Matching-based privacy-preserving average causal effect estimation method and system

Abstract

The invention discloses a matching-based privacy-preserving average causal effect estimation method and system. The method comprises the following steps: firstly, training a logistic regression model, and injecting noise into a model weight; thirdly, calculating the tendency score of each sample by using the disturbed model, and adding noise; then calculating the distance between different samples according to the tendency score of each sample after disturbance, and sorting the distance; thirdly, matching is achieved based on the ranked distance matrixes, so that the potential intervention result of each sample under disturbance setting is calculated, noise is further injected into the sum of the potential intervention results of all the samples, and estimation of the average causal effect is achieved based on the sum of the potential results of disturbance.

Description

Technical Field

[0001] This invention relates to the field of data security technology, and in particular to a matching-based method and system for estimating privacy-preserving average causal effects. Background Technology

[0002] Causal effect estimation aims to quantify the direct impact of an intervention on an outcome variable, distinguishing intervention-induced changes from natural changes using scientific methods. This process is crucial for understanding causal relationships in complex systems. In the medical field, causal effect estimation based on patient data is often used to assist doctors in their judgment. For example, by analyzing whether a patient received treatment and the corresponding health indicators to assess the impact of treatment, doctors can help make better decisions in clinical treatment.

[0003] Matching-based causal effect estimation is a classic solution in causal estimation. It uses statistical techniques to match each treatment unit with one or more control units with similar characteristics to construct an artificial control group. The causal effect is then estimated by comparing the treatment group and the artificial control group. However, using real-world information during the matching process for causal effect estimation may leak patient privacy information. Therefore, ensuring the security of patient privacy data and protecting patient information during causal effect estimation is a problem worthy of in-depth research.

[0004] As a technique with rigorous theoretical safeguards, differential privacy technology introduces random noise into query results, making it impossible for attackers to infer information about a specific individual by comparing query results, even if they possess almost all other data. This has garnered increasing attention. However, causal effect estimation requires multiple uses of the patient's real information, and improving the usability of the results while protecting patient privacy presents a significant challenge. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies in the medical field, which either provide limited privacy protection for patient information or have very low usability of output results, by proposing a matching-based privacy-preserving average causal effect estimation method and system.

[0006] This invention overcomes the shortcomings of the prior art mainly through the following two approaches: on the one hand, perturbation is performed each time patient information is accessed to protect patient privacy; on the other hand, interference caused by noise is reduced by reasonably allocating privacy budgets at different stages and setting the maximum number of times each patient can be matched.

[0007] The objective of this invention is achieved through the following technical solution: This invention discloses a privacy-preserving average causal effect estimation method based on matching, the method comprising: Step one, train a regression model based on the patient's feature vector and intervention values, including the following sub-steps: 1.1 Normalize the patient's feature vector so that the value of the feature vector is between 0 and 1; 1.2 Using the normalized feature vectors as independent variables and the intervention values ​​as dependent variables, a logistic regression model is trained. 1.3 Injecting Gaussian noise into the true weights of the logistic regression model, the corresponding privacy budget is... Thus, the perturbation model weights are obtained; 1.4 Based on the perturbation-based regression model weights, calculate the propensity score for each patient and inject Gaussian noise into it. The corresponding privacy budget is... Thus, a perturbation tendency score is obtained; Step two involves perturbing the true intervention values, grouping patients based on the perturbed intervention values, calculating the distance between each patient and all patients in another group, and sorting them according to the distance. This includes the following sub-steps: 2.1 The real intervention value is perturbed using a random response method, with a corresponding privacy budget of... This allows us to obtain the perturbation intervention value for each patient. 2.2 Patients with a disturbance intervention value of 1 were assigned to the treatment group, and patients with a disturbance intervention value of 0 were assigned to the control group; 2.3 For all patients in the treatment group, based on the patient's perturbation tendency score, calculate the distance from each patient to all patients in the control group, and sort them in ascending order according to the distance to obtain the distance sorting matrix from the treatment group patients to all patients in the control group. 2.4 For all patients in the control group, based on the patient's perturbation tendency score, calculate the distance from each patient to all patients in the treatment group, and sort them in ascending order of distance to obtain the distance ranking matrix from the control group patients to all patients in the treatment group; Step 3, based on the two distance ranking matrices and the perturbation intervention result of each patient, calculate the potential intervention result of each patient in the non-intervention situation during perturbation, and further calculate the sum of the potential intervention results of all patients when the perturbation intervention value is 1 and 0, including the following sub-steps: 3.1 Calculate the maximum matching limit of the processing group under perturbation Maximum matching limit of control group ; 3.2 For all patients in the treatment group, based on their distance matrix to patients in the control group and combined with the maximum matching limit of the control group, calculate the potential intervention outcome for each patient when the perturbation intervention value is 0; 3.3 For all patients in the control group, the potential intervention outcome for each patient with a perturbation intervention value of 1 is calculated based on the distance matrix from the patients in the treatment group and the maximum matching limit of the treatment group. 3.4 Calculate the sum of potential intervention outcomes for all patients at perturbation intervention values ​​of 1 and 0; Step four involves perturbing the sum of potential intervention outcomes for all patients at perturbation values ​​of 1 and 0 using a Gaussian mechanism. The privacy budget allocated for this process is... The average causal effect is estimated based on the perturbation value, including the following sub-steps: 4.1 Gaussian noise was injected to perturb the sum of potential intervention outcomes for all patients at perturbation values ​​of 1 and 0; 4.2 The average causal effect is calculated based on two perturbation values ​​of the potential intervention outcome.

