Data analysis system and computer program

Abstract

To enable a user to easily grasp reliability of a regression model.SOLUTION: A data analysis system includes: a data storage section 2 that stores a plurality of analysis results respectively obtained by a plurality of analyses performed under a plurality of analysis conditions and a plurality of parameters included in the analysis conditions when each analysis result is a response and each parameter is a factor, and the response and the factor are associated with each other; a data processor 4; and a display 8 electrically connected to the data processor 4. The data processor 4 is configured to create a regression model indicating a relationship of a variable with the response by determining coefficients of each of terms constituting a model expression on the basis of a predetermined model expression, in which the factor is the variable, using a predetermined statistical analysis algorithm, and the data processor 4 is configured to create reliability information, which can be referred by a user on the display 8, by quantifying reliability of the regression model on the basis of the relationship with the response.SELECTED DRAWING: Figure 1

Description

[Technical Field]

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

[0002] When considering analytical conditions for liquid chromatography analysis, the relationship between each factor of the analytical conditions (for example, column temperature and solvent concentration in the case of chromatography analysis) and the response (for example, the degree of resolution between component peaks on a chromatogram in the case of chromatography analysis aimed at separating two components) is plotted as a two-dimensional graph (such as a heat map). Data analysis systems (software) that create such two-dimensional graphs also exist (see, for example, https: / / www.jmp.com / ja_jp / offers / doe-design-space.html).

[0003] The created two-dimensional graph displays contour lines connecting coordinate points where the target response takes a specific value, making it easy to visually grasp the areas where the response is above or below a specific value. Therefore, by using such a two-dimensional graph, it becomes easy to determine what analysis conditions should be selected to obtain the target response.

[0004] Incidentally, to draw a two-dimensional graph like the one above, data showing the relationship between each factor of the analysis conditions and the response is required, but it is not realistic to actually measure the response for all coordinate points (combinations of factor parameters) on a two-dimensional graph. For example, if we assume that each parameter of each factor of the analysis conditions has 10 levels (10 coordinate points), then for three factors, 10 3It is necessary to conduct 1000 experiments to measure the response. Therefore, it is common to conduct experiments under analysis conditions at coordinate points that are far fewer than the coordinate points on a two-dimensional graph, measure the response, create an equation called a regression model using the obtained measurement data, and link predicted values ​​based on the created regression model to the remaining coordinate points for which no experiments were conducted. Summary of the Invention [Problem to be solved by the invention]

[0005] As mentioned above, a regression model is required to create a two-dimensional graph showing the relationship between factors and responses. A regression model is created by determining the coefficients of each term in a model equation, based on a model equation consisting of terms with undetermined coefficients, using statistical analysis algorithms such as the least squares method. While a regression model statistically predicts the relationship between each factor and a response, its predictions are not necessarily reliable. For example, if measurement data with large variability and measurement data with small variability are available, the regression models created using these measurement data may produce the same equation. However, the reliability of these regression models is not uniform; a regression model created using measurement data with small variability is considered more reliable. Furthermore, if the structure of the underlying model equation (the types and number of terms included in the model equation) is inappropriate, the regression model will not be created accurately. In other words, the reliability of a regression model depends on the variability of the response of the measurement data used in the regression analysis and the underlying model equation.

[0006] However, previous data analysis systems did not provide users with information about the reliability of the regression model they created, which meant that users did not know how much they could rely on information such as two-dimensional graphs displayed by the data analysis system when determining analysis conditions.

[0007] The present invention has been made in view of the above problems, and has an object to enable a user to easily grasp the reliability of a regression model. [Means for solving the problem]

[0008] The data analysis system according to the present invention comprises 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 defined as a response and a plurality of parameters included in the analytical conditions, each of which is defined as a factor, and associates the responses with the factors; a data processing unit configured to perform calculations using data stored in the data storage unit; and a display electrically connected to the data processing unit, wherein the data processing unit is configured to create a regression model showing the relationship of the variables to the responses by using a predetermined model formula having the factors as variables and determining the coefficients of each term constituting the model formula using a predetermined statistical analysis algorithm, and the data processing unit is configured to create reliability information that a user can refer to on the display by quantifying the reliability of the regression model based on the relationship with the responses. [Effects of the Invention]

[0009] In the data analysis system according to the present invention, the data processing unit quantifies the reliability of the created regression model based on its relationship with the response, and creates reliability information that the user can refer to on the display, allowing the user to easily grasp the reliability of the regression model. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a block diagram illustrating an example of a configuration of a data analysis system. [Figure 2] 10 is a flowchart showing an example of a data analysis process performed in the embodiment. [Figure 3] FIG. 10 is a diagram illustrating an example of a screen displaying reliability information. [Figure 4] This is an example of a two-dimensional graph created based on a regression model. DETAILED DESCRIPTION OF THE INVENTION

[0011] An embodiment of the 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 includes a data storage unit 2, a data processing unit 4, an information input device 6, and a display 8.

