SAMPLE ANALYSIS APPARATUS, SAMPLE ANALYSIS METHOD, PHARMACEUTICAL ANALYSIS APPARATUS, AND PHARMACEUTICAL ANALYSIS METHOD

Abstract

To provide a sample analysis device that can indicate a reasonable confidence interval, as shortening a time required for acquiring necessary data.SOLUTION: A sample analysis device 1 comprises: an acquisition unit 21 that acquires quantitative information on an examined substance existing in a sample; an estimation unit 22 that estimates a parameter posterior distribution of a generalization reaction model generalized by a plurality of reaction models by a Bayes estimation; and a calculation unit 23 that calculates a confidence interval or a quantile point of the quantitative information on the examined substance at an arbitrary time on the basis of the estimated posterior distribution of the parameter by the estimation unit 22.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a sample analyzer and method for analyzing a test substance contained in a sample, and a pharmaceutical analyzer and method for analyzing active ingredients and the like contained in a preparation or the like. [Background technology]

[0002] Stability tests are conducted to evaluate changes in medicines over time. These tests calculate the period during which it is possible to guarantee that the active ingredients of a medicine are within the standard range, or that impurities are below the standard value (validity period). Generally, medicines stored for a certain period in a thermo-hygrostat or similar chamber are subjected to identification and quantification of the active ingredients and impurities using liquid chromatography, and the validity period is calculated based on the results.

[0003] To carry out a stability test, a pharmaceutical needs to be stored for a long period of time. In order to shorten this period, a method of predicting the effective period using a reaction model function (time axis extrapolation) or a method of predicting the effective period under low temperature (low humidity) conditions from the amount of decomposition under high temperature (high humidity) conditions (temperature axis extrapolation) is carried out using the Arrhenius equation. Extrapolation along the time axis is disclosed, for example, in Non-Patent Document 1 below, and extrapolation along the temperature axis is disclosed, for example, in Non-Patent Document 2 below. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] "Evaluation of Stability Test Data for Pharmaceuticals Containing New Active Ingredients" Japan Pharmaceutical Manufacturers Association, Pharmaceutical Publishing Center, March 2005 [Non-Patent Document 2] "ASAPprime (Drug Stability Rapid Assessment Software) WEB Page," FreeThink, [Retrieved May 24, 2021]<URL:https: / / www.ms-scientific.com / products / lifescience / asapprime> Summary of the Invention [Problem to be solved by the invention]

[0005] The results of pharmaceutical stability tests require not only accurate predictions, but also appropriate distributions and confidence intervals. Conventionally, in methods that use model functions, a wide confidence interval is set taking into account model errors, or data is acquired over a sufficiently long period. However, these approaches have led to problems such as an excessively short effective period and a long period of time required to acquire the necessary data.

[0006] An object of the present invention is to provide a sample analysis apparatus and method, and a pharmaceutical analysis apparatus and method, which are capable of presenting a reasonable confidence interval. [Means for solving the problem]

[0007] A sample analyzer according to one aspect of the present invention includes an acquisition unit that acquires quantitative information about a test substance present in a sample, and a generalized reaction model that is generalized by a plurality of reaction models. is read from the storage device, and the generalized reaction model The method includes an estimation unit that estimates the posterior distribution of the parameters by Bayesian estimation, and a calculation unit that calculates a confidence interval or quantile of quantitative information of the test substance at any time based on the posterior distribution of the parameters estimated by the estimation unit.

[0008] A sample analyzer according to another aspect of the present invention includes an acquisition unit that acquires quantitative information about a test substance present in a sample, and a generalized reaction model that is generalized by a plurality of reaction models. is read from the storage device, and the generalized reaction model The method includes an estimation unit that estimates the posterior distribution of the parameters by Bayesian estimation, and a calculation unit that calculates a confidence interval or quantile of the time until quantitative information of the test substance reaches a predetermined threshold based on the posterior distribution of the parameters estimated by the estimation unit.

[0009] A sample analyzer according to another aspect of the present invention includes: an acquisition unit that acquires quantitative information about a test substance present in a sample; Reading out the reaction model stored in the storage device;The apparatus includes an estimation unit that estimates the posterior distribution of parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with a reaction model, and a calculation unit that calculates a confidence interval or a quantile of quantitative information of a test substance at any time based on the posterior distribution of the parameters estimated by the estimation unit.

[0010] A sample analyzer according to another aspect of the present invention includes: an acquisition unit that acquires quantitative information about a test substance present in a sample; Reading out the reaction model stored in the storage device; The apparatus includes an estimation unit that estimates the posterior distribution of parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with a reaction model, and a calculation unit that calculates a confidence interval or a quantile of the time until quantitative information of the test substance reaches a predetermined threshold, based on the posterior distribution of the parameters estimated by the estimation unit.

