Sustained release preparation prescription optimization method based on machine learning and multi-objective genetic algorithm

Abstract

The invention discloses a sustained release preparation prescription optimization method based on machine learning and a multi-objective genetic algorithm, and relates to the field of medicine prescription optimization. The method specifically comprises the following steps: carrying out covariable screening on sustained release preparation data by adopting self-adaptive Lasso; establishing a repeated measurement data model based on the accumulated release degrees at different time points and the drug prescriptions; and combining the model with NSGA-II to realize a multi-objective optimization process. According to the invention, a variable selection method, a repeated measurement data model establishment method and a multi-target genetic algorithm are combined for the first time, and a sustained-release preparation prescription optimization system based on machine learning and the multi-target genetic algorithm is created, so that sustained-release preparation formula optimization is reasonable and feasible; according to the method, the number of times of exploring the optimal prescription ratio through pre-experiments is greatly reduced, manpower, material resources and financial resources are saved, and the method has practical guiding significance and application value for solving the multi-target optimization problem in the field of medicine and pharmacology and can be popularized to application of the multi-target optimization problem in other fields.

Description

Technical Field

[0001] The present invention relates to the field of pharmaceutical prescription optimization, and in particular to a method for optimizing a sustained-release preparation prescription based on machine learning and a multi-objective genetic algorithm. Background Art

[0002] With the rapid development of modern pharmaceutical preparation technology, sustained-release preparations as the third-generation pharmaceutical preparations have attracted more and more attention from medical professionals and scientific researchers. Sustained-release preparations refer to preparations that release drugs slowly and non-constantly in a specified release medium as required (Xu Wen. Research progress of sustained-release and controlled-release preparations of traditional Chinese medicine [J]. Electronic Journal of General Stomatology, 2019, 6(25):11+20). As its theory and technology become more mature, more and more sustained-release drugs are appearing in our lives as common drugs, such as aminophylline sustained-release tablets and ibuprofen sustained-release capsules. Its advantages are reduced frequency of administration and easy use; stable drug release rate, which can prolong the drug's action time in the body, reduce the peak blood drug concentration, and effectively control the fluctuation of blood drug concentration; timed and positioned release can maximize the drug's efficacy and reduce the occurrence of adverse reactions. Compared with sustained-release preparations, ordinary preparations have the disadvantages of high dosing frequency (1.5 to 3 times that of sustained-release preparations), short half-life, large peak-to-valley ratio of blood drug concentration and low safety factor in drug treatment, which are easy to cause adverse reactions or toxic side effects (Philadelphia, Yao Qin. Characteristics and existing problems of sustained-release preparations in clinical applications [J]. Journal of Clinical Rational Drug Use, 2020, 13(31): 177-179). However, the preparation process of sustained-release preparations is relatively complicated. In order to obtain reliable therapeutic effects, the research and development must strictly control the three links of design, model establishment and condition optimization. The degree to which the cumulative release of sustained-release preparations at each time point reaches the release standard will vary due to different excipient ratios during research and development. Therefore, how to choose the best prescription ratio and determine the best process has always been a hot topic of concern in the pharmaceutical community.

[0003] When building a model, we generally study the regression relationship between a scalar response variable and many related covariates. However, as the number of experimental factors increases, more variables enter the model, and the covariates will become high-dimensional. However, the number of covariates is not necessarily the more the better. Too many variables may lead to reduced model stability or poor interpretability and applicability. At this time, it is necessary to screen the covariates to improve the predictability and interpretability of the model. Therefore, how to correctly and effectively screen variables has always been a hot issue in the statistical modeling process. Variable screening mainly selects some variables from a large number of covariates through certain selection criteria, thereby achieving the purpose of reducing the dimension of covariates. Subset selection, as a traditional method of variable screening, is to scan variables according to various rules and then establish a regression model containing different variables. In order to compare which variables are included in the regression model to achieve the best fitting effect, here is a comparison criterion for the advantages and disadvantages of different models, such as the Cp statistic criterion proposed by Mallows (Mallows CL. Some comments on Cp [J]. Technometrics, 1973, 15 (4): 661-675), Akaike [7] The AIC criterion proposed by Schwarz (SCHWARZ G. Estimating the dimension of a mod [J]. Annals of Statistics, 1978, 6: 461-464) and the BIC criterion proposed by Schwarz (SCHWARZ G. Estimating the dimension of a mod [J]. Annals of Statistics, 1978, 6: 461-464). In order to overcome the disadvantage of the subset selection method of finding the optimal subset through a certain step process, many shrinkage algorithms have been proposed so that important variables can be automatically and one-time selected, such as ridge regression, LASSO, etc. These algorithms achieve variable screening by compressing the estimated coefficients toward 0. However, if there are too many variables entering the model, the use of the subset selection method will not only increase the amount of calculation and algorithm complexity, but also slight changes in the data set will cause significant changes in the results of variable screening.