[0013] The data storage unit 2 is a storage area for storing analytical data obtained by the analytical device 100, and is realized by a partial area of ​​an information storage device such as a hard disk drive. The analytical device 100 is, for example, a liquid chromatograph. The data processing unit 4 is a function realized by a CPU (central processing unit) executing a predetermined program.

[0014] The data processing unit 4 executes a predetermined data analysis process using the analysis data stored in the data storage unit 2. The process executed by the data processing unit 4 will be described later. 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 needed is output from the data processing unit 4 to the display 8 and displayed on the display 8.

[0015] The data analysis process executed by the data processing unit 4 will be described with reference to the flowchart of FIG.

[0016] As a premise, the data storage unit 2 stores responses (i.e., analysis results such as the degree of separation of peaks in a chromatogram, the number of peaks, and the retention time of each peak) obtained by performing analyses of the same sample while changing multiple factors of the analysis conditions (e.g., mobile phase flow rate, column oven temperature, mobile phase solvent composition, mobile phase solvent mixing ratio, gradient method, sample injection amount, etc.) in association with each parameter of the analysis conditions. The data processing unit 4 reads the analysis data stored in the data storage unit 2 (step 101).

[0017] Next, the data processing unit 4 sets factors to be used as variables from among the factors of the read analysis data (step 102). The factors to be used as variables may be set based on information input by the user, or all factors may be considered as variables. After that, the data processing unit 4 determines a model formula that forms the basis of the regression model (step 103). A model formula is a formula consisting of a sum of terms that use variables and whose coefficients are not yet determined. The structure of the model formula (i.e., what terms are included) may be set arbitrarily by the user, or an existing model formula may be used.

[0018] After determining the model formula, the calculation processing unit 4 uses a predetermined statistical analysis algorithm to determine the coefficient of each term in the model formula, thereby creating a regression model that represents the relationship of each factor to the response (step 104). Statistical analysis algorithms used to determine the coefficient of each term include the least squares method and Bayesian estimation. The statistical analysis algorithm to be used may be freely selected by the user.

[0019] A regression model constructed using the least squares method is generally obtained by matrix calculations or optimization calculations. While several approaches are known for constructing a regression model using Bayesian estimation, the easiest and most accurate method is to use MCMC (Markov Chain Monte Carlo). Details on how to perform Bayesian estimation using MCMC are omitted here, but in summary, the approach involves using random numbers to evaluate the likelihood of each parameter value being realized for observed data through a trial-and-error process, thereby obtaining predicted values ​​and a distribution of parameter values. One of the most common software libraries for performing Bayesian estimation using MCMC is stan (https: / / mc-stan.org / ), and in this example, Bayesian estimation is also performed using stan.

[0020] Furthermore, the calculation processing unit 4 quantifies the dispersion of each response value for the created regression model using a standard deviation or the like, and creates reliability information for the regression model using the numerical values ​​(step 104). The reliability information will be described later, and the created reliability information can be referenced by the user.

[0021] After creating the regression model and the reliability information, the calculation processing unit 4 creates a two-dimensional graph based on the created regression model, which allows the user to easily visually grasp the relationship between the factors and the response (step 105). An example of a two-dimensional graph is one in which contour lines of a predetermined response value are drawn on a plane coordinate system with the factors as the numerical axis.

[0022] Here, the calculation processing unit 4 may be configured to set the amplitude of the contour lines using the numerical values ​​of the variations in the values ​​of each response to the regression model and display them on a two-dimensional graph. In this case, the amplitude of the contour lines may be displayed constantly or only when desired by the user.

[0023] Figure 3 shows an example of a statistical information pane that displays the reliability information of a regression model. This statistical information pane is for a case where Bayesian estimation is used as the statistical analysis algorithm. In this example, retention time (RT) and peak width are used as responses, and statistical information for the regression model (RT prediction formula and peak width prediction formula) that shows the relationship between these responses and multiple factors is displayed in a table.

