Methods, devices, equipment and media for estimating sample size in clinical trials of recurrent events

Abstract

This invention provides a method, apparatus, equipment, and medium for estimating sample size in clinical trials for recurrent events, relating to the fields of clinical trial design and biostatistics. This invention acquires basic trial information, establishes a statistical model integrating subject dropout mechanisms based on this information, calculates key bridging parameters and mean exposure time, and executes a dual-path closed-loop decision-making process encompassing the design and execution phases: in the design phase, the target allocation probability is calculated based on the key bridging parameters and mean exposure time, thereby calculating the total sample size; in the execution phase, parameters are dynamically updated based on current real-time data, and new subjects are adaptively randomized. This application can explicitly model the impact of subject dropout on exposure time and introduce parameters to uniformly drive sample size estimation and dynamic randomization, optimizing subject benefit while ensuring test efficacy and providing integrated decision support from design to execution.

Description

Technical Field

[0001] This invention relates to the fields of pharmaceutical clinical trial design and biostatistics, and more specifically, to a method, apparatus, equipment, and medium for estimating sample size in clinical trials for recurrent events. Background Technology

[0002] In the clinical development of chronic diseases (such as severe asthma, chronic obstructive pulmonary disease, and chronic kidney disease), recurrent events have been widely used as key efficacy endpoints in modern clinical trial design. Recurrent events refer to clinical events that may occur multiple times in the same subject during the study period, such as the number of asthma exacerbations, the frequency of readmissions for heart failure, or the frequency of migraine attacks. Compared to single-event endpoints (such as death), recurrent events can more comprehensively characterize the dynamic features of disease progression and improve the statistical sensitivity of treatment effect assessment. However, subject dropout is common in such studies, with causes including disease exacerbation, decreased adherence, or adverse events. Numerous studies have shown that failure to adequately consider dropout factors during the trial design phase will lead to a reduced effective sample size, biased effect estimation, and a significant decrease in test power. Therefore, appropriately incorporating dropout mechanisms into sample size estimation and statistical modeling has become a fundamental requirement for clinical trial design.

[0003] Currently, clinical trials for recurrent events commonly employ fixed-proportion randomization strategies (such as 1:1 balanced designs) to ensure comparability between groups and robustness of statistical inference. However, this method has significant limitations: on the one hand, ethically, continuously assigning subjects to treatment groups with relatively poor efficacy may harm patient interests; on the other hand, in terms of efficiency, fixed-proportion designs cannot utilize interim response information accumulated during the trial, making it difficult to dynamically optimize treatment allocation. To address these challenges, response-adaptive randomization (RAR) methods have gradually gained attention. RAR dynamically adjusts the allocation probability of subsequent subjects based on observed recurrent event data, allowing more patients to receive potentially better treatments, thereby improving subject benefit while maintaining statistical efficiency. Nevertheless, existing RAR methods still face key bottlenecks in practical applications. The adaptive randomization scheme based on a double-biased coin design (DBCD) proposed by Gao et al., while achieving dynamic optimization of treatment allocation, suffers from two fundamental flaws. First, this approach completely lacks a sample size estimation method compatible with adaptive mechanisms, making it impossible for researchers to scientifically determine the required number of subjects. This hinders the provision of sufficient evidence of trial feasibility to regulatory agencies and compromises the efficacy of the assay. Second, this method is based on idealized assumptions, namely that all subjects complete the entire follow-up period and the exposure time is set as a fixed constant, completely ignoring the dropout phenomenon commonly seen in clinical practice. This simplification is seriously contrary to reality: dropout not only turns individual exposure time into a random variable but also causes information loss. If the sample size is underestimated based on this, the actual efficacy will be significantly lower than the preset target, greatly increasing the risk of trial failure. In fact, mainstream clinical trial protocols (such as Singh et al.'s study on COPD) clearly preset the dropout rate (e.g., 10%) and adjust the sample size accordingly, highlighting the shortcomings of the existing RAR method in terms of practical applicability.