[0004] In the development and manufacture of sustained-release preparations, in order to ensure the slow release of drugs and prevent sudden release, the Chinese Pharmacopoeia stipulates that the cumulative release at three or more time points should be measured to evaluate the quality of sustained-release preparations. At present, quadratic regression models, multiple linear regression models, etc. are mostly used for optimization modeling of sustained-release preparations at home and abroad, but these traditional modeling methods require the data to be "independent". The cumulative release is the cumulative amount of the drug released at different time points, so the cumulative release at different time points is not independent. The release at the previous time point will affect the release at the next time point, which belongs to repeated measurement data. For repeated measurement data of numerical variables, we often use repeated measurement data analysis of variance, but repeated measurement data analysis of variance requires that the data conform to the normal distribution and cannot have missing values. Once there are missing values, the case can only be deleted, which is a great loss for the sample size. In addition, the generalized estimating equation (GEE) proposed by Liang and Zeger in 1986 (Liang KY, Zeger SL. Longitudinal data analysis using generalized inear models [J]. Biometrics, 1986, 73 (1): 13-22) is also a statistical model commonly used to process longitudinal data. This method introduces nuisance parameters to characterize the conditional correlation structure between the components of the response variable (usually called the working correlation matrix), then constructs an estimating equation containing nuisance parameters, and obtains the estimates of the model regression parameters by solving the system of simultaneous equations. When the working correlation matrix is ​​correctly specified, GEE is usually the most effective parameter estimation method for marginal models. However, when the working correlation matrix is ​​incorrectly specified, the efficiency of GEE estimation may be relatively low. In addition, GEE has the disadvantages of being unable to perform model selection, low estimation efficiency, insufficient robustness, difficulty in model testing, and lack of probabilistic interpretation.

[0005] After the sustained-release preparation model is established, the prescription needs to be screened. When optimizing the prescription, the cumulative release at each time point is required to be as close to the target release as possible within the range allowed by the prescription. Therefore, this evaluation index is a multi-objective optimization problem based on multiple time points. Traditional optimization methods often combine multiple objectives into one objective, such as response surface method (Jiang Lijiao, Tao Guibin, Song Yuan, etc. Optimization of the preparation process of compound preparation SY tablets by central point design-response surface method [J]. Modern Chinese Medicine Research and Practice, 2015, 29(03): 50-52+55. DOI: 10.13728 / j.1673-6427.2015.03.017 and Patel A, Shelat P, Lalwani A. Development and optimization of solid self-nanoemulsifyingdrug delivery system (S-SNEDDS) using Scheffe's design for improvement of oral bioavailability of nelfinavir mesylate [J]. Drug delivery and translationalresearch, 2014, 4(2): 171-186), comprehensive scoring method (Deng Gang, Liang Kewen, Huang Jianjun, etc. Optimization of the extraction process of Gardenia and Poria tablet candy by multi-index comprehensive scoring method combined with Box-Behnken response surface method [J / OL]. Chemical Technology: 1-15 [2024-03-22]), goal programming method (Chen Cheng, Sun Huanxin, Li Xiaojuan. Design and practice of group teaching mode based on goal programming method [J]. Logistics Technology, 2021, 44(12): 163-167. DOI: 10.13714 / j.cnki.1002-3100.2021.12.025), etc. Both the contour map method and the comprehensive scoring method have great subjectivity and local optimal problems. Although the goal programming method can overcome the disadvantages of subjectivity, it is still easy to fall into the local optimal solution, and these traditional methods can only provide a unique optimal solution. Summary of the invention

[0006] The present invention provides a method for optimizing the prescription of a sustained-release preparation based on machine learning and a multi-objective genetic algorithm in order to solve the problems that a variety of methods have large computational complexity and algorithm complexity when optimizing the prescription, cannot perform model selection, are inefficient and lack robustness, are difficult to use for model verification, lack probabilistic interpretability, are subjective, and are prone to falling into local optimality in the development and research of sustained-release preparations.

[0007] As a traditional method for variable screening, the subset selection method is to scan variables according to various rules and then establish a regression model containing different variables. Generally, the Cp statistic criteria, AIC criteria, BIC criteria, etc. are used to compare the advantages and disadvantages of different models, and finally the model corresponding to the minimum criterion is taken as the optimal model. Optimal subset selection and stepwise selection are two commonly used subset selection methods, but the optimal subset method has the defect that when the number of variables grows exponentially and high or ultra-high dimensions appear, the calculation amount and algorithm complexity will be greatly increased. The disadvantage of the stepwise selection method is that the prediction variance of the selected model is large and the accuracy is low. For variable screening, the coefficient compression method that can perform parameter estimation and variable selection at the same time is currently used more. Among them, the Lasso method is widely used. Its principle is to compress the coefficients in the model according to the absolute value function of the coefficients in the model, so that the coefficients of some variables with very weak effects on the evaluation index Y can be compressed to a very small value until it becomes 0, and the corresponding variable can be deleted at this time. In general, the Lasso method can screen variables with greater influence and obtain the corresponding optimal model, thereby reducing experimental time and cost and improving experimental efficiency. Compared with the traditional subset selection methods such as stepwise regression and forward method, the process is discrete, disordered and has high variance. Lasso is a continuous and orderly process with a small variance, which can be calculated quickly and reduce the prediction error of the whole model. However, since Lasso uses the same penalty level for all independent variables indiscriminately when estimating coefficients, there is no distinction between primary and secondary variables, and it is very likely that some important variables will be deleted. The adaptive Lasso is to adjust its weight coefficient adaptively according to the size of the estimated value of the traditional Lasso. When the coefficient estimated by Lasso is very small, the adaptive Lasso will give it a larger weight, so that it can be quickly compressed to 0, so it overcomes the disadvantage that the traditional Lasso gives a large degree of compression for variables with larger coefficients, and can screen out fewer and reasonable variables compared to Lasso. Therefore, the present invention will use the adaptive Lasso to screen the covariates of the sustained-release preparation test data.