[0011] The present invention is also directed to a sample analysis method, a pharmaceutical analysis apparatus and a pharmaceutical analysis method. Effect of the Invention

[0012] According to the present invention, it is possible to provide a sample analysis device and method, and a pharmaceutical analysis device and method, which are capable of presenting a reasonable confidence interval. [Brief description of the drawings]

[0013] [Figure 1] 1 is a configuration diagram of a sample analyzer according to an embodiment of the present invention. [Diagram 2] 1 is a functional block diagram of a sample analyzer according to an embodiment of the present invention. [Diagram 3] FIG. 13 is a diagram showing extrapolation along the time axis. [Figure 4] FIG. 1 is a diagram illustrating an example of a reaction model. [Diagram 5] FIG. 13 is a diagram showing extrapolation in the temperature axis direction. [Figure 6] 3 is a flowchart showing an analysis method according to the first embodiment. [Figure 7] FIG. 13 is a diagram showing simulation data. [Figure 8] FIG. 13 is a diagram showing the posterior distribution of peak area ratios estimated by Bayesian estimation using simulation data. [Figure 9] 13 is a flowchart showing an analysis method according to a first modified example of the first embodiment. [Figure 10] 13 is a flowchart showing an analysis method according to a second embodiment. [Figure 11] 13 is a flowchart showing an analysis method according to a modified example of the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] Next, a sample analyzing apparatus and method and a pharmaceutical analyzing apparatus and method according to embodiments of the present invention will be described with reference to the accompanying drawings.

[0015] (1) Configuration of the sample analyzer FIG. 1 is a configuration diagram of a sample analyzer 1 according to an embodiment. The sample analyzer 1 of this embodiment acquires measurement data MD of a sample obtained by a liquid chromatograph, a gas chromatograph, a mass spectrometer, or the like. The measurement data MD has quantitative information of a test substance present in the sample. Specifically, the measurement data MD has data on the peak area ratio of the test substance present in the sample. In this embodiment, a case where a pharmaceutical product (a pharmaceutical product or an active pharmaceutical ingredient) is used as the sample will be described as an example. Specifically, in this embodiment, the measurement data MD is data on the ratio of the peak area of ​​an impurity to the peak area of ​​an active ingredient contained in the pharmaceutical. The measurement data MD has data on the peak area ratio for a plurality of times.

[0016] The sample analyzer 1 of this embodiment is configured with a personal computer. As shown in Figure 1, the sample analyzer 1 includes a CPU (Central Processing Unit) 11, a RAM (Random Access Memory) 12, a ROM (Read Only Memory) 13, an operation unit 14, a display 15, a storage device 16, a communication interface (I / F) 17, and a device interface (I / F) 18.

[0017] The CPU 11 performs overall control of the sample analyzer 1. The RAM 12 is used as a work area when the CPU 11 executes a program. The ROM 13 stores various data, programs, etc. The operation unit 14 accepts input operations by the user. The operation unit 14 includes a keyboard, a mouse, etc. The display 15 displays information such as analysis results. The storage device 16 is a storage medium such as a hard disk. The storage device 16 stores a program P1 and measurement data MD.

[0018] Program P1 estimates possible values ​​(posterior distribution) of parameters of a generalized reaction model generalized by multiple reaction models by Bayesian estimation. Program P1 also estimates possible values ​​(posterior distribution) of parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with a reaction model. Program P1 also calculates a confidence interval or quantile of quantitative information of a test substance at any time based on the posterior distribution of the estimated parameters. Program P1 also calculates a confidence interval or quantile of the time until the quantitative information of a test substance reaches a predetermined threshold value based on the posterior distribution of the estimated parameters.

[0019] The communication interface 17 is an interface for performing wired or wireless communication with other computers. The device interface 18 is an interface for accessing a storage medium 19 such as a CD, a DVD, or a semiconductor memory.

[0020] (2) Functional configuration of the sample analyzer Fig. 2 is a block diagram showing the functional configuration of the sample analyzer 1. In Fig. 2, the control unit 20 is a functional unit that is realized by the CPU 11 executing the program P1 while using the RAM 12 as a work area. The control unit 20 includes an acquisition unit 21, an estimation unit 22, a calculation unit 23, and an output unit 24. In other words, the acquisition unit 21, the estimation unit 22, the calculation unit 23, and the output unit 24 are functional units that are realized by the execution of the program P1. In other words, each of the functional units 21 to 24 can be said to be a functional unit provided in the CPU 11.

[0021] The acquisition unit 21 inputs the measurement data MD. For example, the acquisition unit 21 inputs the measurement data MD from another computer or an analysis device via the communication interface 17. Alternatively, the acquisition unit 21 inputs the measurement data MD stored in the storage medium 19 via the device interface 18.

[0022] The estimation unit 22 estimates the posterior distribution of the parameters of the generalized reaction model by Bayesian estimation using the measurement data MD. The generalized reaction model is a model generalized by a plurality of reaction models. The estimation unit 22 also estimates the posterior distribution of the parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with the reaction model.

