the factors to be the variable; a structure setting step of setting a structure of a model expression that uses the set variable; a model expression determination step of determining the model expression on the basis of, the set structure; and an approximate expression determination step of determining a coefficient of each term constituting the model expression by regression analysis.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a data analysis system, a data analysis method, and a computer program for analyzing the relationship between an analysis result obtained by performing an analysis such as a liquid chromatography analysis under a plurality of analysis conditions and the analysis conditions. [Background technology]

[0002] In the pharmaceutical industry, analytical methods such as liquid chromatography are used to check for impurities that are mixed in during manufacturing. In this case, it is necessary to detect as many components as possible contained in the target substance, so it is necessary to search for the "optimum analytical conditions" that will cause as many component peaks to appear in the chromatogram. In order to search for the "optimum analytical conditions," it is necessary to consider all analytical conditions by changing multiple parameters such as the flow rate of the mobile phase, the temperature of the separation column, and the composition of the mobile phase (the mixture ratio of the solvents that make up the mobile phase). However, it would take an enormous amount of time to perform analysis under all analytical conditions and obtain data. Therefore, a method is sometimes used in which the relationship between the analytical conditions and the analytical results is approximated using regression analysis, and the "optimum analytical conditions" are searched for using the approximated results. Summary of the Invention [Problem to be solved by the invention]

[0003] In the method using regression analysis, each parameter of the analysis conditions is treated as a factor, and the analysis results under each analysis condition (such as the degree of separation of peaks in the chromatogram, the number of peaks, and the retention time of each peak) are treated as a response, and an approximation equation is created that approximates the relationship between the factors and the response. To create an approximation equation, it is first necessary to prepare a model equation that serves as the basis for the approximation equation, and once the model equation is set, the coefficients of each term that makes up the model equation are determined by regression analysis using the least squares method or the like.

[0004] In conventional analytical systems, an approximation formula is created by determining the coefficients of each calculation term using a least squares method or the like based on a specified model formula. However, recent research has revealed that, depending on the type of analytical condition parameters, there are some that have a relationship between the analytical results that is not expressed in the specified model formula. Therefore, regression analysis based on a specified model formula cannot derive an accurate approximation formula that shows the relationship between the analytical conditions, including such parameters, and the analytical results.

[0005] The present invention has been made in consideration of the above problems, and has an object to increase the degree of freedom in constructing a model equation that is the basis of regression analysis, and to increase the accuracy of the derived approximation equation. [Means for solving the problem]

[0006] The data analysis system according to the present invention includes a data storage unit that stores a plurality of analysis results obtained by a plurality of analyses performed under a plurality of analytical conditions, each of which is a response, a plurality of parameters included in the analytical conditions, each of which is a factor, and associates the responses and the factors with each other; a data processing unit that is configured to create an approximation equation that shows a relationship between the response and the variable, using at least one of the factors as a variable; and an information input device for a user to input information to the data processing unit, wherein the data processing unit is configured to execute a variable setting step that causes a user to set at least one of the factors to be the variable; a structure setting step that causes the user to arbitrarily set a structure of a model formula that is a basis of the approximation formula using the variables set in the variable setting step; a model formula determination step that determines the model formula based on the structure set by the user in the structure setting step; and an approximation formula determination step that determines the coefficients of each term constituting the model formula determined in the model formula determination step by regression analysis, thereby determining the approximation formula.

[0007] The data analysis method according to the present invention includes an analysis data preparation step of preparing a plurality of analysis results obtained by a plurality of analyses performed under a plurality of analysis conditions, each of which is defined as a response, and a plurality of parameters included in the analysis conditions, each of which is defined as a factor, in a state in which the responses and the factors are associated with each other; a variable setting step of arbitrarily setting at least one of the factors to be used as a variable; a structure setting step of arbitrarily setting the structure of a model formula that is a basis for an approximation formula that shows the relationship of the variable to the response, using the variable set in the variable setting step; a model formula determination step of determining the model formula based on the structure set in the structure setting step; and an approximation formula determination step of determining, by regression analysis, the coefficients of each term constituting the model formula determined in the model formula determination step, thereby determining the approximation formula. Effect of the Invention

[0008] The data analysis system according to the present invention is configured to allow the user to set at least one parameter to be used as a variable among multiple parameters included in the analysis conditions, and to allow the user to arbitrarily set the structure of a model formula that is the basis of an approximation formula using the set variables, thereby improving the freedom to construct the model formula that is the basis of the regression analysis and the accuracy of the derived approximation formula.