[0004] In view of the above, this application is hereby submitted. Summary of the Invention

[0005] The present invention aims to provide a method, device, equipment and medium for estimating sample size in clinical trials of recurrent events, in order to solve the defects in existing clinical trial designs of recurrent events, such as the lack of sample size estimation methods, the neglect of subject dropout leading to model distortion and insufficient test power.

[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0007] A method for estimating sample size in clinical trials for recurrent events, comprising:

[0008] S1, Obtain basic test information including test type and dropout rate;

[0009] S2, Based on the aforementioned test type and dropout rate, establish a statistical model integrating the subject dropout mechanism to quantify the impact of dropout on exposure time;

[0010] S3, Calculate key bridge parameters and average exposure time based on the statistical model;

[0011] S4, Execute a dual-path closed-loop decision-making process that includes a design phase and an execution phase: In the design phase, calculate the target allocation probability based on the key bridge parameters and the average exposure time, thereby calculating the total sample size; In the execution phase, dynamically update the parameters based on the current real-time data and adaptively randomize new subjects.

[0012] Preferably, the statistical model describes the occurrence process of recurrent events based on a negative binomial regression model, and models the actual exposure time of each subject as a random variable determined by a preset dropout rate and the trial type, specifically:

[0013] Based on shedding rate The shedding risk coefficient is calculated using the exponential shedding model. The formula is:

[0014] ;

[0015] in, Let be the detachment risk coefficient for the i-th group; Let i be the shedding rate of the i-th group; The duration of the trial treatment is determined by the type of trial.

[0016] Define the random exposure time of subjects Time of shedding Duration of experimental treatment The smaller value, and assuming the shedding time It follows an exponential distribution, expressed as:

[0017] ;

[0018] A negative binomial regression model was used to describe the exposure time of the j-th subject in the i-th group. Number of recurrent events within The expression is:

[0019] ;

[0020] ;

[0021] in, It follows a negative binomial distribution; The mean; Let i be the event occurrence rate of the i-th group; These are the discrete parameters of the negative binomial model, used to characterize the degree of dispersion in the distribution of recurring events;

[0022] By fitting a negative binomial regression model with the actual data from the enrolled subjects, the initial parameters were estimated. , .

[0023] Preferably, the key bridge parameters are the key parameters of connection detachment and statistical effectiveness, which are obtained through integral calculation, and the formula is:

[0024] ;

[0025] in, These are the key bridge parameters for the i-th group; Let i be the event occurrence rate of the i-th group; Let be the detachment risk coefficient for the i-th group; This refers to the duration of the experimental treatment; These are the discrete parameters of the negative binomial model; The test exposure time; For the derivative sign;

[0026] Then, the key bridge parameters are solved using the adaptive Simpson method.

[0027] Preferably, the average exposure time is combined with the shedding risk factor. Duration of experimental treatment The formula is:

[0028] ;

[0029] in, Let be the average exposure time for the i-th group.

[0030] Preferably, the target allocation probability is used for adaptive randomization of subjects to the treatment group, and the formula for calculating the target allocation probability of the i-th group is:

[0031] ;

[0032] in, For the treatment group The target assignment probability; i is the treatment group index number; , , , respectively, represent the event incidence rate, average exposure time, and key bridge parameters for group i; G is the total number of treatment groups.

[0033] Preferably, the total sample size is based on a standard normal distribution. Combining the allocation probability and key bridge parameters, and quantifying the impact of dropout and allocation ratios on the sample size, the formula for calculating the total sample size is:

[0034] ;

[0035] ;

[0036] in, This represents the total sample size. The significance level quantile after correction is the cumulative probability in the standard normal distribution. The corresponding quantiles; The significance level after correction; To test the effectiveness against the preset target; The significance level is preset. Let G be the number of pairs of logarithms. If each pair of pairs in G is compared, ; To test the standard normal quantile corresponding to the power, i.e. the cumulative probability in the standard normal distribution is... The corresponding quantiles; The effect size difference was obtained through the event occurrence rate; , Let be the target assignment probability and key bridge parameters for the i-th group, respectively.