[0008] The data type of sustained-release preparations belongs to repeated measurement data, which is characterized by the correlation of the observations of the same individual at different time points, and the differences between different individuals. This makes the components of the observation vector of each individual have some correlation, such as autocorrelation, exchangeable correlation, independent correlation and other structures. In this way, repeated measurement data forms a special covariance structure matrix, which leads to the difficulty of modeling. For the modeling method of the cumulative release of sustained-release preparations, quadratic regression model and multiple linear regression model are currently used at home and abroad. Since the cumulative release of sustained-release preparations is correlated and the traditional modeling method cannot reveal its characteristics, the conclusions drawn will be invalid. Generalized estimating equations (GEE) are statistical analysis methods used to analyze data with non-independent characteristics. When using GEE to establish a model, three working correlation matrices (exchangeable correlation, autocorrelation, and unstructured correlation) need to be used for modeling respectively. The mean square error (MSE) and mean absolute error (MAD) are used to evaluate the results of the three matrices, and then the appropriate working correlation matrix is ​​selected. Although the generalized estimating equation takes the data correlation problem into consideration when modeling, it does not have a real likelihood function, and it is difficult to select the model using the likelihood-based information criteria AIC and BIC. In 2000, Qu et al. improved the generalized estimating equation and proposed the quadratic inference function (QIF), which made up for the shortcomings of GEE, could do goodness-of-fit test, and could use AIC and BIC indicators to evaluate the model effect and select the optimal model. QIF expands the inverse matrix of the working correlation matrix into a base matrix, avoiding the estimation of annoying parameters. When the working correlation matrix is ​​specified incorrectly, the parameters estimated by QIF are also optimal, while the generalized estimating equation is not optimal, and the QIF estimated parameters are more effective and robust. Therefore, the present invention will adopt QIF to establish a repeated measurement data model on the basis of covariate screening.

[0009] For multi-objective optimization problems based on multiple time points, traditional optimization methods such as contour map method, comprehensive scoring method, and goal programming method often combine multiple objectives into one objective. These methods are extremely subjective and easily lead to local optimality. They can only give a unique solution for a single objective, which violates the principle of multi-objective solution. The genetic algorithm (Genetic Algorithm) developed in recent years can solve the above problems well. This is a randomized search method, and the random process draws on the evolutionary laws of the biological world. Because the cumulative release of sustained-release preparations at each time point is mutually restricted and mutually exclusive, it is necessary to coordinate and compromise each objective during optimization to find a solution set with relatively better solutions for all objectives, that is, a Pareto non-inferior solution set. This set can provide decision makers with a set of artificially selectable, reasonable, and feasible solutions. The improved non-inferior classification genetic algorithm (NSGA-Ⅱ) was proposed by Deb et al. in 2000 as an improved multi-objective genetic algorithm, which shows strong advantages in multi-objective optimization. The basic idea of ​​the NSGA-Ⅱ algorithm is: first, randomly generate an initial population of size N, and after non-dominated sorting, obtain the first generation of offspring population through the three basic operations of selection, crossover, and mutation of the genetic algorithm; second, starting from the second generation, merge the parent population and the offspring population, perform fast non-dominated sorting, and calculate the crowding degree of individuals in each non-dominated layer at the same time, and select suitable individuals to form a new parent population according to the non-dominated relationship and the crowding degree of the individuals; finally, generate a new offspring population through the basic operations of the genetic algorithm: and so on, until the conditions for the end of the program are met. Its characteristics are the introduction of a fast non-dominated sorting algorithm, an elite strategy, and the use of crowding and crowding comparison operators, which reduce the complexity of the calculation, so that the relatively frontier individuals in the Pareto optimal solution can be evenly and stably expanded to the entire solution set, that is, the Pareto domain, thereby ensuring the diversity of the population. Therefore, the present invention uses an improved non-inferior classification genetic algorithm to optimize the prescription of sustained-release preparations.