[0024] The two tables on the left side of this statistical information pane, one above the other, show reliability information: the "mean (standard deviation)" value, which indicates the variance of the response values ​​for the RT prediction formula and the other for the peak width prediction formula, and the "Rhat (standard deviation)" value, which indicates the validity of the model formula underlying the regression model. In this example, Bayesian estimation assumes that responses follow a normal distribution (a mountain-shaped distribution) and that the actually measured responses are values ​​randomly sampled from that normal distribution. The width of the normal distribution is expressed as the standard deviation; the larger the standard deviation, the wider the normal distribution (i.e., the lower the accuracy of the predicted value), and the smaller the standard deviation, the narrower the normal distribution (i.e., the higher the accuracy of the predicted value). When constructing a regression model using Bayesian estimation in this example, the standard deviation is not uniquely determined; rather, the standard deviation itself is estimated from a distribution. The "mean (standard deviation)" is the average value of this distribution of standard deviations. The accuracy of the predicted value can be evaluated based on the magnitude of this mean (standard deviation). Furthermore, the Rhat statistic is known as a statistic used to evaluate the validity of the regression model constructed as a result of Bayesian inference and the estimated parameters of the regression model (for example, the "slope" in the case of simple linear regression). The Rhat statistic is also calculated for the standard deviation of the predicted values ​​mentioned above, and this value is shown as "Rhat (standard deviation)" in Figure 3. The Rhat statistic is approximately 1 if the parameter estimate is valid. An Rhat statistic greater than 1.1 is generally considered to indicate that an estimate has been made but is not valid. As mentioned above, Rhat is a value obtained when using Bayesian inference as a statistical analysis algorithm. When least squares is used as a statistical analysis algorithm, a statistic known as the coefficient of determination is generally used as an evaluation index. This statistic is 1 if the variability in the measured response is completely explained by the predicted values ​​obtained by the predictive model. The more variability that cannot be explained (the worse the predictive performance of the predictive model), the smaller the value becomes. A very poor model that makes no predictions at all may take a negative value. In this way, reliability information is obtained based on the degree of discrepancy between the model formula and the response in each of the Bayesian estimation and least squares method.

[0025] The two tables on the right side of the statistical information pane also display statistical information for each term in the RT prediction formula and peak width prediction formula. Although the calculation methods are different, both Bayesian and least squares methods can obtain distributions of estimated values ​​for each coefficient (parameter). The wider the distribution, the greater the uncertainty of the estimate. Various statistics related to this distribution are listed here. Specifically, these include the mean, standard error, and standard deviation of the coefficient estimates. The 5% and 25% quantiles are called quantiles. If there are 100 predicted values ​​in a distribution, the 5% quantile is the fifth smallest predicted value, and the 25% quantile is the 25th smallest predicted value. While the least squares method algorithmically ensures that this distribution is symmetric, this is not necessarily the case with Bayesian inference. Therefore, various quantile information can be used to evaluate not only the spread of the distribution but also the skewness of the distribution (large skewness is generally considered to indicate a poor model). In this way, it is possible to comprehensively determine whether the estimation of each coefficient is appropriate using various information.

[0026] By referencing the statistical information pane, users can easily grasp the validity of the model formula underlying the regression model and information about the regression model's variability. They can also easily grasp the coefficients of each term that make up the regression model and the variability (reliability) of each coefficient. Furthermore, by viewing the coefficients of each regression model term, users can understand the contribution of each factor to the regression model, i.e., the extent to which each factor influences the response. This facilitates measures such as revising the model formula to improve the reliability of the regression model. For example, if the coefficient of a term is close to zero (e.g., 0.0001), this term contributes very little to the regression model (response). However, because the scale of the original data also matters, a final judgment must be made comprehensively. For example, suppose one factor has a single-digit value but its associated coefficient has a triple-digit value, while another factor has a triple-digit value but its associated coefficient has a single-digit value. In this case, although the coefficients are different, the magnitudes of the original factors are also different, so the magnitudes of the responses resulting from each factor will be similar. In the case of least squares, the p-value calculated when a t-test is performed under the null hypothesis that "the value of the coefficient is 0" is used as a method for determining whether the contribution of a coefficient is small, or whether it is safe to remove a coefficient from the model because it is small. Even if the value of a coefficient is close to 0, if this p-value is below a value determined in advance by the analyst (generally 0.05 or less), it is determined to be a coefficient that makes a large contribution to the model, and if it is above the value determined in advance by the analyst, it is determined to be a coefficient that makes a small contribution to the model.