[0009] In the data analysis method according to the present invention, at least one parameter among a plurality of parameters included in the analysis conditions is arbitrarily set as a variable, and the set variable is used to arbitrarily set the structure of a model formula that is the basis of an approximation formula with the analysis results as a response, thereby improving the degree of freedom in constructing the model formula that is the basis of regression analysis and the accuracy of the derived approximation formula. [Brief description of the drawings]

[0010] [Figure 1] 1 is a flow chart illustrating an embodiment of a data analysis method. [Diagram 2] FIG. 2 is a block diagram showing an example of a configuration of a data analysis system that executes the data analysis method. [Diagram 3] 13 is an example of a model formula setting screen. [Figure 4] 13 is an example of a detailed setting screen for a model formula. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, an embodiment of a data analysis system and a data analysis method will be described with reference to the drawings.

[0012] First, the data analysis method of this embodiment will be described with reference to the flow chart of FIG.

[0013] First, analytical data to be used in regression analysis is prepared (step 101). The analytical data is the analytical results (e.g., the degree of separation of peaks in a chromatogram, the number of peaks, the retention time of each peak, etc.) obtained by performing an analysis of the same sample while changing a number of analytical condition parameters (e.g., the flow rate of the mobile phase, the temperature of the column oven, the composition of the mobile phase solvent, the mixing ratio of the mobile phase solvent, the gradient method, the sample injection amount, etc.) for each analysis, which are associated with each parameter of the analytical conditions. In regression analysis, the analytical results obtained by the analysis are defined as "responses," and each parameter of the analytical conditions is defined as "factors."

[0014] Next, based on the prepared analysis data, factors to be used as variables in the approximation formula to be created are selected and set from among the parameters of the analysis conditions (step 102). In setting the variables, any one or more of the multiple parameters included in the analysis conditions can be set as variables. After setting the variables, the structure of a model formula that is the basis of the approximation formula showing the relationship of the variables to the response is set (step 103). The structure of the model formula can also be set arbitrarily. For example, an existing structure that uses only the four arithmetic operations, such as linear expressions and quadratic expressions, can be adopted as the structure of the model formula, or a new structure that incorporates any operation, such as a square root, a power of a variable, an exponential function, or a logarithmic function, can be adopted as the structure of the model formula.

[0015] After the structure of the model formula is set, the model formula is determined based on the set structure (step 104). A model formula is a formula consisting of a sum of terms with variable coefficients. After the model formula is determined, the coefficients of each term in the model formula are determined by regression analysis, and an approximation formula is determined based on this (steps 105 and 106). As the regression analysis used to determine the coefficients of each term, in addition to the least squares method, Bayesian estimation, etc. can be used. The method of regression analysis may be arbitrarily set by the user. After the approximation formula is determined by regression analysis, processing such as drawing an approximation curve can be executed.

[0016] FIG. 2 shows an example of the configuration of a data analysis system for executing the above-mentioned data analysis method.

[0017] The data analysis system 1 is realized by an electronic computer having a computer program installed therein for carrying out the above-mentioned data analysis method, and includes a data storage unit 2, a data processing unit 4, an information input device 6, and a display 8.

[0018] The data storage unit 2 is a storage area for storing the analysis data obtained by the analysis device 100, and is 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. The data processing unit 4 performs analysis on the analysis data stored in the data storage unit 2 using the above-mentioned data analysis method. An information input device 6 and a display 8 are connected to the data processing unit 4. The information input device 6 is realized by a keyboard, a mouse, etc., and a user can input information to the data processing unit 4 through the information input device 6. Information to be presented to the user as necessary is output from the data processing unit 4 to the display 8 and displayed on the display 8.

[0019] When performing regression analysis using the above data analysis system 1, the user specifies analytical data to be the subject of regression analysis from among the data stored in the data storage unit 2 (preparation of analytical data). When the analytical data to be the subject of regression analysis is specified, the data processing unit 4 displays a model formula setting screen for setting a model formula on the display 8, and displays information required for setting the model formula on the model formula setting screen.