[0023] The calculation unit 23 calculates a confidence interval or a quantile of the quantitative information of the test substance at any time, based on the posterior distribution of the parameters estimated by the estimation unit 22. The calculation unit 23 also calculates a confidence interval or a quantile of the time until the quantitative information of the test substance reaches a predetermined threshold, based on the posterior distribution of the parameters estimated by the estimation unit 22.

[0024] The output unit 24 causes the display 15 to display the confidence interval or quantile of the quantitative information of the test substance. The output unit 24 also causes the display 15 to display the confidence interval or quantile of the time until the quantitative information of the test substance reaches a predetermined threshold.

[0025] A case will be described in which the program P1 is stored in the storage device 16 as an example. In another embodiment, the program P1 may be provided by being stored in a storage medium 19. The CPU 11 may access the storage medium 19 via the device interface 18, and store the program P1 stored in the storage medium 19 in the storage device 16 or the ROM 13. Alternatively, the CPU 11 may access the storage medium 19 via the device interface 18, and execute the program P1 stored in the storage medium 19.

[0026] (3) Prediction based on measurement data (3-1) Extrapolation along the time axis Before describing the analysis method using the sample analyzer 1 of this embodiment, we will explain extrapolation in the time axis direction based on the measurement data MD that is the basis for carrying out the analysis method of this embodiment. Figure 3 is a diagram showing extrapolation in the time axis direction. In Figure 3, the horizontal axis is the number of days (hours) and the vertical axis is the ratio of the peak area of ​​the impurities to the peak area of ​​the main component. In the case of medicines, the vertical axis is the ratio of the peak area of ​​the impurities to the peak area of ​​the active ingredient.

[0027] In FIG. 3, the plotted points are the measurement data MD. The measurement data MD is data of the peak area ratio acquired over a number of days. In the example of FIG. 3, the measurement data MD is data acquired from the first day to around 400 days. A model M1 shown in the figure is fitted by executing regression on this acquired measurement data MD. By fitting the model M1, the peak area ratio in future days such as 600 days and 800 days is estimated from the measurement data MD up to about 400 days. By fitting the model M1 in this way, the peak area ratio is extrapolated in the time axis direction. Similarly, by fitting the model M1, it is also possible to interpolate the peak area ratio in the time axis direction.

[0028] FIG. 4 is a diagram showing an example of a reaction model. 4In the figure, each reaction model is expressed in two forms: differential form and integral form. In the figure, α is the conversion rate, a value between 0 and 1 that indicates the degree of reaction progress. k is the reaction rate constant. By applying one of the reaction models to the measurement data MD and estimating parameters such as k by regression, extrapolation (and interpolation) to the time axis becomes possible. When regressing using the differential form, it is necessary to solve the differential equation by transforming it into dα / dt=kf(α), but it has the characteristic that the model formula is easier to generalize than the integral form.

[0029] (3-2) Extrapolation in temperature direction Next, the extrapolation in the temperature axis direction based on the measurement data MD that is the basis for carrying out the analysis method of this embodiment will be described. Fig. 5 is a diagram showing the extrapolation in the temperature axis direction. In Fig. 5, the horizontal axis is the number of days (time), and the vertical axis is the ratio of the peak area of ​​the impurities to the peak area of ​​the main component. In the case of medicines, the vertical axis is the ratio of the peak area of ​​the impurities to the peak area of ​​the active ingredient.

[0030] As in FIG. 3, the plotted points in FIG. 5 are measurement data MD, which are peak area ratio data obtained over multiple days. 5 In the figure, the black circles represent measurement data MD acquired under high temperature conditions (harsh conditions), and the black triangles represent measurement data MD acquired under low temperature conditions (normal storage conditions). 5 In the example above, the measurement data MD under both high and low temperature conditions are data acquired from the first day to around the 60th day. Then, by using the Arrhenius equation shown below, the data under low temperature conditions can be predicted from the measurement data MD acquired under high temperature conditions. This allows the peak area ratios under low temperature conditions (normal storage conditions) to be estimated for future days such as 100 days, 200 days, 1 year, and 2 years. In this way, the peak area ratios are extrapolated in the temperature axis direction.

[0031] The reaction rate constant k for a single reaction does not change when the temperature and humidity are constant, but when they change, it can be assumed to follow the Arrhenius equation shown in Equation 1 or the modified Arrhenius equation shown in Equation 2.

[0032]

number

[0033]

number

[0034] In Equation 1 and Equation 2, R is the gas constant, T is the absolute temperature, and H is the relative humidity. A is the frequency factor, E is the activation energy, and B is a parameter for humidity. The parameters (A, E, B) are specific to each reaction, but do not necessarily hold true under conditions where the physical properties change, such as in the case of non-crystals or in the case of very high temperature and humidity. If the time it takes for a sample to decompose to a certain amount is t, then k×t is constant. Therefore, by obtaining the parameters (A, E, B) for an unknown reaction from the measurement data MD obtained at multiple temperatures or humidities, the measurement results under harsh conditions can be used to predict the results under normal storage conditions, as shown in Figure 5. Here, we have explained the extrapolation along the temperature axis, but the same method is used for extrapolation along the humidity axis.