[0008] Furthermore, in step 1.3, the formula for perturbing the model weights is: In the formula The training weights that represent the model. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The corresponding noise variance is calculated based on the sensitivity of the weights.

[0009] Furthermore, in step 1.4, the formula for perturbing the propensity score is: In the formula The propensity score is calculated based on the perturbation-based model weights. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The corresponding noise variance is calculated based on the sensitivity of the propensity score.

[0010] Furthermore, in step 2.1, the probability of outputting the true intervention value using a random response is considered. The formula is: According to the above formula, the original intervention value has a probability Output the true value, with probability. Output the flipped spurious value.

[0011] Furthermore, in steps 2.3 and 2.4, the distance metric function used is: In the formula Representing the patient The perturbation tendency score.

[0012] Further, in step 3.1, the calculation and The specific steps are as follows: a) Calculate the sample size of the perturbation treatment group. Sample size of the control group and disturbance ; b) Set the number of matching neighbors And statistically analyze the distance ranking matrix of all samples in the perturbation. The maximum number of occurrences among neighboring samples ; c) Calculate intermediate variables as follows: In the formula The result is rounded to the nearest whole number. This represents taking the maximum value of the result within the parentheses. This represents the privacy budget corresponding to step four, used to perturb the sum of potential intervention outcomes for the patient. Represents the error coefficient. The maximum value of the number of samples in the processing group and the control group representing the disturbance; d) If Less than ,but , ,otherwise , .

[0013] Furthermore, in step 3.2, the specific steps for calculating the potential intervention outcomes for patients in the perturbation treatment group are as follows: a) Initialize the number of matches for all patients in the disturbance control group to 0; b) Iterate through all patients in the perturbation treatment group in sequence, sorting the list according to each patient's distance from the perturbation control group. After excluding patients in the perturbation control group who have reached the maximum number of matches, select the patients with the smallest distance. Patients in the control group (using a set) (This indicates that the number of times these extracted disturbance control group patients were matched is incremented by 1); c) Calculate the patient's condition according to the following formula. Potential intervention outcome when the perturbation intervention value is 0 : In the formula Patients representing the disturbance control group The actual intervention results.

[0014] Furthermore, in step 3.3, the specific steps for calculating the potential intervention outcomes for patients in the disturbance control group are as follows: a) Initialize the number of matches for all patients in the initial perturbation treatment group to 0; b) Iterate through all patients in the disturbance control group in sequence, sort the list according to each patient's distance from the treatment group, and after excluding patients in the disturbance treatment group who have reached the maximum number of matches, take the patients with the smallest distance. Patients in a treatment group (using a set) (This indicates that the number of times these extracted perturbation treatment group patients were matched is incremented by 1); c) Calculate the patient's condition according to the following formula. Potential intervention outcome when the perturbation intervention value is 1 : In the formula Patients representing the disturbance treatment group The actual intervention results.

[0015] Furthermore, in step 3.4, the specific steps for calculating the sum of potential intervention outcomes for all patients at perturbation intervention values ​​of 1 and 0 are as follows: a) Calculate the sum of potential intervention outcomes for all patients with a perturbation value of 1 as follows: In the formula A collection representing all patients. Representing the patient Potential intervention outcomes with a perturbation intervention value of 1; b) Calculate the sum of potential intervention outcomes for all patients with a perturbation value of 0 as follows: In the formula A collection representing all patients. Representing the patient Potential intervention outcomes with a perturbation intervention value of 0.