[0020] An example of the model formula setting screen is shown in Figure 3. In this example, the model formula setting screen has a variable setting field, a model formula type setting field, and a preview field.

[0021] The variable setting field displays a list of factors (parameters included in the analysis conditions) that can be set as variables. The user can select one or more factors to be used as variables in the approximation formula. In this example, two factors have been selected, and each factor is set to be variable X1 and X2.

[0022] In the model formula type setting field, the structure of the model formula can be set. In this example, simple setting and detailed setting can be selected. In simple setting, maximum orders of model formula 1 and 2 are provided as options for the model formula structure, and the user can easily set the structure of a linear or quadratic model formula by selecting one of the maximum orders. Furthermore, in simple setting, it is possible to select whether or not to incorporate an interaction term in the model formula, and the user can easily set the structure of a model formula that uses an interaction term.

[0023] When the user selects detailed setting in the model formula type setting field, the data processing unit 4 executes the model formula arbitrary setting mode, and displays a model formula detailed setting screen as shown in Fig. 4 on the display 8. In the model formula detailed setting screen, in addition to the four arithmetic operations, options for arithmetic terms such as square root, power of coefficient, exponential function, and logarithmic function are provided, and the user can set the structure of any model formula using any arithmetic term from these options.

[0024] The data processing unit 4 is configured to create a model formula of a structure set by simple setting or detailed setting, and display it in a preview field. In the example of FIG. 3, the model formula "Y = aX1 2 +bX2 + cX1 +dX2 + f" is displayed. In the model formula, X1 and X2 are variables (factors), Y is the response, and a~f are the coefficients of each term.

[0025] The user checks the model formula displayed in the preview field, and when executing a regression analysis with that model formula, inputs an instruction to determine the model formula into the data processing unit 4. This determines the model formula that is the basis of the regression analysis. In the example of FIG. 3, a "Decide" button is located at the bottom right, and by pressing this "Decide" button (for example, by moving the cursor to the Decide button with the mouse and clicking), an instruction to determine the model formula is input into the data processing unit 4.

[0026] Once the model formula is determined, the data processing unit 4 determines the coefficients of each term constituting the model formula (a, b, c, d, and f in Figs. 3 and 4) using a regression analysis technique such as the least squares method. In the regression analysis, the coefficients are repeatedly fine-tuned so that the response value Y calculated by applying each factor to each variable in the model formula approaches the actual response value, and the coefficients when the calculated response value Y most closely approximates the actual response value are obtained. By determining the coefficients of each term in the model formula, an approximation formula that approximates the relationship of the factors to the response is determined.

[0027] After the approximation formula is determined, the data processing unit 4 can have a function of drawing an approximation line or the like based on the approximation formula and displaying it on the display 8. Based on the information such as the approximation line displayed on the display 8, the user can perform processing such as determining optimal analysis conditions for the target sample.

[0028] The above-described embodiment is merely an example of the data analysis system, the data analysis method, and the computer program according to the present invention. The embodiments of the data analysis system, the data analysis method, and the computer program according to the present invention are as follows.

[0029] In one embodiment of the data analysis system according to the present invention, the data analysis system includes a data storage unit that stores a plurality of analysis results obtained by a plurality of analyses performed under a plurality of analytical conditions, each of which is a response, a plurality of parameters included in the analytical conditions, each of which is a factor, and associates the responses and the factors with each other; a data processing unit that is configured to create an approximation equation that shows a relationship between the response and the variable, using at least one of the factors as a variable; and an information input device for a user to input information to the data processing unit, wherein the data processing unit is configured to execute a variable setting step that causes a user to set at least one of the factors to be the variable; a structure setting step that causes the user to arbitrarily set a structure of a model formula that is a basis of the approximation formula using the variables set in the variable setting step; a model formula determination step that determines the model formula based on the structure set by the user in the structure setting step; and an approximation formula determination step that determines the coefficients of each term constituting the model formula determined in the model formula determination step by regression analysis, thereby determining the approximation formula.