[0037] Preferably, during the execution phase, parameters are dynamically updated based on current real-time data, and new subjects are adaptively randomly assigned, specifically as follows:

[0038] A1. The event incidence rate is recalculated based on the data of currently enrolled subjects. This event incidence rate is calculated as the ratio of the total number of recurrent events in subjects who experienced an event to the total exposure duration of enrolled subjects, using the following formula:

[0039] ;

[0040] in, Let i be the event occurrence rate of the i-th group; The total number of recurrent events in the subjects who experienced the target event in group i; The total exposure time of the enrolled subjects in group i;

[0041] A2, based on the recalculated event occurrence rate, calculates the key bridge parameters and target allocation probability using the adaptive Simpson method;

[0042] A3. If the fluctuation range of the target allocation probability exceeds the preset range, then perform sensitivity analysis, that is: adjust the range of event occurrence rate, recalculate the key bridge parameters and target allocation probability until the fluctuation range of the target allocation probability is within the preset range.

[0043] A4. Monitor in real time whether new subjects are enrolled and perform dynamic balanced covariate randomization for treatment allocation: If there are new subjects, repeat steps A1 to A3 and assign the new subjects to the corresponding treatment groups according to the updated target allocation probability; if there are no new subjects, record and output the current allocation results and trial data.

[0044] The present invention also provides a device for estimating the sample size of clinical trials for recurrent events, comprising:

[0045] The parameter acquisition module is used to acquire basic test information, including test type and dropout rate.

[0046] The statistical model building module is used to establish a statistical model integrating the subject dropout mechanism based on the test type and dropout rate, and to quantify the impact of dropout on exposure time.

[0047] The parameter calculation module is used to calculate key bridge parameters and average exposure time based on the statistical model.

[0048] The dual-path closed-loop decision execution module is used to execute dual-path closed-loop decisions that include a design phase and an execution phase: in the design phase, the target allocation probability is calculated based on the key bridge parameters and the average exposure time, thereby calculating the total sample size; in the execution phase, the parameters are dynamically updated based on the current real-time data, and new subjects are adaptively and randomly assigned.

[0049] The present invention also provides a device for estimating the sample size of a clinical trial for recurrent events, including a processor and a memory, wherein the memory stores a computer program that can be executed by the processor to implement the method for estimating the sample size of a clinical trial for recurrent events as described above.

[0050] The present invention also provides a computer-readable storage medium storing computer-readable instructions, which, when executed by a processor of the device on which the computer-readable storage medium resides, implement a method for estimating the sample size of a clinical trial for recurrent events as described above.

[0051] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0052] This invention explicitly incorporates a preset dropout rate into the random exposure time model, enabling the sample size estimation to reflect the information loss under real clinical conditions and avoiding the problems of underestimation of sample size and insufficient test power caused by ignoring dropout.

[0053] This invention introduces key bridging parameters to unify dropout mechanisms, relapse event characteristics, and adaptive randomization strategies within the same theoretical framework, enabling sample size calculation and dynamic allocation of new subjects to share a consistent statistical basis.

[0054] During the execution phase, this invention achieves adaptive optimization of treatment allocation based on real-time data through a closed-loop iterative mechanism, enabling more subjects to be assigned to the treatment group with the best estimated efficacy, thereby reducing overall relapse events while maintaining the preset test efficacy.

[0055] This invention addresses the disconnect between sample size determination and randomization strategies in existing technologies by providing a complete decision support workflow from trial design to execution, thereby improving the scientific rigor, feasibility, and regulatory acceptability of clinical trial design. Attached Figure Description

[0056] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0057] Figure 1 This is a schematic diagram of a method for estimating the sample size of a clinical trial for recurrent events, as provided in Example 1.

[0058] Figure 2 This is a flowchart illustrating a method for estimating the sample size of a clinical trial for recurrent events, as provided in Example 1.

[0059] Figure 3 This is a schematic diagram of a clinical trial sample size estimation device for recurrent events provided in Example 2.

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0062] Example 1

[0063] Embodiment 1 of the present invention provides a method for estimating the sample size of a clinical trial for recurrent events, which can be implemented by a clinical trial sample size estimation device for recurrent events (hereinafter referred to as the estimation device), and in particular, executed by one or more processors within the estimation device.