[0035] (4) First embodiment Next, an analysis method according to the first embodiment will be described with reference to the flowchart in Fig. 6. The analysis method according to the first embodiment is extrapolation along the time axis using the reaction model described in (3-1). The flowchart in Fig. 6 shows processing executed by the CPU 11 shown in Fig. 1. That is, the processing is executed by each of the functional units 21 to 24 shown in Fig. 2 by the CPU 11 operating the program P1 while using hardware resources such as the RAM 12.

[0036] In step S11, the acquisition unit 21 acquires quantitative information on the test substance present in the sample. Specifically, the acquisition unit 21 acquires data on the ratio of the peak area of ​​the impurity to the peak area of ​​the active ingredient contained in the medicine. Next, in step S12, the estimation unit 22 estimates the posterior distribution of the parameters of the generalized reaction model generalized by multiple reaction models by Bayesian estimation.

[0037] The generalized reaction model will now be described. When it is difficult to narrow down a specific reaction model from the measurement data MD, multiple reaction models are generalized. Equation 3 and Equation 4 are examples of the generalized reaction model.

[0038]

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[0039]

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[0040] Equation 3 is an example of constructing a generalized reaction model by adding multiple reaction models. This generalized reaction model is a model obtained by adding the P2 model and the D1 model among the reaction models shown in FIG. 4. Equation 4 is an example of a generalized reaction model constructed by including multiple reaction models. This generalized reaction model is a model that includes the F1 model and the F2 model among the reaction models shown in FIG. 4.

[0041] The estimation unit 22 applies the generalized response model shown in the formulas 3 and 4, etc., performs Bayesian estimation using the measurement data MD acquired by the acquisition unit 21, and acquires the posterior distribution of the parameters.

[0042] An example of the analysis method of this embodiment will be described using simulation data SD instead of measurement data MD. Fig. 7 is a diagram showing simulation data SD. Simulation data SD is data of peak area ratios from 0 to about 300 days. This simulation data SD is data created based on a reaction function TD (true function).

[0043] Fig. 8 shows the posterior distribution of the response model estimated by Bayesian estimation after applying a generalized response model to the simulation data SD shown in Fig. 7. In Fig. 8, the shaded area indicates the 95% confidence interval of the posterior distribution of the response model. The dashed line in Fig. 8 is the median of the posterior distribution of the response model. The solid line in Fig. 8 is the response function TD (true function) of the simulation data SD shown in Fig. 7.

[0044] To obtain the probability distribution shown in Fig. 8, an appropriate prior distribution was given to the generalized response model, and Bayesian inference was performed using the simulation data SD. After a warm-up period of a specified number of steps, Bayesian inference was performed by executing a specified number of steps of the Markov chain Monte Carlo method (MCMC method) for statistical calculations.

[0045] Returning to the flowchart of Fig. 6, next, in step S13, the calculation unit 23 calculates a confidence interval or a quantile of the quantitative information of the test substance at any time based on the posterior distribution of the reaction model estimated by the estimation unit 22. That is, the calculation unit 23 calculates a confidence interval or a quantile of the value of the peak area ratio at any time. For example, the calculation unit 23 calculates a confidence interval or a quantile of one year, two years, three years, etc., for the peak area ratio of the impurity to the active ingredient contained in the medicine. The calculated confidence interval or quantile may be displayed on the display 15 by the output unit 24.

[0046] Even when prediction is performed by combining multiple reaction models, if parameter values ​​that reduce the error for the acquired data are calculated, the effect of the analysis method of this embodiment cannot be obtained. The method of calculating parameter values ​​that reduce the error is excellent in terms of obtaining a model function that fits well from a model that can be expressed, but it cannot be said to be appropriate when it is desired to calculate a confidence interval while taking into account the possibility that it follows another model.

[0047] For example, consider constructing a response model y=ax+bx^2 as a model that adds a linear model y=ax and a quadratic function model y=bx^2. This model can express two models and their additive models. Even if the acquired data "actually follows a linear model, but has become a quadratic function due to measurement error," if you use this model to fit the data to reduce the error, it will become a quadratic function, and the possibility that it is a linear model will not be taken into account.