[0016] Furthermore, in step 4.1, the specific steps for injecting Gaussian noise into the sum of potential intervention results are as follows: a) The perturbation value for calculating the sum of potential intervention outcomes when the perturbation intervention value is 1 is as follows: In the formula This represents the sum of potential intervention outcomes when the perturbation intervention value is 1. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The sensitivity to the sum of potential intervention outcomes when the perturbation intervention value is 1 (i.e. ,in The noise variance can be calculated from the maximum change in the intervention result. b) The perturbation value for calculating the sum of potential intervention outcomes when the perturbation intervention value is 0 is as follows: In the formula This represents the sum of potential intervention outcomes when the perturbation intervention value is 0. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The sensitivity to the sum of potential intervention outcomes when the perturbation intervention value is 0 (i.e. ,in The noise variance can be calculated from the maximum change in the intervention result.

[0017] Furthermore, in step 4.2, the specific formula for calculating the average causal effect is as follows: Another aspect of the present invention discloses a matching-based privacy-preserving average causal effect estimation system, the system comprising: Privacy-preserving model building module: Based on the patient's feature vector and intervention value, train a logistic regression model, then inject noise into the trained model weights, calculate the propensity score based on the perturbed model weights, and inject noise into the propensity score; Privacy-preserving distance calculation module: The actual intervention value is perturbed by random response, and then patients are grouped based on the perturbed intervention value. The distance between each patient and all patients in another group is calculated and sorted to obtain two distance sorting matrices. Privacy-preserving outcome assessment module: Based on the perturbation intervention value and two distance ranking matrices, calculate the potential intervention outcome for each patient under the perturbation-free condition. Further calculate the sum of potential intervention outcomes for all patients when the perturbation intervention value is 1 and 0, and inject Gaussian noise into the sum of potential intervention outcomes to perturb it. Finally, calculate the average causal effect to reflect the degree of influence of the intervention variable on the medical indicators corresponding to the intervention outcome.

[0018] The beneficial effects of this invention are as follows: 1. By perturbing real information while satisfying differential privacy, the patient's privacy information is effectively protected; 2. By reasonably allocating privacy budgets at each stage and limiting the maximum number of matches for each patient, the impact of noise can be minimized; 3. A matching-based privacy-preserving average causal effect estimation method was designed, which maximizes the usability of the average causal effect estimate while fully protecting patient privacy. Attached Figure Description

[0019] Figure 1 A flowchart of a privacy-preserving average causal effect estimation method based on matching is provided for an embodiment of the present invention; Figure 2 An example of normalized patient information provided in an embodiment of the present invention; Figure 3 A method based on the embodiments of the present invention is provided. Figure 2 Example of calculating disturbance intervention value; Figure 4 A method based on the embodiments of the present invention is provided. Figure 2 and Figure 3 Example of calculating potential intervention outcomes; Figure 5 This is a block diagram of a privacy-preserving average causal effect estimation system based on matching, provided for an embodiment of the present invention. Detailed Implementation

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0022] like Figure 1 As shown in this embodiment, a privacy-preserving average causal effect estimation method based on matching is provided. Based on the patient's feature vector, intervention value, and intervention result in the medical field, the average causal effect is calculated using a matching method while satisfying differential privacy throughout the process. This assesses the impact of a specified intervention variable on the intervention result in the medical field, providing a reference for doctors' clinical treatment. The specific steps are as follows: Step one: Train a regression model based on the patient's feature vector and intervention values, for example... Figure 2 As shown, the patient's feature vector includes age, weight, gender, and heart rate. The intervention variable represents whether medication is being taken, with intervention values ​​including 1 (corresponding to medication) and 0 (corresponding to no medication). The intervention result corresponds to the patient's blood glucose (in millimoles per liter), and includes the following sub-steps: 1.1 Normalize the patient's feature vector so that the value of the feature vector is between 0 and 1, for example... Figure 2This presents a summary of patient information containing 900 patients and 4 feature vectors, with the values ​​of the feature vectors all normalized. 1.2 Using the normalized feature vectors as independent variables and the intervention values ​​as dependent variables, a logistic regression model is trained, for example... Figure 2 The model uses four feature vectors as independent variables and intervention values ​​consisting of 0 and 1 as dependent variables, based on which a logistic regression model can be trained. 1.3 Injecting Gaussian noise into the true weights of the logistic regression model, the corresponding privacy budget is... For example, setting Thus, the perturbation model weights are obtained; 1.4 Perturbation-based regression model weights: Using the patient's feature vector as input, the output of the regression model is calculated. This output is used as each patient's propensity score regarding medication use, and Gaussian noise is injected into it. The corresponding privacy budget is... For example, setting Thus, a perturbation tendency score is obtained; The specific implementation details are as follows: The formula for perturbing the weights of the logistic regression model is: In the formula The training weights that represent the model. The relaxation factor (e.g., set to 1e-5) is based on the privacy budget. relaxation coefficient The corresponding noise variance can be calculated from the sensitivity of the weights.