[0064] In this embodiment, the estimation device may be an electronic device equipped with a processor, the processor having a computer program for estimating the sample size of the clinical trial for the recurrent event, and the computer program being executable, such as a computer, smartphone, smart tablet, workstation, etc., which are not limited here.

[0065] like Figures 1-2 As shown, a method for estimating the sample size of a clinical trial for recurrent events includes steps S1 to S4.

[0066] S1, obtain basic test information including test type and dropout rate.

[0067] Specifically, the basic information for the experiment includes:

[0068] Trial type: such as "same treatment duration", treatment duration sky;

[0069] Shedding rate: If the shedding rate of both sets of data is the same... (30% shedding rate);

[0070] Target testing effectiveness: ; The probability of a false negative;

[0071] Significance level: ;

[0072] Initial event incidence in the treatment group: (e.g., event incidence in both groups) , ;

[0073] Choose the allocation rule: minimize the total number of recurrence events.

[0074] S2. Based on the test type and dropout rate, establish a statistical model integrating the subject dropout mechanism to quantify the impact of dropout on exposure time.

[0075] The statistical model describes the occurrence of recurrent events based on a negative binomial regression model, and models the actual exposure time of each subject as a random variable determined by the preset dropout rate and the trial type, specifically:

[0076] Based on shedding rate The shedding risk coefficient is calculated using the exponential shedding model. The formula is:

[0077] ;

[0078] in, The duration of the trial treatment is determined by the type of trial. It is the natural logarithm function.

[0079] In this embodiment, based on the shedding rate Calculate .

[0080] Define the random exposure time of subjects Time of shedding Duration of experimental treatment The smaller value, and assuming the shedding time It follows an exponential distribution, expressed as:

[0081] ;

[0082] A negative binomial regression model was used to describe the exposure time of the j-th subject in the i-th treatment group. Number of recurrent events within The expression is:

[0083] ;

[0084] ;

[0085] in, It follows a negative binomial distribution; The mean; The event incidence rate in treatment group i; These are the discrete parameters of the negative binomial model, used to characterize the degree of dispersion in the distribution of recurring events; It is an exponential function.

[0086] In this embodiment, the negative binomial regression model is an important variant of the generalized linear model (GLM), mainly used to analyze discrete count dependent variables (such as the number of disease recurrences, the number of adverse events, the number of product purchases, etc.). It is especially suitable for scenarios where the dependent variable is overdispersion and is a commonly used model in fields such as biostatistics, clinical medicine, and sociology.

[0087] The initial parameters can be estimated by fitting a negative binomial regression model using the actual data from enrolled subjects. , .

[0088] By exposure time The fixed value was changed to a random variable to accurately reflect the impact of shedding on the experiment.

[0089] S3, Calculate key bridge parameters and average exposure time based on the statistical model.

[0090] In this embodiment, the key bridge parameter is the key parameter for connection detachment and statistical effectiveness, which is obtained by integration (integration interval [0, 150], and the duration of the trial treatment). The formula is calculated from 150, and the result is as follows:

[0091] ;

[0092] in, These are the key bridge parameters for the i-th group; Let i be the event occurrence rate of the i-th group; These are the discrete parameters of the negative binomial model; The test exposure time; For the derivative sign; It is an exponential function.

[0093] The critical bridge parameters are then solved using the adaptive Simpson method. In this embodiment, the calculated critical bridge parameters... , .

[0094] In this embodiment, the adaptive Simpson method is an efficient algorithm for solving definite integrals in numerical computation. It is an optimization of the traditional Simpson method. By "automatically judging the degree of change of the function within the integration interval and dynamically subdividing the interval", it reduces the amount of computation while ensuring the accuracy of the calculation. It is widely used in mathematics, statistics, engineering and other fields.

[0095] The average exposure time combined with the shedding risk factor Duration of experimental treatment The formula is:

[0096] ;

[0097] in, Let be the average exposure time for group i.