[0010] At present, there are many theoretical studies on sustained-release preparations and repeated measurement data at home and abroad, but there are few studies on the use of genetic algorithms for sustained-release preparation prescription optimization, and there is no report on the application of machine learning algorithms and repeated measurement data model building methods to sustained-release preparation prescription optimization. In summary, the present invention will use adaptive Lasso for covariate screening, use QIF to build a model to solve the problem that the experimental data contains repeated measurement characteristics, and finally use the NSGA-Ⅱ toolkit coded by the research group to achieve optimization, create a sustained-release preparation prescription optimization system, and provide an analysis strategy for the research on sustained-release preparation prescription optimization.

[0011] The present invention is achieved through the following technical solution: a method for optimizing the prescription of a sustained-release preparation based on machine learning and a multi-objective genetic algorithm, comprising the following steps:

[0012] S1: Adaptive Lasso was used to screen the covariates of the sustained-release preparation data as follows:

[0013] When estimating the coefficients of the adaptive lasso, the penalty weight is added to the penalty term of the lasso, that is:

[0014]

[0015] For n groups of observations, each group of observations consists of a response variable y i and p dependent independent variables x i Composition; In addition, x ij is the explanatory variable, is a convex loss function, is the penalty function; where λ n is a non-negative adjustment parameter, and the adaptive weight is selected j = 1, 2, ..., p, and the positive value γ is a power of the adaptive weight and is related to the order. The adaptive lasso can maintain the consistency of the estimation results and is easy to calculate. The prediction values ​​estimated by the model are often more accurate.

[0016] S2: Establish a model based on the cumulative release at different time points and drug prescription; the details are as follows:

[0017] S2-1: Model construction: The inverse matrix of the working correlation matrix is ​​approximated by the linear combination of multiple basis matrices:

[0018]

[0019] a i ,…,a m is a constant term, M1 is the unit matrix, M2,…,M m It is determined by the assumed working correlation matrix structure; there are two cases: ① Assuming R(α) is a commutative matrix, then formula (2) is expressed as R -1 =a1M1+a2M2, where M1 is the identity matrix and M2 is a matrix with 0 on the diagonal and 1 in other positions; ② Assuming R(α) is a first-order autoregressive correlation matrix, R -1 Represented as R -1 =a1M1+a2M2+a3M3, where M1 is still the unit matrix, and M2 is a matrix with diagonal elements of 0 and elements in other positions of 1. In the matrix M3, except for the elements at positions (1,1) and (n,n), which are 1, the rest are 0.

[0020] Substitute formula (2) into the quasi-likelihood estimation equation: The following estimated equation is obtained:

[0021]

[0022] In this equation, the parameters a1, a2, …, a are not directly m Instead of estimating, an extended score function is introduced based on GEE:

[0023]

[0024] Since in the extended score function In the equation, the number of parameters to be estimated q is less than the number of estimated equations r. If each equation is equal to 0, then for the regression coefficient, it is impossible to obtain a consistent estimate. Therefore, the idea of ​​generalized moment estimation is used: that is, when r>q, by The specified linear combination of the r estimated equations is set as close to 0 as possible to obtain the estimate of the regression coefficient β. The equation in formula (4) is combined and optimized, and the quadratic inference function is defined:

[0025]

[0026] Formula (5) is a quadratic inference function. When it takes the minimum value, the optimal parameter estimation can be achieved;

[0027] S2-2: Construct evaluation indicators: Use Akaike Information Criterion AIC and Bayesian Information Criterion BIC to judge the quality of the model:

[0028] S2-2-1: When the sample size is small, AIC is an indicator used to evaluate the model fitting effect and quality. Its formula is as follows:

[0029] AIC=-2logL(θ|z)+2M (6)

[0030] Among them, m represents the number of parameters; It is the log-likelihood function, which is the sum of the log-likelihood functions of all observations. The lower the AIC index value, the better the established model and the better the fitting effect. Therefore, among the multiple models available, the model with the smallest AIC value is selected. When the sample size is too large, the true influence of the model parameter M is masked due to the large value of its likelihood function, and the AIC criterion generally fails.

[0031] S2-2-2: When the sample size is too large, Schwarz proposed BIC to overcome the shortcomings of the AIC criterion. BIC is used in the selection of statistical models. The specific formula is as follows:

[0032] BIC=-2log(θ|z)+Mlnn (7)

[0033] m represents the number of parameters, n represents the sample size, and Mlnn is used instead of 2M in AIC; BIC is more superior because it takes the sample size of the data into account. Similarly, the lower the BIC, the better the fit of the model. The quadratic inference function can produce likelihood ratio test results, such as Q statistics, AIC, BIC, etc. In the goodness of fit test, H0 assumes that the model is valid, and P>0.05 indicates that the model fits well; the present invention uses both AIC and BIC indicators to preliminarily evaluate the modeling effect of QIF.

[0034] S3: Combine the model established in step S2 with NSGA-II to achieve a multi-objective optimization process.