[0023] The formula for perturbing the propensity score is: In the formula The propensity score is calculated based on the perturbation-based model weights. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The corresponding noise variance can be calculated from the sensitivity of the propensity score.

[0024] Step two involves perturbing the true intervention values, grouping patients based on the perturbed intervention values, calculating the distance between each patient and all patients in another group, and sorting them according to the distance. This includes the following sub-steps: 2.1 The real intervention value is perturbed using a random response method, with a corresponding privacy budget of... For example, setting This allows us to obtain the perturbation intervention value for each patient, for example... Figure 3 The disturbance intervention value in the last column; The specific implementation details are as follows: The probability of outputting the true intervention value using a random response. The formula is: According to the above formula, the original intervention value has a probability Output the true value, with probability. Output the flipped spurious value.

[0025] 2.2 Patients with a disturbance intervention value of 1 were assigned to the treatment group, and patients with a disturbance intervention value of 0 were assigned to the control group; 2.3 For all patients in the treatment group, based on the patient's perturbation tendency score, calculate the distance from each patient to all patients in the control group, and sort them in ascending order according to the distance, thus obtaining the distance sorting matrix from the treatment group patients to all patients in the control group. 2.4 For all patients in the control group, based on the patient's perturbation tendency score, calculate the distance from each patient to all patients in the treatment group, and sort them in ascending order according to the distance to obtain the distance sorting matrix from the control group patients to all patients in the treatment group. The specific implementation details are as follows: The distance metric function used is: In the formula Representing the patient The perturbation tendency score.

[0026] Step 3: Based on the two distance ranking matrices and the perturbation intervention results for each patient, calculate the potential intervention results for each patient in the uninterventional scenario during perturbation. Further calculate the sum of the potential intervention results for all patients when the perturbation intervention value is 1 and 0, including the following sub-steps: 3.1 Calculate the maximum matching limit of the processing group under perturbation Maximum matching limit of control group ; The specific implementation details are as follows: a) Calculate the sample size of the perturbation treatment group. Sample size of the control group and disturbance ; b) Set the number of matching neighbors And statistically analyze the distance ranking matrix of all samples in the perturbation. The maximum number of occurrences among neighboring samples ; c) Calculate intermediate variables as follows: In the formula The result is rounded to the nearest whole number. This represents taking the maximum value of the result within the parentheses. This represents the privacy budget corresponding to step four, used to perturb the sum of potential intervention outcomes for the patient. This represents the error coefficient (set manually, for example, to 0.001). The maximum value of the number of samples in the processing group and the control group representing the disturbance; d) If Less than ,but , ,otherwise , .

[0027] 3.2 For all patients in the treatment group, based on their distance matrix to patients in the control group and combined with the maximum matching upper limit of the control group, calculate the potential intervention outcome for each patient when the perturbation intervention value is 0, for example... Figure 4 Example of the results in column 7; The specific implementation details are as follows: a) Initialize the number of matches for all patients in the disturbance control group to 0; b) Iterate through all patients in the perturbation treatment group in sequence, sorting the list according to each patient's distance from the perturbation control group. After excluding patients in the perturbation control group who have reached the maximum number of matches, select the patients with the smallest distance. Patients in the control group (using a set) (This indicates that the number of times these extracted disturbance control group patients were matched is incremented by 1); c) Calculate the patient's condition according to the following formula. Potential intervention outcome when the perturbation intervention value is 0 : In the formula Patients representing the disturbance control group The actual intervention results.