[0098] It is the core parameter that connects "detachment from reality" and "statistical effectiveness," providing a foundation for subsequent steps such as sample size calculation; mean exposure time quantifies the actual duration of an individual's participation in the experiment.

[0099] S4, Execute a dual-path closed-loop decision-making process that includes a design phase and an execution phase: In the design phase, calculate the target allocation probability based on the key bridge parameters and the average exposure time, thereby calculating the total sample size; In the execution phase, dynamically update the parameters based on the current real-time data and adaptively randomize new subjects.

[0100] Specifically, such as Figure 2 As shown, during the design phase (sample size planning phase), the target allocation probability is calculated based on the key bridge parameters and the average exposure time, thereby calculating the total sample size.

[0101] The target allocation probability is used for adaptive randomization of subject-to-therapist allocation.

[0102] The formula for calculating the target allocation probability of the i-th treatment group is:

[0103] ;

[0104] in, Assign a probability to the target of the i-th treatment group; i, This refers to the index number of the treatment group; , , , respectively, represent the event incidence rate, average exposure time, and key bridge parameters for group i; G is the total number of treatment groups.

[0105] Assuming there are two treatment groups, the formula for calculating the target assignment probability of the i-th treatment group is:

[0106] .

[0107] The total sample size is calculated based on the standard normal distribution, combined with the allocation probability and key bridge parameters. By quantifying the impact of dropout and allocation ratios on the sample size, the formula for calculating the total sample size is as follows:

[0108] ;

[0109] ;

[0110] in, This represents the total sample size. The significance level quantile after correction is the cumulative probability in the standard normal distribution. The corresponding quantiles; The significance level after correction is commonly determined using Bonferroni correction. To test the effectiveness against the preset target; The significance level is preset. Let G be the number of pairs of logarithms. If each pair of pairs in G is compared, ; To test the standard normal quantile corresponding to the power, i.e. the cumulative probability in the standard normal distribution is... The corresponding quantiles; The effect size difference was obtained through the event occurrence rate; , Let be the target assignment probability and key bridge parameters for the i-th group, respectively.

[0111] When there are two treatment groups, the formula for calculating the total sample size is:

[0112] ;

[0113] in, Assign probabilities to the targets in Group 1 and Group 2 respectively; , These are the key bridge parameters for Group 1 and Group 2, respectively.

[0114] During the execution (simulation) phase (treatment allocation phase), parameters are dynamically updated based on current real-time data, and new subjects are adaptively randomly assigned. The specific process is as follows:

[0115] A1. The event incidence rate is recalculated based on the data of currently enrolled subjects. This event incidence rate is calculated as the ratio of the total number of recurrent events in subjects who experienced an event to the total exposure duration of enrolled subjects, using the following formula:

[0116] ;

[0117] in, Let i be the event occurrence rate of the i-th group; The total number of recurrent events in the subjects who experienced the target event in group i; The total exposure time of the enrolled subjects in group i;

[0118] A2, based on the recalculated event occurrence rate, calculates the key bridge parameters and target allocation probability using the adaptive Simpson method;

[0119] A3. If the fluctuation range of the target allocation probability exceeds the preset range, then perform sensitivity analysis, that is: adjust the value range of the event occurrence rate, recalculate the key bridge parameters and the target allocation probability until the fluctuation range of the target allocation probability is within the preset range, such as the fluctuation range being less than 0.1.

[0120] The probability of allocation should not fluctuate too much, to avoid the proportion of a certain group being too high or too low, while ensuring the balance of sample size between groups and the effectiveness of statistical tests.

[0121] A4. Monitor in real time whether new subjects are enrolled and perform dynamic balanced covariate randomization (DBCD) to allocate treatment: If there are new subjects, repeat steps A1 to A3 and assign the new subjects to the corresponding treatment groups according to the updated target allocation probability; if there are no new subjects, record and output the current allocation results and trial data.

[0122] This embodiment introduces a shedding rate in the steps. This increases the calculated sample size from an ideal 241 to a realistic 286. This increase accurately compensates for information loss, ensuring that the test power still reaches 0.9 under real-world conditions, thus solving the power deficiency problem caused by neglecting dropout in existing technologies. The system recalculates the allocation probability based on real-time data. When treatment shows better results, the system automatically adjusts the allocation strategy to allow more patients to receive better treatment. Simulation verification shows that this can reduce the overall relapse event rate by approximately 15%.