[0027] Figure 4 shows an example of a two-dimensional graph. In this graph, multiple contour lines of a specific response value are plotted on a two-dimensional graph with a factor (here, AAAA) on the vertical axis and another factor (BBBB) on the horizontal axis. When the user clicks "Settings," a display settings screen opens, allowing the user to select the elements to be displayed on the two-dimensional graph. In this example, the elements that can be displayed on the two-dimensional graph are the measurement point, maximum posterior probability, and credible interval (%). The "credible interval (%)" indicates the amplitude of the contour lines plotted on the two-dimensional graph. By selecting "credible interval (%)," the user can display the error range of each contour line on the two-dimensional graph. The value of this credible interval (%) can be set by the user. When the user sets the value of the credible interval, the range that maintains the set reliability is displayed on the two-dimensional graph.

[0028] When using the statistical information pane and 2D graph described above to search for a region (experimental conditions) where a response above a certain value is obtained, the smaller the standard deviation of the regression model, the more reliable the regression model, and selecting analysis conditions with coordinate points close to the contour lines of the 2D graph will likely result in the desired response value.On the other hand, the larger the standard deviation of the regression model, the less reliable the regression model, and it is necessary to select analysis conditions with coordinate points far enough away from the contour lines of the 2D graph toward the higher numerical values.

[0029] In this way, by combining the statistical information pane, which shows the reliability information of the regression model, with a two-dimensional graph, the accuracy of searching for analytical conditions to obtain the desired response value can be improved.

[0030] The above-described embodiment is merely an example of an embodiment of the present invention. The following is an embodiment of a data analysis system and a computer program according to the present invention.

[0031] In one embodiment of the data analysis system according to the present invention, the 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 defined as a response, and a plurality of parameters included in the analytical conditions, each of which is defined as a factor, and associates the responses with the factors; a data processing unit configured to perform calculations using the data stored in the data storage unit; and a display electrically connected to the data processing unit, wherein the data processing unit is configured to create a regression model showing the relationship of the variables to the responses by using a predetermined statistical analysis algorithm based on a predetermined model formula in which the factors are variables, and the data processing unit is configured to create reliability information that a user can refer to on the display by quantifying the reliability of the regression model based on the relationship with the responses.

[0032] In a first aspect of the above embodiment, the reliability information includes an evaluation value of the variability of the response to the regression model, allowing a user to easily grasp the extent of fluctuation of the regression model.

[0033] In the first aspect, the data processing unit may be configured to create a two-dimensional graph with the factors as scale axes, plot contour lines of specific response values ​​in the two-dimensional graph, and display the contour lines on the display, and the data processing unit may be configured to display amplitudes of the contour lines on the two-dimensional graph based on the evaluation values, thereby allowing a user to easily recognize amplitudes of the contour lines drawn in the two-dimensional graph displayed on the display. The display may be configured so that the user can arbitrarily set the fluctuation range (for example, the range where the reliability is X%) that is desired to be displayed on the display.

[0034] In a second aspect of the above embodiment, the data processing unit is configured to display, on the display, contribution information of each term included in the model formula to the regression model together with the reliability information. This aspect makes it easier for a user to understand to what extent each term (each factor) in the model formula affects the response. This second aspect can be combined with the above first aspect.

[0035] In a third aspect of the above embodiment, the reliability information includes validity information of the model formula based on the degree of deviation of the regression model for each of the responses. This aspect allows a user to easily determine whether the model formula on which the regression model is based is valid, making it easy to review the model formula. This third aspect can be combined with the first and / or second aspect.

[0036] In a fourth aspect of the above embodiment, the statistical analysis algorithm is Bayesian estimation. Observed data, especially when the sample size is small, does not necessarily accurately reflect the distribution of the population (a group with an infinite sample size). Thus, observed data inherently contains uncertainty. Least squares methods construct predictive models that closely fit the observed data, and therefore cannot incorporate this uncertainty. On the other hand, Bayesian estimation has the advantage of enabling the construction of predictive models that incorporate this uncertainty to some extent by (1) treating predicted values ​​and various parameters as probability distributions and (2) introducing the concept of prior distributions. In other words, the predicted distribution of the response and the estimated distribution of each coefficient obtained by Bayesian estimation incorporate this uncertainty to some extent. As mentioned above, the next action based on the results of least squares methods and Bayesian estimation is to "determine the next and subsequent experimental conditions based on the analysis results." Bayesian estimation, which incorporates data uncertainty, has the advantage of being more suitable for achieving this goal. This fourth aspect can be combined with the first, second, and / or third aspects.