[0035] Genetic algorithm (GA) is a type of random search algorithm that simulates biological natural selection and natural evolution. It has been widely used because it is suitable for solving highly complex nonlinear problems, and it has good versatility. The advantages of genetic algorithms are fully demonstrated when solving complex system optimization problems with only a single goal. However, optimization problems in the real world are usually multi-attribute, and the multiple goals that are optimized simultaneously interact and conflict with each other. For example, the cumulative release of a drug at various time points in the body. In order to achieve the optimization of the overall goal, it is usually necessary to comprehensively consider the conflicting sub-goals, that is, to compromise the sub-goals. Therefore, multi-objective genetic algorithms have emerged for optimization problems with multiple goals. Step S3 is as follows:

[0036] The algorithm flow of NSGA-Ⅱ is as follows: First, a parent population P of size n is randomly generated. n After non-dominated sorting, the offspring population Q is obtained through selection, crossover, and mutation n ; Then the two populations are combined to obtain a population R of size 2n n , and perform non-inferior classification operations on them; finally calculate the crowding degree of all individuals in each non-inferior level; generate the next generation population P according to the principle of crowding degree selection operator n+1 , the evolutionary generation is n+1, and it is determined whether the population evolutionary generation is greater than the maximum evolutionary generation; if so, the algorithm ends, otherwise it continues to evolve; this cycle continues until it evolves to the specified maximum evolutionary generation and the conditions for the program to end are met.

[0037] In step S3, NSGA-Ⅱ was born to solve the defects of NSGA, such as high computational complexity and time-consuming, no elite strategy, manually specified sharing radius, and easy subjective influence. The following three improvements were made: a fast non-dominated sorting method was adopted to reduce the computational complexity of the algorithm. From O(mN3) to O(mN2), m represents the number of objective functions, and N represents the size of the population; the crowding degree and crowding degree comparison operator are used to replace the sharing strategy of manually adjusting the selected sharing radius, and then used as the winning standard in the same-level comparison after quick sorting, so that individuals can be expanded in the Pareto domain and evenly distributed, and the diversity of the population can be maintained; the elite strategy is adopted, and its specific idea is to put the parent population and its child population together to compete, and select the better next generation population through competition, so that the excellent parent generation will be retained in the next generation, thereby expanding the diversity of the population and the sampling space. Therefore, NSGA-Ⅱ is a relatively efficient optimization method for multi-objective optimization problems.

[0038] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a method for optimizing the prescription of a sustained-release preparation based on machine learning and a multi-objective genetic algorithm, which for the first time combines a covariate selection method with a repeated measurement data model building method and a multi-objective genetic algorithm to create a system for optimizing the prescription of a sustained-release preparation based on machine learning and a multi-objective genetic algorithm. The system provides a set of reasonable and feasible solutions for optimizing the formulation of a sustained-release preparation, which can greatly reduce the number of times preliminary experiments are used to explore the optimal preparation conditions, save manpower, material resources and financial resources, and has practical guiding significance and application value for solving multi-objective optimization problems in the field of medicine, and can be extended to the application of multi-objective optimization problems in other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is an algorithm flow chart of step S3 of the present invention.

[0040] Figure 2 It is the technical roadmap of the present invention.

[0041] Figure 3 It is a cross-validation error curve of a specific embodiment of the present invention.

[0042] Figure 4 It is an adaptive LASSO coefficient path diagram of a specific embodiment of the present invention.

[0043] Figure 5 This is the maximum fitness evolution curve of NSGA-II of a specific embodiment of the present invention.

[0044] Figure 6 It is the average fitness evolution curve of NSGA-II of a specific embodiment of the present invention. DETAILED DESCRIPTION

[0045] The present invention is further described below in conjunction with specific embodiments.

[0046] The specific embodiment of the present invention adopts the above method to perform verification calculation.

[0047] Salbutamol sulfate is a water-soluble short-acting β2 agonist used to treat bronchoconstriction and bronchospasm in patients with reversible obstructive airway disease and chronic obstructive pulmonary disease. The data in "Optimization of the formulation of hydrophilic matrix sustained-release tablets of salbutamol sulfate by response surface methodology" published by Chaibva, Walker et al. in the Journal of Drug Development and Technology in 2012 are cited as the test data of the present invention. The formulation factors of the metronidazole antibacterial film are hydroxypropyl methylcellulose ( K100M, X1), xanthan gum (Xanthan gum, X2), carboxyvinyl polymer ( 974P, X3), ethyl cellulose aqueous dispersion ( X4), the response variable is the amount of drug dissolved at 1, 2, 4, 6, 8 and 12 hours (Y1, Y2, Y4, Y6, Y8 and Y 12 ), the level range of each formula factor and the release standards of salbutamol sulfate hydrophilic matrix sustained-release tablets at different time points are shown in Table 1. A central composite experimental design was adopted, and the experimental scheme and results are shown in Table 2. We found that in the experimental results of 30 schemes, the release of no scheme met the release standards at the same time, and the best scheme only had releases at three time points that met the requirements. Therefore, it is necessary to optimize the preparation process conditions based on mathematical modeling combined with a multi-objective optimization method to obtain a relatively optimal solution that allows as many salbutamol sulfate sustained-release tablets as possible to meet the release requirements at the time point.