[0030] In a first aspect of the above embodiment of the data analysis system, a display electrically connected to the data processing unit is provided, and the data processing unit is configured to display options for the structure of the model formula and / or options for terms to be incorporated into the model formula on the display in the structure setting step to allow a user to select an option at will, thereby allowing the user to set the structure of the model formula. With this aspect, a user can easily set a model formula of an arbitrary structure.

[0031] In the first aspect, the data processing unit is configured to be able to execute a model formula arbitrary setting mode in which a user inputs an arbitrary structure of the model formula in the structure setting step. This eliminates limitations on the structure of the model formula, and even when a new relationship between a factor and a response is found, it becomes possible to create an approximation formula taking such a relationship into consideration.

[0032] In the first aspect, the data processing unit is configured to display a preview of the model formula of the structure set by the user on the display in the structure setting step. This aspect allows the user to check the model formula of the structure set by the user, and prevents the model formula of an incorrect structure from being created.

[0033] In a second aspect of the above embodiment of the data analysis system, the analysis is a liquid chromatography analysis, the analysis result is any one of the number of peaks in a chromatogram, the degree of separation of the peaks in the chromatogram, and the retention time of the peaks appearing in the chromatogram, and the analysis conditions include, as the parameters, at least one of the types of one or more solvents constituting a mobile phase, the flow rates of each of the one or more solvents, the temperature of a separation column, and the amount of sample injected. This second aspect can be combined with the above first aspect.

[0034] In a third aspect of the above embodiment of the data analysis system, the regression analysis is a least squares method. This third aspect can be combined with the first aspect and / or the second aspect.

[0035] In a fourth aspect of the embodiment of the data analysis system, the regression analysis is Bayesian estimation. This fourth aspect can be combined with the first aspect and / or the second aspect.

[0036] In one embodiment of the data analysis method according to the present invention, the method includes an analysis data preparation step of preparing a plurality of analysis results obtained by a plurality of analyses performed under a plurality of analysis conditions, each of which is defined as a response, and a plurality of parameters included in the analysis conditions, each of which is defined as a factor, in a state in which the responses and the factors are associated with each other; a variable setting step of arbitrarily setting at least one of the factors to be used as a variable; a structure setting step of arbitrarily setting the structure of a model formula that is a basis for an approximation formula that shows the relationship of the variable to the response, using the variable set in the variable setting step; a model formula determination step of determining the model formula based on the structure set in the structure setting step; and an approximation formula determination step of determining, by regression analysis, the coefficients of each term constituting the model formula determined in the model formula determination step, thereby determining the approximation formula.

[0037] In a first aspect of the above embodiment of the data analysis method, in the structure setting step, the structure of the model formula is set using a structure and / or a term selected from a plurality of options for the structure of the model formula prepared in advance and / or a plurality of options for the terms to be incorporated into the model formula prepared in advance. With this aspect, a model formula of any structure can be easily set.

[0038] In the first aspect, the structure of the model formula is arbitrarily created in the structure setting step. This eliminates limitations on the structure of the model formula, and even when a new relationship between a factor and a response is found, it becomes possible to create an approximation formula that takes such a relationship into consideration.

[0039] In a second aspect of the above embodiment of the data analysis method, the analysis is a liquid chromatography analysis, the analysis result is any one of the number of peaks in a chromatogram, the degree of separation of the peaks in the chromatogram, and the retention time of the peaks appearing in the chromatogram, and the analysis conditions include, as the parameters, at least one of the types of one or more solvents constituting a mobile phase, the flow rates of each of the one or more solvents, the temperature of a separation column, and the amount of sample injected. This second aspect can be combined with the above first aspect.

[0040] In a third aspect of the above embodiment of the data analysis method, the regression analysis is a least squares method. This third aspect can be combined with the first aspect and / or the second aspect.

[0041] In a fourth aspect of the above embodiment of the data analysis method, the regression analysis is Bayesian estimation. This fourth aspect can be combined with the above first aspect and / or second aspect.