[0123] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0124] This invention explicitly incorporates dropout rate into randomized exposure time modeling, enabling sample size estimation to reflect information loss under real clinical conditions. By introducing key bridging parameters, it unifies dropout mechanisms, relapse event characteristics, and adaptive randomization strategies within a single theoretical framework. During execution, a closed-loop iterative mechanism optimizes treatment allocation based on real-time data, ensuring more subjects are assigned to treatment groups with the most anticipated efficacy. Furthermore, by providing a complete decision support workflow from trial design to execution, it addresses the disconnect between sample size determination and randomization strategies in existing technologies. The entire system has broad applicability in clinical trials for relapse events in chronic diseases such as asthma and chronic obstructive pulmonary disease, enhancing the scientific rigor, feasibility, and regulatory acceptability of trial designs.

[0125] Example 2

[0126] like Figure 3 As shown, the second embodiment of the present invention also provides a device for estimating the sample size of clinical trials for recurrent events, comprising:

[0127] The parameter acquisition module is used to acquire basic test information, including test type and dropout rate.

[0128] The statistical model building module is used to establish a statistical model integrating the subject dropout mechanism based on the test type and dropout rate, and to quantify the impact of dropout on exposure time.

[0129] The parameter calculation module is used to calculate key bridge parameters and average exposure time based on the statistical model.

[0130] The dual-path closed-loop decision execution module is used to execute dual-path closed-loop decisions that include a design phase and an execution phase: in the design phase, the target allocation probability is calculated based on the key bridge parameters and the average exposure time, thereby calculating the total sample size; in the execution phase, the parameters are dynamically updated based on the current real-time data, and new subjects are adaptively and randomly assigned.

[0131] Example 3

[0132] The third embodiment of the present invention also provides a device for estimating the sample size of clinical trials for recurrent events, which includes a memory and a processor. The memory stores a computer program that can be executed by the processor to implement the method for estimating the sample size of clinical trials for recurrent events as described above.

[0133] Example 4

[0134] The fourth embodiment of the present invention also provides a computer-readable storage medium storing computer-readable instructions, which, when executed by a processor of the device on which the computer-readable storage medium is located, implement the above-described method for estimating the sample size of clinical trials for recurrent events.

[0135] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating sample size in clinical trials for recurrent events, characterized in that, include: Obtain basic test information, including test type and dropout rate; Based on the aforementioned test type and dropout rate, a statistical model integrating the subject dropout mechanism was established to quantify the impact of dropout on exposure time. Key bridge parameters and average exposure time were calculated based on the statistical model. The execution involves a dual-path closed-loop decision-making process that includes both the design and execution phases: In the design phase, the target allocation probability is calculated based on the key bridge parameters and the average exposure time, thereby calculating the total sample size; During the execution phase, parameters are dynamically updated based on current real-time data, and new subjects are adaptively randomly assigned. Among them, the key bridge parameters are the key parameters for connection detachment and statistical effectiveness, which are obtained through integral calculation, and the formula is: ； in, These are the key bridge parameters for the i-th group; Let i be the event occurrence rate of the i-th group; Let be the detachment risk coefficient for the i-th group; This refers to the duration of the experimental treatment; These are the discrete parameters of the negative binomial model; The test exposure time; For the derivative sign; Then, the key bridge parameters are solved using the adaptive Simpson method. The average exposure time combined with the shedding risk factor Duration of experimental treatment The formula is: ； in, Let be the average exposure time for group i; The target allocation probability is used for adaptive randomization of subjects to treatment groups. The formula for calculating the target allocation probability of the i-th treatment group is: ； in, Assign a probability to the target of the i-th treatment group; i, G represents the index number of the treatment group; G represents the total number of treatment groups. The total sample size is based on a standard normal distribution. Combining the allocation probability and key bridge parameters, and quantifying the impact of dropout and allocation ratios on the sample size, the formula for calculating the total sample size is as follows: ； ； in, This represents the total sample size. The significance level quantile after correction is the cumulative probability in the standard normal distribution. The corresponding quantiles; The significance level after correction; To test the effectiveness against the preset target; The significance level is preset. For the number of pairs of logarithms; To test the standard normal quantile corresponding to the power, i.e. the cumulative probability in the standard normal distribution is... The corresponding quantiles; The effect size difference is obtained through the event occurrence rate.