[0048] In addition, salbutamol sulfate sustained-release tablets are composed of four formulations. If the traditional Scheffe polynomial is used to establish a model, plus the interaction between time points and formulations, the polynomial model contains a total of 21 covariates. Too many covariates will largely lead to the inability to reasonably estimate parameters, which will directly affect the optimization effect of the optimal ratio.

[0049] Table 1 Factors and levels of study variables

[0050]

[0051] Table 2 Central composite experimental design and observation results

[0052]

[0053]

[0054] The prescription optimization results of this embodiment are as follows:

[0055] (I) Covariate screening results

[0056] The msgps, glmnet and other software packages in R software were used to fit the adaptive LASSO to screen the covariates and perform ten-fold cross validation to obtain λ min =0.02596,λ lse =0.18311. The adaptive LASSO variable fitting results are shown in Table 3. According to the CP criterion, 13 covariates were retained. The cross-validation error curve and adaptive LASSO coefficient path diagram are shown in Figure 3 , Figure 4 .

[0057] Table 3 Adaptive LASSO covariate fitting results based on CP criterion

[0058]

[0059] (II) QIF model fitting

[0060] A quadratic inference function model was established for the data without covariate screening and the data after covariate screening, and the model fitting effect was evaluated by AIC and BIC, thereby evaluating the feasibility and applicability of the adaptive LASSO-QIF joint algorithm used in the present invention.

[0061] ① QIF model fitting results without covariate screening

[0062] As can be seen from Table 5, the model constructed using QIF is as follows:

[0063] Y t =39.2085-0.2013*X1-0.02*X2+1.2572*X3+0.1403*X4-0.0125*X1*X3+0.0177*X1*X4-

[0064] 0.0347*X2*X3-0.0134*X2*X4-0.0475*X3*X4+0.0008*X1*X2*X3-0.001*X1*X3*X4+0.0014*X2*X3*X4+14.4775*t-0.4148*t 2 -0.0028*X1*t+0.0063*X2*t-0.0267*X3*t-0.0284*X4*t.

[0065] As shown in Table 4, the model constructed by QIF is statistically significant (Q = 6.000, P = 0.99971), and the model fitting effect is good (AIC = 50, BIC = 45.4187).

[0066] Table 4 QIF model goodness of fit test results

[0067]

[0068] Table 5 QIF model fitting results Note: Bold fonts indicate that the observations are statistically significant

[0069]

[0070]

[0071] ② QIF model fitting results after variable screening:

[0072] As can be seen from Table 7, the model constructed using QIF is as follows:

[0073] Y t =45.5186-0.1907*X1-0.4524*X2+0.5409*X3+0.3643*X4+0.0017*X1*X2-0.0097*X2*

[0074] X3-0.1334*X3*X4+11.4022t-0.5861*t*t+0.1013*X3*t+0.0668*X4*t

[0075] As shown in Table 6, the model constructed by QIF is statistically significant (Q = 6.000, P = 0.96649), and the model fitting effect is good (AIC = 34, BIC = 31.0846). Compared with the QIF model without variable screening, the QIF model after variable screening has smaller AIC and BIC values, better model fitting effect, and subsequent prescription optimization can be carried out.

[0076] Table 6 QIF model goodness of fit test results

[0077]

[0078] Table 7 QIF model fitting results Note: Bold fonts indicate that the observations are statistically significant

[0079]

[0080] Substituting different time points (t=1, 2, 4, 6, 8, 12) into the above model, the cumulative release model at each time point can be obtained:

[0081] Y1=56.3347-0.1907*X1-0.4524*X2+0.6422*X3+0.4311*X4+0.0017*X1*X2-0.0097*X2*

[0082] X3-0.1334*X3*X4

[0083] Y2=65.9786-0.1907*X1-0.4524*X2+0.7435*X3+0.4979*X4+0.0017*X1*X2-0.0097*X2*

[0084] X3-0.1334*X3*X4

[0085] Y4=81.7498-0.1907*X1-0.4524*X2+0.9461*X3+0.6315*X4+0.0017*X1*X2-0.0097*X2*

[0086] X3-0.1334*X3*X4

[0087] Y6=92.8322-0.1907*X1-0.4524*X2+1.1487*X3+0.7651*X4+0.0017*X1*X2-0.0097*X2*

[0088] X3-0.1334*X3*X4

[0089] Y8=99.2258-0.1907*X1-0.4524*X2+1.3513*X3+0.8987*X4+0.0017*X1*X2-0.0097*X2*

[0090] X3-0.1334*X3*X4

[0091] Y 12 =97.9466-0.1907*X1-0.4524*X2+1.7565*X3+1.1659*X4+0.0017*X1*X2-0.0097*X2*

[0092] X3-0.1334*X3*X4

[0093] (III) NSGA-Ⅱ multi-objective optimization results:

[0094] ①Transformation of objective function

[0095] This embodiment takes into account the standards of drug release at each time point and implements corresponding conversions on each sub-objective function so that the multi-objective genetic algorithm can be used for prescription optimization later. The conversions are as follows:

[0096] When t = 1h: Q1 = -(Y1-37) 2

[0097] When t = 2h: Q2 = -(Y2-51) 2

[0098] When t = 4h: Q4 = -(Y4-68) 2

[0099] When t = 6h: Q6 = -(Y6-79) 2

[0100] When t = 8h: Q8 = -(Y8-87) 2

[0101] When t = 12h: Q 12 =-(Y 12 -95) 2

[0102] Q1=-(19.3347-0.1907*X1-0.4524*X2+0.6422*X3+0.4311*X4+0.0017*X1*X2-0.0097*X2*X3-0.1334*X3*X4) 2

[0103] Q2=-(14.9786-0.1907*X1-0.4524*X2+0.7435*X3+0.4979*X4+0.0017*X1*X2-0.0097*X2*X3-0.1334*X3*X4) 2

[0104] Q4=-(13.7498-0.1907*X1-0.4524*X2+0.9461*X3+0.6315*X4+0.0017*X1*X2-0.0097*X2*X3-0.1334*X3*X4) 2

[0105] Q6=-(13.8322-0.1907*X1-0.4524*X2+1.1487*X3+0.7651*X4+0.0017*X1*X2-0.0097*X2*X3-0.1334*X3*X4) 2

[0106] Q8=-(12.2258-0.1907*X1-0.4524*X2+1.3513*X3+0.8987*X4+0.0017*X1*X2-0.0097*X2*X3-0.1334*X3*X4) 2

[0107] Q 12=-(2.9466-0.1907*X1-0.4524*X2+1.7565*X3+1.1659*X4+0.0017*X1*X2-0.0097*X2*X3-0.1334*X3*X4) 2

[0108] ②Software and parameter settings

[0109] The multi-objective optimization was performed using the MATLAB R2009a software genetic algorithm SGALAB1003beta5008-plug-in toolbox. Parameter settings: initial population 50, maximum evolutionary generations 100, single-point crossover probability 0.8, mutation probability 0.05, and random search 30 times.

[0110] ③Pareto optimal solution set

[0111] The non-inferior solutions obtained by NSGA-Ⅱ random search 30 times are shown in Table 8. If researchers intend to save the dosage of the formula under the premise of meeting the requirements of the objective function, they can choose Scheme 5 as the optimal process conditions: X1 = 28 mg, X2 = 31 mg, X3 = 6 mg, X4 = 7% w / w, and the cumulative release of salbutamol sulfate sustained-release tablets at 6 time points is 37.9%, 53.4%, 69.4%, 79.8%, 88.4%, 98.5%, of which the cumulative release at 4 time points is within the required range, and the cumulative release at the other two time points is less than the release requirements, which are 0.4% and 1.5%, respectively. In general, it can be considered that the release requirements are met and the optimization effect is satisfactory. If researchers want to prepare salbutamol sulfate sustained-release tablets that are closer to the release requirements, they can choose Scheme 9 as the optimal process conditions: X1 = 100 mg, X2 = 1 mg, X3 = 6 mg, X4 = 9% w / w, and the cumulative releases of salbutamol sulfate sustained-release tablets at 6 time points are 37.6%, 53.6%, 69.4%, 80.1%, 88.9%, and 97.6%, respectively. The cumulative releases at 4 time points are within the required range; the cumulative releases at the other two time points are very close to the release requirements, at 0.6% and 0.6%, respectively. Overall, it can be considered that the release requirements are met and the optimization effect is satisfactory.

[0112] Table 8 NSGA-Ⅱ random search results Note: Bold fonts represent ideal formula optimization solutions

[0113]

[0114]

[0115]

[0116] (IV) Comparison of optimization effects:

[0117] The optimization results of the example application of the present invention are compared with the optimization results of the original article ("Optimizing the prescription of salbutamol sulfate hydrophilic matrix sustained-release tablets by response surface method"), see Table 9. In the original article, the response surface method was used to analyze and optimize the factors and interactions affecting the in vitro release characteristics of salbutamol sulfate sustained-release dosage forms, and the optimized formula obtained was X1=31 mg, X2=35.31 mg, X3=10.01 mg, X4=18.5% w / w; the predicted cumulative release at each time point was 38.73%, 50.05%, 66.00%, 80.73%, 87.09%, 97.00%, respectively. Compared with the improved non-inferior classification genetic algorithm, which can obtain a set of Pareto solutions to choose from, the response surface method used in the original article can only subjectively obtain a unique solution. For researchers, it is impossible to choose according to the experimental conditions and target requirements, and the solution provided by the present invention requires relatively few formula materials. At the same time, the quadratic equation used in the original text failed to consider the correlation between the cumulative release and the influence of the measurement time point on the release, which has certain defects. The optimization system proposed in the present invention can greatly reduce the number of preliminary tests for exploring the optimal preparation conditions, save material and financial resources, and has practical guiding significance and application value for solving multi-objective optimization problems in the medical field, and can be extended to multi-objective optimization problems in other fields.