[0042] An embodiment of a computer program according to the invention is adapted to perform the above-mentioned data analysis method when executed on a computer. [Explanation of symbols]

[0043] 1. Data Analysis System 2 Data storage section 4 Data Processing Section 6. Information input device 8. Display

Claims

1. a data storage unit that stores, as responses, the degree of peak separation of a plurality of chromatograms obtained by a plurality of chromatographic analyses of the same sample performed under a plurality of analytical conditions, and as factors, a plurality of parameters included in the analytical conditions, and that stores the responses and the factors in association with each other; A data processing unit configured to create an approximation equation showing a relationship of the variable to the response, the data processing unit being configured to set at least one of the factors as a variable; an information input device for a user to input information to the data processing unit, The data processing unit includes: a variable setting step for allowing a user to set at least one of the factors to be the variable; a structure setting step for allowing a user to arbitrarily set a structure of a model formula that is a basis of the approximation formula using the variables set in the variable setting step; a model formula determination step of determining the model formula based on the structure set by a user in the structure setting step; an approximation equation determination step of determining, by regression analysis, coefficients of each term constituting the model equation determined in the model equation determination step, thereby determining the approximation equation.

2. a display electrically connected to the data processing unit; 2. The data analysis system according to claim 1, wherein the data processing unit is configured to, in the structure setting step, display options for the structure of the model formula and / or options for terms to be incorporated into the model formula on the display to allow a user to select arbitrarily, thereby allowing the user to set the structure of the model formula.

3. The data analysis system according to claim 2 , wherein the structure of the model formula includes at least one term of an arithmetic operation.

4. The data analysis system according to claim 2 or 3, wherein the structure of the model formula includes at least one term of a square root, a power, an exponential function, or a logarithmic function.

5. 3. The data analysis system according to claim 2, wherein the data processing unit is configured to be able to execute a model formula arbitrary setting mode in the structure setting step, which enables a user to input a structure of an arbitrary model formula.

6. The data analysis system according to claim 2 , wherein the data processing unit is configured to display, on the display, a preview of a model formula of the structure set by the user in the structure setting step.

7. the chromatographic analysis is a liquid chromatographic analysis; 7. The data analysis system according to claim 1, wherein the analysis conditions include, as the parameters, at least one of the following: type of one or more solvents constituting a mobile phase, a flow rate of each of the one or more solvents, a temperature of a separation column, and a sample injection amount.

8. The data analysis system according to claim 1 , wherein the regression analysis is a least squares method.

9. The data analysis system according to claim 1 , wherein the regression analysis is Bayesian estimation.

10. an analytical data preparation step in which the degree of peak separation of a plurality of chromatograms obtained by a plurality of chromatographic analyses of the same sample performed under a plurality of analytical conditions is defined as a response, a plurality of parameters included in the analytical conditions is defined as a factor, and the responses and the factors are prepared in a state in which they are associated with each other; a variable setting step of arbitrarily setting at least one of the factors to be a variable; a structure setting step of arbitrarily setting a structure of a model formula that is a basis of an approximation formula showing a relationship of the variables to the response, using the variables set in the variable setting step; a model formula determination step of determining the model formula based on the structure set in the structure setting step; an approximation equation determination step of determining, by regression analysis, coefficients of each term constituting the model equation determined in the model equation determination step, thereby determining the approximation equation.

11. 11. The data analysis method according to claim 10, wherein in the structure setting step, the structure of the model formula is set using a structure and / or a term selected from a plurality of options for the structure of the model formula prepared in advance and / or a plurality of options for terms to be incorporated into the model formula prepared in advance.

12. The data analysis method according to claim 10 or 11, wherein a structure of any one of the model formulas is created in the structure setting step.

13. The data analysis method according to claim 12 , wherein the structure includes at least one term of an arithmetic operation.

14. 14. The data analysis method according to claim 12 or 13, wherein the structure includes at least one term of a square root, a power, an exponential function, or a logarithmic function.

15. the chromatographic analysis is a liquid chromatographic analysis; 15. The data analysis method according to claim 10, wherein the analysis conditions include, as the parameters, at least one of the following: type of one or more solvents constituting a mobile phase, a flow rate of each of the one or more solvents, a temperature of a separation column, and a sample injection amount.

16. The data analysis method according to claim 10 , wherein the regression analysis is a least squares method.

17. The data analysis method according to claim 10 , wherein the regression analysis is Bayesian estimation.

18. A computer program adapted to, when executed on a computer, carry out the data analysis method according to any one of claims 10 to 17.

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