[0028] 3.3 For all patients in the control group, based on their distance matrix to patients in the treatment group and combined with the maximum matching limit of the treatment group, calculate the potential intervention outcome for each patient when the perturbation intervention value is 1, for example... Figure 4 Example of the results in column 8; The specific implementation details are as follows: a) Initialize the number of matches for all patients in the initial perturbation treatment group to 0; b) Iterate through all patients in the disturbance control group in sequence, sorting the list according to each patient's distance from the disturbance treatment group. After excluding patients in the disturbance treatment group who have reached the maximum number of matches, select the patients with the smallest distance. Patients in a treatment group (using a set) (This indicates that the number of times these extracted perturbation treatment group patients were matched is incremented by 1); c) Calculate the patient's condition according to the following formula. Potential intervention outcome when the perturbation intervention value is 1 : In the formula Patients representing the disturbance treatment group The actual intervention results.

[0029] 3.4 Calculate the sum of potential intervention outcomes for all patients at perturbation intervention values ​​of 1 and 0; The specific implementation details are as follows: a) Calculate the sum of potential intervention outcomes for all patients with a perturbation value of 1 as follows: In the formula A collection representing all patients. Representing the patient Potential intervention outcomes with a perturbation intervention value of 1. For example, for Figure 4 Sum the values ​​in the column corresponding to a perturbation intervention value of 1 for potential intervention outcomes. .

[0030] b) Calculate the sum of potential intervention outcomes for all patients with a perturbation value of 0 as follows: In the formula A collection representing all patients. Representing the patient Potential intervention outcomes with a perturbation intervention value of 0. For example, for Figure 4 Sum the values ​​in the column corresponding to a perturbation intervention value of 0 for potential intervention outcomes. .

[0031] Step four involves perturbing the sum of potential intervention outcomes for all patients at perturbation values ​​of 1 and 0 using a Gaussian mechanism. The privacy budget allocated for this process is... For example, setting The average causal effect is estimated based on the perturbation value, including the following sub-steps: 4.1 Gaussian noise was injected to perturb the sum of potential intervention outcomes for all patients at perturbation values ​​of 1 and 0; The specific implementation details are as follows: a) The perturbation value for calculating the sum of potential intervention outcomes when the perturbation intervention value is 1 is as follows: In the formula This represents the sum of potential intervention outcomes when the perturbation intervention value is 1. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The sensitivity to the sum of potential intervention outcomes when the perturbation intervention value is 1 (i.e. ,in The noise variance can be calculated from the maximum change in the intervention result, for example. Figure 4 Potential intervention results after perturbation ; b) The perturbation value for calculating the sum of potential intervention outcomes when the perturbation intervention value is 0 is as follows: In the formula This represents the sum of potential intervention outcomes when the perturbation intervention value is 0. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The sensitivity to the sum of potential intervention outcomes when the perturbation intervention value is 0 (i.e. ,in The noise variance can be calculated from the maximum change in the intervention result, for example. Figure 4 Potential intervention results after perturbation .

[0032] 4.2 The average causal effect is calculated based on two perturbation values ​​of the potential intervention outcome.

[0033] The specific implementation details are as follows: The specific formula for calculating the average causal effect is as follows: For example, according to Figure 4 The final calculated average causal effect This indicates that patients taking medication experienced an average decrease in blood glucose of 1 mmol / L compared to those not taking medication, a result that can provide important reference for doctors' clinical treatment.

[0034] Another aspect of this invention discloses a matching-based privacy-preserving average causal effect estimation system, such as... Figure 5 As shown, the system includes the following modules: Privacy-preserving model building module: Based on the patient's feature vector and intervention value, train a logistic regression model, then inject noise into the trained model weights, calculate the propensity score based on the perturbed model weights, and inject noise into the propensity score; Privacy-preserving distance calculation module: The actual intervention value is perturbed by random response, and then patients are grouped based on the perturbed intervention value. The distance between each patient and all patients in another group is calculated and sorted to obtain two distance sorting matrices. Privacy-preserving outcome assessment module: Based on the perturbation intervention value and two distance ranking matrices, calculate the potential intervention outcome for each patient under the perturbation-free condition. Further calculate the sum of potential intervention outcomes for all patients when the perturbation intervention value is 1 and 0, and inject Gaussian noise into the sum of potential intervention outcomes to perturb it. Finally, calculate the average causal effect to reflect the degree of influence of the intervention variable on the medical indicators corresponding to the intervention outcome.