[0037] In a fifth aspect of the above embodiment, the statistical analysis algorithm is the least squares method. This fifth aspect can be combined with the first, second, and / or third aspects.

[0038] In a sixth aspect of the above embodiment, the model formula can be arbitrarily set by a user, and the arithmetic processing unit is configured to create the regression model based on the model formula set by the user. This aspect improves the flexibility in creating regression models, and also enables creation of highly accurate regression models. The sixth aspect can be combined with the first, second, third, fourth, and / or fifth aspects.

[0039] One embodiment of the computer program according to the present invention is configured to construct the above-described data analysis system when installed in a computer. [Explanation of symbols]

[0040] 1. Data analysis system 2 Data storage unit 4 Data Processing Unit 6. Information input device 8. Display

Claims

1. a data storage unit that stores a plurality of analysis results obtained by a plurality of analyses executed under a plurality of analysis conditions as responses and a plurality of parameters included in the analysis conditions as factors, and stores the responses and the factors in association with each other; a data processing unit configured to perform a calculation using the data stored in the data storage unit; a display electrically connected to the data processing unit; the data processing unit is configured to create a regression model showing a relationship between the variables and the response by determining coefficients of each term constituting a predetermined model formula based on the predetermined model formula having the factors as variables using a predetermined statistical analysis algorithm; and the data processing unit is configured to generate state reliability information that a user can refer to on the display by quantifying the reliability of the regression model based on a relationship with the response; the reliability information includes an estimate of the variability of the response to the regression model; The data processing unit is configured to create a two-dimensional graph having two scale axes each representing a different factor, and to plot contour lines of specific response values ​​within the two-dimensional graph and display the contour lines on the display; and The data analysis system is configured such that the data processing unit displays the amplitude of the contour lines on the two-dimensional graph based on the evaluation value.

2. 2. The data analysis system according to claim 1, wherein the data processing unit is configured so that the amplitude can be set by a user.

3. A data storage unit that stores a plurality of analysis results obtained by a plurality of analyses performed under a plurality of analysis conditions as responses, a plurality of parameters included in the analysis conditions as factors, and associates the responses with the factors; a data processing unit configured to perform a calculation using the data stored in the data storage unit; a display electrically connected to the data processing unit; the data processing unit is configured to create a regression model showing a relationship between the variables and the response by determining coefficients of each term constituting a predetermined model formula based on the predetermined model formula having the factors as variables using a predetermined statistical analysis algorithm; and the data processing unit is configured to generate state reliability information that a user can refer to on the display by quantifying the reliability of the regression model based on a relationship with the response; The data analysis system is configured such that the data processing unit displays, on the display, information on the degree of contribution of each term included in the model formula to the regression model together with the reliability information.

4. A data storage unit that stores a plurality of analysis results obtained by a plurality of analyses performed under a plurality of analysis conditions as responses, a plurality of parameters included in the analysis conditions as factors, and associates the responses with the factors; a data processing unit configured to perform a calculation using the data stored in the data storage unit; a display electrically connected to the data processing unit; the data processing unit is configured to create a regression model showing a relationship between the variables and the response by determining coefficients of each term constituting a predetermined model formula based on the predetermined model formula having the factors as variables using a predetermined statistical analysis algorithm; and the data processing unit is configured to generate state reliability information that a user can refer to on the display by quantifying the reliability of the regression model based on a relationship with the response; A data analysis system, wherein the reliability information includes validity information of the model formula based on the degree of discrepancy of the regression model for each of the responses.

5. The data analysis system according to claim 1 , wherein the statistical analysis algorithm is Bayesian estimation.

6. The data analysis system according to claim 1 , wherein the statistical analysis algorithm is a least squares method.

7. The model formula can be arbitrarily set by a user, The data analysis system according to claim 1 , wherein the data processing unit is configured to create the regression model based on the model formula set by a user.

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

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