[0048] In this embodiment, the parameters are estimated by applying an approach based on Bayes' theory to this model. In Bayes' estimation, instead of obtaining parameter values ​​that reduce the error, a "distribution" of the parameters is obtained after setting a reasonable error distribution and prior distribution. Therefore, even in the above case where "it actually follows a linear model, but becomes a quadratic function due to measurement error," it is possible to obtain a parameter distribution that takes into account the case where it appears to be a linear model due to error. In addition, in the example of generalization by addition shown in Equation 3, it is also possible to take into account the case where reactions occur in parallel. In other words, a model can be constructed even when two reactions of the same type occur in parallel. On the other hand, the example of generalization by inclusion shown in Equation 4 has the advantage that the number of parameters can be reduced compared to the method by addition.

[0049] (5) Modification 1 of the First Embodiment In the above-described first embodiment, the calculation unit 23 calculates a confidence interval or a quantile of the quantitative information of the test substance at any time based on the posterior distribution of the parameters estimated by the estimation unit 22. In the first modification of the first embodiment, a confidence interval of the time until the quantitative information of the test substance reaches a predetermined threshold is calculated.

[0050] Fig. 9 is a flowchart according to the first modification. Steps S21 and S22 are similar to steps S11 and S12 described in Fig. 6. In step S21, the acquisition unit 21 acquires data on the ratio of the peak area of ​​impurities to the peak area of ​​an active ingredient contained in a medicine. In step S22, the estimation unit 22 estimates the posterior distribution of parameters of a generalized reaction model generalized by multiple reaction models by Bayesian estimation.

[0051] In step S23, the calculation unit 23 calculates a confidence interval or a quantile of the time until the quantitative information of the test substance reaches a predetermined threshold, based on the posterior distribution of the parameters estimated by the estimation unit 22. For example, the calculation unit 23 calculates a confidence interval or a quantile of the number of days (hours) until the peak area ratio of the impurity reaches a predetermined threshold. This makes it possible to present a confidence interval or a quantile of the effective storage period of the medicine when an acceptable value for the peak area ratio of the impurity of the medicine is set.

[0052] (6) Modification 2 of the First Embodiment In the analysis method using Bayesian estimation according to the first embodiment, more efficient estimation is possible by determining an accelerated reaction. When the quadratic approximation of the measurement data MD is positive, the reaction model function has a characteristic of being downwardly convex. This indicates that the reaction of the sample proceeds at an accelerated rate. Therefore, the measurement data MD is subjected to a quadratic approximation, and processing is switched depending on whether or not it is possible to reject the fact that the quadratic coefficient is positive.

[0053] (6-1: If we can reject that the quadratic coefficient is positive) Bayesian estimation is performed by excluding reaction models that show an accelerated reaction from the reaction model candidates. Specifically, in the case of generalization by addition, the accelerated reaction models are excluded from the candidates. In addition, in the case of generalization by inclusion, restrictions are placed on the parameter ranges or some parameters are deleted. In this way, if the possibility of an accelerated reaction can be rejected from the measurement data MD, more accurate Bayesian estimation can be performed by placing restrictions on the generalized reaction model.

[0054] (6-2: The positive second-order coefficient cannot be rejected, but the material decomposes to the standard value under the temperature and humidity conditions.) We perform Bayesian estimation while including the accelerated response model. Because the active ingredient has already been decomposed to the reference value, it is unlikely that the confidence interval of the posterior distribution will widen significantly.

[0055] (6-3: The second-order coefficient cannot be rejected as positive, but it has not been decomposed to the criterion value) When Bayesian estimation is performed including an accelerated reaction model, the confidence interval of the posterior distribution may become significantly wider. In this case, it becomes difficult to present a practical confidence interval or quantile. Therefore, measurement data MD is continued to be acquired until the decomposition of the active ingredient reaches the reference value. While continuing to acquire measurement data MD, judgments (6-1) to (6-3) are made again.

[0056] In this way, according to Modification 2, the accuracy of the estimation result by Bayesian estimation can be improved by rejecting cases where the reaction proceeds at an accelerated rate. When an accelerated reaction model is used as is to perform extrapolation in the time axis direction, there is a problem that minute errors become larger over time and the confidence interval becomes significantly wider, but according to Modification 2, such a problem can be avoided.

[0057] (7) Modification of the First Embodiment 3 Variations 3 is a method for probabilistically selecting multiple response models when constructing a generalized response model.

[0058] (7-1: Add two or more reaction models together to obtain the probability that each reaction model will be selected) As described above, a generalized reaction model is constructed by addition or inclusion. At this time, by adding new parameters or changing the distribution settings, the probability that the actual reaction follows the reaction model can be obtained. For example, if the differential form P2 model and D1 model are candidates, a new discrete parameter p that takes two values ​​{0, 1} is added as shown in formula 5.

[0059]

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[0060] The distribution of p can be obtained by performing Bayesian estimation on the generalized response model shown in equation 5. Here, p is a discrete parameter that takes on either 0 or 1. If the "probability of taking p=0" is the probability that the D1 model is selected, and the "probability of taking p=1" is the probability that the P2 model is selected, then the probability that the measurement data MD follows a specific model can be obtained. The same is true for generalization using three or more response models. Furthermore, it is also possible to construct the generalized response model shown in equation 6.