[0118] Table 9 Comparison of optimization effects

[0119]

[0120] The scope of protection claimed by the present invention is not limited to the above specific embodiments. For those skilled in the art, the present invention may have various deformations and changes. Any modifications, improvements and equivalent substitutions made within the concept and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing the prescription of a sustained-release preparation based on machine learning and a multi-objective genetic algorithm, characterized in that: The steps include: S1: Adaptive Lasso was used to screen covariates for sustained-release preparation data; S2: Establish a model based on the cumulative release at different time points and drug prescription; S3: Combine the model established in step S2 with NSGA-II to achieve a multi-objective optimization process.

2. The method for optimizing the sustained-release preparation prescription based on machine learning and multi-objective genetic algorithm according to claim 1, characterized in that: Step S1 is specifically as follows: When estimating the coefficients of the adaptive lasso, the penalty weight is added to the penalty term of the lasso, that is: For n groups of observations, each group of observations consists of a response variable y i and p dependent independent variables x i Composition; In addition, x ij is the explanatory variable, is a convex loss function, is the penalty function; where λ n is a non-negative adjustment parameter, and the adaptive weight is selected Positive values ​​of γ are a power of the adaptive weight and are related to the order.

3. The method for optimizing the sustained-release preparation prescription based on machine learning and multi-objective genetic algorithm according to claim 2, characterized in that: Step S2 is specifically as follows: S2-1: Model construction: The inverse matrix of the working correlation matrix is ​​approximated by the linear combination of multiple basis matrices: a i ,…,a m is a constant term, M1 is the unit matrix, M2,…,M m It is determined by the assumed working correlation matrix structure; there are two cases: ① Assuming R(α) is a commutative matrix, then formula (2) is expressed as R -1 =a1M1+a2M2, where M1 is the identity matrix and M2 is a matrix with 0 on the diagonal and 1 in other positions; ② Assuming R(α) is a first-order autoregressive correlation matrix, R -1 Represented as R -1 =a1M1+a2M2+a3M3, where M1 is still the unit matrix, and M2 is a matrix with diagonal elements of 0 and elements in other positions of 1. In the matrix M3, except for the elements at positions (1,1) and (n,n), which are 1, the rest are 0. Substitute formula (2) into the quasi-likelihood estimation equation: The following estimated equation is obtained: In this equation, the parameters a1, a2, …, a are not directly m Instead of estimating, an extended score function is introduced based on GEE: Since in the extended score function In the equation, the number of parameters to be estimated q is less than the number of estimated equations r. If each equation is equal to 0, then for the regression coefficient, it is impossible to obtain a consistent estimate. Therefore, the idea of ​​generalized moment estimation is used: that is, when r>q, by The specified linear combination of the r estimated equations is set as close to 0 as possible to obtain the estimate of the regression coefficient β. The equation in formula (4) is combined and optimized, and the quadratic inference function is defined: Formula (5) is a quadratic inference function. When it takes the minimum value, the optimal parameter estimation can be achieved; S2-2: Construct evaluation indicators: Use Akaike Information Criterion AIC and Bayesian Information Criterion BIC to judge the quality of the model: S2-2-1: When the sample size is small, AIC is an indicator used to evaluate the model fitting effect and quality. Its formula is as follows: AIC=-2logL(θ|z)+2M (6) Among them, m represents the number of parameters; It is the log-likelihood function, which is the sum of the log-likelihood functions of all observations. Therefore, among the multiple models available for selection, the model with the smallest AIC value is selected; S2-2-2: When the sample size is too large, BIC is proposed to overcome the shortcomings of the AIC criterion. BIC is used in the selection of statistical models. The specific formula is as follows: BIC=-2log(θ|z)+M ln n (7) m represents the number of parameters, n represents the sample size, and Mlnn is used instead of 2M in AIC. In the goodness-of-fit test, H0 assumes that the model is valid, and P>0.05 indicates that the model fits well. AIC and BIC are used to preliminarily evaluate the modeling effect of QIF.

4. The method for optimizing the sustained-release preparation prescription based on machine learning and multi-objective genetic algorithm according to claim 3, characterized in that: Step S3 is as follows: The algorithm flow of NSGA-Ⅱ is as follows: First, a parent population P of size n is randomly generated. n After non-dominated sorting, the offspring population Q is obtained through selection, crossover, and mutation n ; Then the two populations are combined to obtain a population P of size 2n n , and perform non-inferior classification operations on them; finally calculate the crowding degree of all individuals in each non-inferior level; generate the next generation population P according to the principle of crowding degree selection operator n+1 , the evolutionary generation is n+1, and it is determined whether the population evolutionary generation is greater than the maximum evolutionary generation; if so, the algorithm ends, otherwise it continues to evolve; this cycle continues until it evolves to the specified maximum evolutionary generation and the conditions for the program to end are met.

5. The method for optimizing the sustained-release preparation prescription based on machine learning and multi-objective genetic algorithm according to claim 4, characterized in that: In step S3, NSGA-II also adopts an elite strategy, which is to combine the parent individuals and the offspring individuals in each generation of evolution, and obtain the crossover "parent" of the next generation through competition. This approach can enable the excellence of several individuals in the parent generation to be inherited.

Images