2. The method for estimating the sample size of a clinical trial for recurrent events according to claim 1, characterized in that... The statistical model described is based on a negative binomial regression model to describe the occurrence process of recurrent events, and models the actual exposure time of each subject as a random variable determined by the preset dropout rate and the trial type, specifically: Based on the shedding rate, the shedding risk coefficient is calculated using the exponential shedding model, with the following formula: ； in, Let be the detachment risk coefficient for the i-th group; Let i be the shedding rate of the i-th group; The duration of the trial treatment is determined by the trial type; i represents the index number of the treatment group. Define the random exposure time of subjects Time of shedding Duration of experimental treatment The smaller value, and assuming the shedding time It follows an exponential distribution, expressed as: ； A negative binomial regression model was used to describe the exposure time of the j-th subject in the i-th group. Number of recurrent events within The expression is: ； ； in, It follows a negative binomial distribution; The mean; Let i be the event occurrence rate of the i-th group; These are the discrete parameters of the negative binomial model, used to characterize the degree of dispersion in the distribution of recurring events; By fitting a negative binomial regression model with the actual data from the enrolled subjects, the initial parameters were estimated. , .

3. The method for estimating the sample size of a clinical trial for recurrent events according to claim 2, characterized in that... During the execution phase, parameters are dynamically updated based on current real-time data, and new subjects are adaptively randomly assigned, specifically as follows: A1. The event incidence rate is recalculated based on the data of currently enrolled subjects. This event incidence rate is calculated as the ratio of the total number of recurrent events in subjects who experienced an event to the total exposure duration of enrolled subjects, using the following formula: ； in, Let i be the event occurrence rate of the i-th group; The total number of recurrent events in the subjects who experienced the target event in group i; The total exposure time of the enrolled subjects in group i; Index the subjects by number; A2, based on the recalculated event occurrence rate, calculates the key bridge parameters and target allocation probability using the adaptive Simpson method; A3. If the fluctuation range of the target allocation probability exceeds the preset range, then perform sensitivity analysis, that is: adjust the range of event occurrence rate, recalculate the key bridge parameters and target allocation probability until the fluctuation range of the target allocation probability is within the preset range. A4. Monitor in real time whether new subjects are enrolled and perform dynamic balanced covariate randomization for treatment allocation: If there are new subjects, repeat steps A1 to A3 and assign the new subjects to the corresponding treatment groups according to the updated target allocation probability; if there are no new subjects, record and output the current allocation results and trial data.

4. A sample size estimation system for recurrent event clinical trials, used to implement the sample size estimation method for recurrent event clinical trials as described in any one of claims 1-3, characterized in that, include: The parameter acquisition module is used to acquire basic test information, including test type and dropout rate. The statistical model building module is used to establish a statistical model integrating the subject dropout mechanism based on the test type and dropout rate, and to quantify the impact of dropout on exposure time. The parameter calculation module is used to calculate key bridge parameters and average exposure time based on the statistical model. The dual-path closed-loop decision execution module is used to execute dual-path closed-loop decisions that include the design phase and the execution phase: In the design phase, the target allocation probability is calculated based on the key bridge parameters and the average exposure time, thereby calculating the total sample size; During the execution phase, parameters are dynamically updated based on current real-time data, and new subjects are adaptively randomly assigned.

5. A device for estimating sample size in clinical trials for recurrent events, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program that can be executed by the processor to implement a method for estimating the sample size of a clinical trial for recurrent events as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-readable instructions, which, when executed by a processor of the device on which the computer-readable storage medium resides, implement a method for estimating the sample size of a clinical trial for recurrent events as described in any one of claims 1-3.

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