[0061]

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[0062] In formula 6, we can obtain the probability of taking p1=0, p2=1, the probability of taking p1=1, p2=0, and the probability of taking p1=1, p2=1, so it is possible to include parallel patterns as candidates. Also, instead of adding a discrete parameter p, we can consider a method of imposing a spike and slab distribution (a combination of the discrete probability of taking 0 and a continuous distribution) on k.

[0063] (7-2: Discretize the order parameters of the generalized model and obtain the probability that each model will be selected) For example, when the differential form P2 model and D1 model are candidates, as shown in Equation 7, the following generalized model using parameters (c, m, n) is considered.

[0064]

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[0065] In this case, the P2 model f(α) = 2α^(1 / 2) can be expressed as (c,m,n) = (2,0.5,0), and the D1 model f(α) = 1 / (2α) can be expressed as (c,m,n) = (0.5,-1,0). Therefore, similar to (7-1), by constructing a generalized response model as shown in equation 8, making the possible values ​​of the parameters (c,m,n) discrete, and performing Bayesian estimation, it is possible to obtain the probability of following a specific response model.

[0066]

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[0067] (7-3: Prepare two or more prior distributions and obtain the possible probabilities for each prior distribution set) For example, when the differential form P2 model and D1 model are candidates, a generalized model using parameters (c, m, n) as shown in Equation 9 is considered, similar to (7-1).

[0068]

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[0069] In this case, instead of making the possible values ​​of the parameters (c, m, n) discrete, it is possible to achieve something similar by preparing multiple sets of prior distributions for the parameters (c, m, n). To take an extreme example, prior distribution X1 assumes that (c, m, n) is distributed to only one point (2, 0.5, 0) (other parameters are set appropriately). If (c, m, n) is distributed to only one point (0.5, -1, 0), and prior distribution X2 similar to prior distribution X1 is prepared for the rest, and estimation is performed assuming that one of the two prior distributions is selected, the probability that the two prior distribution sets can be taken is obtained, and the same effect as (7-2) can be obtained. In addition, when setting a prior distribution, it is possible to specify it as a distribution rather than just a single point, so it is possible to specify a "group" of model functions with a range, and it is possible to set an appropriate prior distribution for each group for parameters other than the parameters (c, m, n). In addition, generalized expressions for addition such as (7-1) can also be handled by prior distributions in the same way.

[0070] (8) Second embodiment Next, an analysis method according to the second embodiment will be described with reference to the flowchart in Fig. 10. The analysis method according to the second embodiment is an extrapolation in the temperature axis direction using the Arrhenius equation or the modified Arrhenius equation described in (3-2). The flowchart in Fig. 10 shows the process executed by the CPU 11 shown in Fig. 1.

[0071] In step S31, the acquisition unit 21 acquires quantitative information on the test substance present in the sample. Specifically, the acquisition unit 21 acquires data on the ratio of the peak area of ​​the impurity to the peak area of ​​the active ingredient contained in the medicine. Here, the measurement data MD acquired in step S31 is data acquired under high temperature conditions (harsh conditions). Next, in step S32, the estimation unit 22 applies the Arrhenius equation (Formula 1) or the modified Arrhenius equation (Formula 2) to the reaction model equation (Formula 8), and estimates the posterior distribution of the parameters (A, E, B, etc.) on the temperature axis and humidity axis and the parameters (m, n, etc.) that determine the reaction model by Bayesian estimation. As a result, the measurement data MD is extrapolated in the temperature axis direction and the time axis direction, and the confidence interval or quantile of the peak area ratio at any time under low temperature conditions (normal storage conditions) can be calculated. In this way, the estimation unit 22 estimates the posterior distribution of the parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with the reaction model.

[0072] Next, in step S33, the calculation unit 23 calculates a confidence interval or a quantile of the quantitative information of the test substance at an arbitrary time based on the posterior distribution of the parameters estimated by the estimation unit 22. That is, the calculation unit 23 calculates a confidence interval or a quantile of the value of the peak area ratio at an arbitrary time. For example, the calculation unit 23 calculates a confidence interval or a quantile of one year, two years, three years, etc., for the peak area ratio of an impurity to an active ingredient contained in a pharmaceutical. The calculated confidence interval or quantile may be displayed on the display 15 by the output unit 24.

[0073] (9) Modification of the Second Embodiment In the second embodiment, the calculation unit 23 calculates a confidence interval or a quantile of the quantitative information of the test substance at any time based on the posterior distribution of the parameters estimated by the estimation unit 22. In a modification of the second embodiment, a confidence interval of the time until the quantitative information of the test substance reaches a predetermined threshold is calculated.