[0035] All relevant content of each step involved in the above method embodiments can be referenced from the functional description of the corresponding functional module, and will not be repeated here.

[0036] The above description is merely a preferred embodiment of the present invention. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention using the methods and techniques disclosed above, or modify them into equivalent embodiments with equivalent changes, without departing from the scope of the technical solutions of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall still fall within the protection scope of the technical solutions of the present invention.

Claims

1. A privacy-preserving average causal effect estimation method based on matching, characterized in that, The method includes: Step one, train a regression model based on the patient's feature vector and intervention values, including the following sub-steps: 1.1 Normalize the patient's feature vector so that the value of the feature vector is between 0 and 1; 1.2 Using the normalized feature vectors as independent variables and the intervention values ​​as dependent variables, a logistic regression model is trained. 1.3 Injecting Gaussian noise into the true weights of the logistic regression model, the corresponding privacy budget is... Thus, the perturbation model weights are obtained; 1.4 Disturbance-based regression model weights, calculate the propensity score corresponding to each patient, and inject Gaussian noise, the corresponding privacy budget is , so as to obtain the disturbed propensity score; Step two involves perturbing the true intervention values, grouping patients based on the perturbed intervention values, calculating the distance between each patient and all patients in another group, and sorting them according to the distance. This includes the following sub-steps: 2.1 The true intervention value is perturbed using the randomized response method, and the corresponding privacy budget is Thus, the perturbed intervention value corresponding to each patient is obtained. 2.2 Patients with a disturbance intervention value of 1 were assigned to the treatment group, and patients with a disturbance intervention value of 0 were assigned to the control group; 2.3 For all patients in the treatment group, based on the patient's perturbation tendency score, calculate the distance from each patient to all patients in the control group, and sort them in ascending order according to the distance to obtain the distance sorting matrix from the treatment group patients to all patients in the control group. 2.4 For all patients in the control group, based on the patients' perturbation tendency scores, the distance from each patient to all patients in the treatment group is calculated and sorted in ascending order according to the distance to obtain the distance sorting matrix from the control group patients to all patients in the treatment group. Step 3: Based on the two distance ranking matrices and the perturbation intervention results for each patient, calculate the potential intervention results for each patient in the uninterventional scenario during perturbation. Further calculate the sum of the potential intervention results for all patients when the perturbation intervention value is 1 and 0, including the following sub-steps: 3.1 Calculate the maximum matching upper bound of the processing group under perturbation and the maximum matching upper bound of the control group ; 3.2 For all patients in the treatment group, based on their distance matrix to patients in the control group and combined with the maximum matching limit of the control group, calculate the potential intervention outcome for each patient when the perturbation intervention value is 0; 3.3 For all patients in the control group, the potential intervention outcome for each patient with a perturbation intervention value of 1 is calculated based on the distance matrix from the patients in the treatment group and the maximum matching limit of the treatment group. 3.4 Calculate the sum of potential intervention outcomes for all patients at perturbation intervention values ​​of 1 and 0; Step four, the sum of potential intervention outcomes for all patients at intervention values of 1 and 0 are perturbed using a Gaussian mechanism, which allocates a privacy budget of and the average causal effect is estimated based on the perturbed values.

2. The privacy-preserving average causal effect estimation method based on matching according to claim 1, characterized in that, In step 1.3, the formula for perturbing the model weights is: In the formula The training weights that represent the model. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The corresponding noise variance is calculated based on the sensitivity of the weights.

3. The matching-based privacy-preserving average causal effect estimation method according to claim 1, characterized in that, In step 1.4, the formula for perturbing the propensity score is: In the formula The propensity score is calculated based on the perturbation-based model weights. Represents the relaxation coefficient, based on the privacy budget. relaxation coefficient The corresponding noise variance is calculated based on the sensitivity of the propensity score.

4. The matching-based privacy-preserving average causal effect estimation method according to claim 1, characterized in that, In step 2.1, the probability of outputting a true intervention value using a random response The formula is: According to the above formula, the original intervention value has a probability The output real value has a probability The output flipped false value.

5. The privacy-preserving average causal effect estimation method based on matching according to claim 1, characterized in that, In steps 2.3 and 2.4, the distance metric function used is: wherein represent the patient's disturbance tendency scores, respectively.