[0074] Fig. 11 is a flowchart according to the modified example. Steps S41 and S42 are the same as steps S31 and S32 described in Fig. 10. In step S43, the calculation unit 23 calculates a confidence interval or a quantile of the time until the quantitative information of the test substance reaches a predetermined threshold based on the posterior distribution of the parameters estimated by the estimation unit 22. For example, the calculation unit 23 calculates a confidence interval or a quantile of the number of days (hours) until the peak area ratio of the impurity reaches a predetermined threshold. This makes it possible to present a confidence interval or a quantile of the effective storage period of the medicine when an acceptable value of the peak area ratio of the impurity of the medicine is set.

[0075] (10) Other modifications In each of the above-described embodiments, the sample analyzer 1 is a pharmaceutical analyzer. The sample analyzer 1 of the present embodiments can be used to obtain quantitative information on test substances in various samples other than pharmaceuticals. The list of reaction models shown in FIG. 4 is an example. The reaction model to which the analysis method of the present embodiments is applied is not particularly limited.

[0076] (11) Description It will be appreciated by those skilled in the art that the exemplary embodiments described above are examples of the following aspects.

[0077] (Section 1) A sample analyzer according to one embodiment comprises: an acquisition unit for acquiring quantitative information of a test substance present in a sample; Generalized reaction model generalized by multiple reaction models is read from the storage device, and the generalized reaction model An estimation unit that estimates the posterior distribution of the parameters of by Bayesian estimation; A calculation unit calculates a confidence interval or a quantile of the quantitative information of the test substance at an arbitrary time based on the posterior distribution of the parameters estimated by the estimation unit.

[0078] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0079] (Section 2) A sample analyzer according to another aspect of the present invention comprises: an acquisition unit for acquiring quantitative information of a test substance present in a sample; Generalized reaction model generalized by multiple reaction models is read from the storage device, and the generalized reaction model An estimation unit that estimates the posterior distribution of the parameters of by Bayesian estimation; A calculation unit calculates a confidence interval or a quantile of the time until the quantitative information of the test substance reaches a predetermined threshold based on the posterior distribution of the parameters estimated by the estimation unit.

[0080] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0081] (Section 3) In the sample analyzer according to claim 1 or 2, The estimation unit may probabilistically select one of the plurality of reaction models.

[0082] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0083] (Section 4) In the sample analyzer according to claim 1 or 2, The estimation unit may estimate a posterior distribution by Bayesian estimation by setting combinations of the multiple response models as multiple prior distributions, and select the multiple response models based on the estimated posterior distributions.

[0084] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0085] (Section 5) In the sample analyzer according to any one of claims 1 to 4, The generalized response model may be obtained by adding up the multiple response models.

[0086] It is also possible to apply an appropriate reaction model to complex reactions.

[0087] (Section 6) In the sample analyzer according to any one of claims 1 to 4, The generalized reaction model may be one model that encompasses the multiple reaction models.

[0088] It is also possible to apply an appropriate reaction model to complex reactions.

[0089] (Section 7) In the sample analyzer according to any one of claims 1 to 6, The estimation unit may switch between the plurality of reaction models to be applied depending on whether or not the reaction of the sample includes an accelerating reaction.

[0090] The accuracy of the estimation results obtained by Bayesian estimation can be improved.

[0091] (Section 8) 8. The sample analyzer according to claim 7, The estimation unit may use a quadratic approximation to determine whether or not an accelerating response is included.

[0092] The accuracy of the estimation results obtained by Bayesian estimation can be improved.

[0093] (Section 9) A sample analyzer according to another aspect of the present invention comprises: an acquisition unit for acquiring quantitative information of a test substance present in a sample; Reading out the reaction model stored in the storage device; Arrhenius equation or modified Arrhenius equation and The above an estimation unit that estimates a posterior distribution of parameters by Bayesian estimation by combining the parameter distribution and a reaction model; A calculation unit calculates a confidence interval or a quantile of the quantitative information of the test substance at an arbitrary time based on the posterior distribution of the parameters estimated by the estimation unit.

[0094] It is possible to provide reasonable confidence intervals while reducing the time required to obtain the necessary data.

[0095] (Section 10) A sample analyzer according to another aspect of the present invention comprises: an acquisition unit for acquiring quantitative information of a test substance present in a sample; Reading out the reaction model stored in the storage device; Arrhenius equation or modified Arrhenius equation and The above an estimation unit that estimates a posterior distribution of parameters by Bayesian estimation by combining the parameter distribution and a reaction model; A calculation unit calculates a confidence interval or a quantile of the time until the quantitative information of the test substance reaches a predetermined threshold based on the posterior distribution of the parameters estimated by the estimation unit.

[0096] It is possible to provide reasonable confidence intervals while reducing the time required to obtain the necessary data.

[0097] (Section 11) A sample analysis method according to another embodiment includes the steps of: Obtaining quantitative information about the analyte present in the sample; Generalized reaction model generalized by multiple reaction models is read from the storage device, and the generalized reaction model A step of estimating the posterior distribution of the parameters of by Bayesian estimation; and calculating a confidence interval or quantile of the quantitative information of the test substance at any time based on the posterior distribution of the estimated parameters.

[0098] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0099] (Section 12) A sample analysis method according to another embodiment includes the steps of: Obtaining quantitative information about the analyte present in the sample; Generalized reaction model generalized by multiple reaction models is read from the storage device, and the generalized reaction model A step of estimating the posterior distribution of the parameters of by Bayesian estimation; The method includes a step of calculating a confidence interval or quantile of the time until the quantitative information of the test substance reaches a predetermined threshold value based on the posterior distribution of the estimated parameters.

[0100] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0101] (Section 13) A sample analysis method according to another embodiment includes the steps of: Obtaining quantitative information about the analyte present in the sample; Reading out the reaction model stored in the storage device; Arrhenius equation or modified Arrhenius equation and The above a step of estimating a posterior distribution of parameters by Bayesian estimation by combining the response model with the and calculating a confidence interval or quantile of the quantitative information of the test substance at any time based on the posterior distribution of the estimated parameters.

[0102] It is possible to provide reasonable confidence intervals while reducing the time required to obtain the necessary data.

[0103] (Section 14) A sample analysis method according to another embodiment includes the steps of: Obtaining quantitative information about the analyte present in the sample; Reading out the reaction model stored in the storage device; Arrhenius equation or modified Arrhenius equation and The above a step of estimating a posterior distribution of parameters by Bayesian estimation by combining the response model with the The method includes a step of calculating a confidence interval or quantile of the time until the quantitative information of the test substance reaches a predetermined threshold value based on the posterior distribution of the estimated parameters.

[0104] It is possible to provide reasonable confidence intervals while reducing the time required to obtain the necessary data.

[0105] (Section 15) A pharmaceutical analysis device according to another aspect includes: In the sample analyzer according to claim 1, 2, 9 or 10, the sample includes a formulation or an active ingredient, and the test substance includes an active ingredient or an impurity present in the formulation or the active ingredient.

[0106] The reliability of the estimation results obtained by Bayesian estimation can be improved.

[0107] (Section 16) A pharmaceutical analysis method according to another embodiment includes the steps of: In the sample analysis method according to item 11, 12, 13 or 14, the sample contains a formulation or a drug substance, and the test substance contains an active ingredient or an impurity present in the formulation or the drug substance.

[0108] The reliability of the estimation results obtained by Bayesian estimation can be improved. [Explanation of symbols]

[0109] 1... sample analyzer, 11... CPU, 12... RAM, 13... ROM, 14... operation unit, 15... display, 16... storage device, 21... acquisition unit, 22... estimation unit, 23... calculation unit, 24... output unit, P1... program, MD... measurement data

Claims

1. an acquisition unit for acquiring quantitative information of a test substance present in a sample; an estimation unit that reads out a reaction model stored in a storage device and estimates a posterior distribution of parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with the reaction model; a calculation unit that calculates a confidence interval or a quantile of the quantitative information of the test substance at an arbitrary time based on the posterior distribution of the parameters estimated by the estimation unit.

2. an acquisition unit for acquiring quantitative information of a test substance present in a sample; an estimation unit that reads out a reaction model stored in a storage device and estimates a posterior distribution of parameters by Bayesian estimation by combining the Arrhenius equation or the modified Arrhenius equation with the reaction model; A calculation unit that calculates a confidence interval or quantile of the time until the quantitative information of the test substance reaches a predetermined threshold based on the posterior distribution of the parameters estimated by the estimation unit.

3. Obtaining quantitative information about the analyte present in the sample; A step of reading out a reaction model stored in a storage device, and estimating a posterior distribution of parameters by Bayesian estimation by combining the reaction model with the Arrhenius equation or the modified Arrhenius equation; and calculating a confidence interval or quantile of the quantitative information of the test substance at any time based on the posterior distribution of the estimated parameters.

4. Obtaining quantitative information about the analyte present in the sample; A step of reading out a reaction model stored in a storage device, and estimating a posterior distribution of parameters by Bayesian estimation by combining the reaction model with the Arrhenius equation or the modified Arrhenius equation; A sample analysis method comprising a step of calculating a confidence interval or quantile of the time it takes for the quantitative information of the test substance to reach a predetermined threshold based on the posterior distribution of the estimated parameters.

5. A pharmaceutical analysis apparatus, wherein the sample comprises a formulation or an active pharmaceutical ingredient, and the test substance comprises an active ingredient or an impurity present in the formulation or the active pharmaceutical ingredient, in the sample analysis apparatus described in claim 1 or claim 2.

6. A pharmaceutical analysis method, in which the sample comprises a formulation or an active pharmaceutical ingredient, and the test substance comprises an active ingredient or an impurity present in the formulation or the active pharmaceutical ingredient, in the sample analysis method described in claim 3 or claim 4.

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