6. The matching-based privacy-preserving average causal effect estimation method according to claim 1, characterized in that, In step 3.1, the calculation and is performed as follows: a) Calculate the sample size of the perturbation treatment group. Sample size of the control group and disturbance ; b) Set the number of matching neighbors And statistically analyze the distance ranking matrix of all samples in the perturbation. The maximum number of occurrences among neighboring samples ; c) calculating intermediate variables As follows: wherein representing rounding the result, representing taking the maximum of the results inside the parentheses, representing a privacy budget for the sum of the potential intervention results that perturb the patient, representing an error coefficient, ; d) if less than then , , else , .

7. The privacy-preserving average causal effect estimation method based on matching according to claim 1, characterized in that, In step 3.2, the specific steps for calculating the potential intervention outcomes for patients in the perturbation treatment group are as follows: a) Initialize the number of matches for all patients in the disturbance control group to 0; b) Iterate through all patients in the perturbation treatment group in sequence, sorting the list according to each patient's distance from the perturbation control group. After excluding patients in the perturbation control group who have reached the maximum number of matches, select the patients with the smallest distance. A control group of patients, using a set This indicates that the number of times these extracted perturbation control group patients were matched is incremented by 1; c) calculating the patient's Potential intervention outcome at a perturbation intervention value of 0 : In the formula represent patients in the disturbance control group actual intervention results; In step 3.3, the specific steps for calculating the potential intervention outcomes for patients in the disturbance control group are as follows: a) Initialize the number of matches for all patients in the initial perturbation treatment group to 0; b) Iterate through all patients in the disturbance control group in sequence, sort the list according to each patient's distance from the treatment group, and after excluding patients in the disturbance treatment group who have reached the maximum number of matches, take the patients with the smallest distance. Patients in a treatment group, using a set This indicates that the number of matches for these extracted perturbation treatment group patients will be incremented by 1; c) calculating the patient's score according to the formula Potential intervention outcome at a perturbation intervention value of 1 : In the formula Representative patients in the perturbation treatment group Actual intervention outcomes.

8. The privacy-preserving average causal effect estimation method based on matching according to claim 1, characterized in that, In step four, Gaussian noise is injected to perturb the sum of potential intervention outcomes for all patients when the perturbation intervention value is 1 and 0. The specific steps are as follows: a) The perturbation value for calculating the sum of potential intervention outcomes when the perturbation intervention value is 1 is as follows: wherein representing the sum of potential intervention results for a perturbation intervention value of 1, representing a relaxation coefficient based on the privacy budget , the relaxation coefficient and the sensitivity of the sum of potential intervention results for a perturbation intervention value of 1, a corresponding noise variance is calculated; b) The perturbation value for calculating the sum of potential intervention outcomes when the perturbation intervention value is 0 is as follows: wherein represents the sum of potential intervention results when the perturbation intervention value is 0, based on the privacy budget , the relaxation coefficient and the sensitivity of the sum of potential intervention results when the perturbation intervention value is 0, the corresponding noise variance is calculated.

9. The matching-based privacy-preserving average causal effect estimation method according to claim 1, characterized in that, In step four, the average causal effect is calculated as: In the formula These are the perturbation values ​​representing the sum of potential intervention outcomes when the perturbation intervention value is 1 and 0, respectively. The number of samples in the treatment group. This represents the sample size for the control group.

10. A privacy-preserving average causal effect estimation system based on matching, characterized in that, The system employs the matching-based privacy-preserving average causal effect estimation method according to any one of claims 1-9, comprising: Privacy-preserving model building module: Based on the patient's feature vector and intervention value, a logistic regression model is trained, and then noise is injected into the weights of the trained model. Based on the perturbed model weights, a propensity score is calculated, and noise is injected into the propensity score. Privacy-preserving distance calculation module: The actual intervention value is perturbed by random response, and then patients are grouped based on the perturbed intervention value. The distance between each patient and all patients in another group is calculated and sorted to obtain two distance sorting matrices. Privacy-preserving outcome assessment module: Based on the perturbation intervention value and two distance ranking matrices, calculate the potential intervention outcome for each patient under the perturbation-free condition. Further calculate the sum of potential intervention outcomes for all patients when the perturbation intervention value is 1 and 0, and inject Gaussian noise into the sum of potential intervention outcomes to perturb it. Finally, calculate the average causal effect to reflect the degree of influence of the intervention variable on the medical indicators corresponding to the intervention outcome.

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