Method and system for assessing drug effectiveness in the presence of a partially cured population

Abstract

The present application relates to a method and system for evaluating drug effectiveness in the presence of a partially cured population, the method comprising the steps of: obtaining observational study sample data, determining proxy variables and covariates, and dividing the sample into a treatment group and a control group according to a treatment protocol; performing parameter estimation on the treatment group and the control group using a mixed cure model respectively to obtain a latent incurable rate and a survival function of non-cured persons for the treatment group and the control group; calculating a drug cure rate causal effect parameter based on the latent incurable rate of the treatment group and the control group; calculating a survival function of an incurable main layer based on the latent incurable rate of the treatment group and the control group and the survival function of non-cured persons; and evaluating the effectiveness of the drug based on the drug cure rate causal effect parameter and the survival function of the incurable main layer.

Description

Technical Field

[0001] This invention relates to the field of drug efficacy evaluation technology, and in particular to a method and system for evaluating drug efficacy in a population with partial cure. Background Technology

[0002] In medical clinical research, the assessment of drug efficacy is one of the most important criteria for drug evaluation and is of great significance. Medical research often focuses on the timing of a specific event. For example, in acute lymphoblastic leukemia (ALL) studies, doctors are primarily concerned with the time of relapse or death of the patient. With advancements in medical technology, many diseases can now be partially cured. Again, taking ALL as an example, its cure rate has increased from less than 10% in the 1960s to 70% today. Therefore, accurately evaluating drug efficacy in the presence of a partially cured population is crucial. Typically, drug efficacy assessment requires randomized, double-blind clinical trials. However, in practice, due to ethical considerations, randomized trials may be difficult to conduct. For example, when a relatively effective drug already exists, evaluating the efficacy of a newly developed drug requires doctors to recommend the drug based on the patient's condition and obtain the patient's consent. In such cases, because the use of drugs in observational studies does not meet the requirements of randomized trials, directly using such data for drug efficacy assessment may be inaccurate. This invention focuses on solving the problem of accurately assessing drug efficacy in observational clinical studies where a partially cured population exists.

[0003] In medical research, if the primary outcome is the timing of an event (such as death or relapse), it is usually assumed that all individuals will experience that event. However, in reality, a subset of individuals often do not experience this event even after long-term follow-up; this group can be considered cured after treatment. To better capture this characteristic, researchers have proposed extending traditional survival analysis models to cure models. The most widely used model is the hybrid cure model, which combines two sub-models (survival time sub-model and cure rate sub-model) using a binary latent variable B.

[0004] In clinical research, the existence of a portion of the population that can be completely cured makes it difficult to well define the primary outcome, or the outcome may exist but not accurately reflect the research's focus. Initially, researchers proposed parametric and semi-parametric methods to estimate survival time in the presence of cured individuals. Subsequently, to further enhance model flexibility, non-parametric mixed cure models were proposed, and their identifiability was investigated. Furthermore, many researchers have studied hypothesis testing based on cure models. However, due to the potential presence of unobserved covariates, existing methods may not accurately assess drug efficacy. This is because current methods only focus on estimating model parameters, and the resulting estimated parameters may not accurately reflect drug efficacy. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a method and system for evaluating the effectiveness of drugs in a population with partial cure, in order to solve the problem that existing methods only focus on the parameters of the estimation model, and the estimated parameters obtained cannot accurately reflect the effectiveness of the drug.

[0006] On one hand, embodiments of the present invention provide a method for evaluating the effectiveness of a drug in a population with partial cure, comprising the following steps:

[0007] Obtain observational study sample data, identify proxy variables and covariates, and divide the samples into treatment and control groups according to the treatment plan;

[0008] The mixed cure model was used to estimate parameters in the treatment group and the control group to obtain the potential incurability rate and survival function of the uncured individuals in the treatment group and the control group.

[0009] Calculate the causal parameters of drug cure rate based on the potential incurability of the treatment and control groups;

[0010] The survival function of the incurable principal layer was calculated based on the potential incurability rate of the treatment and control groups and the survival function of the incurable individuals.

[0011] The effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer.

[0012] Based on further improvements to the above method, a mixed cure model was used for parameter estimation in both the treatment and control groups to obtain the potential incurability rate and survival functions of those who were not cured in both groups, including:

[0013] Using the proxy variables and covariates as explanatory variables and the potential cure status of the samples as response variables, the semi-parametric estimation method was used to estimate the potential incurability rates of the treatment group and the control group.

[0014] Using the proxy variables and covariates as explanatory variables and the latent survival function of the samples as the response variable, the survival function of the uncured individuals in the treatment group and the control group was obtained by semi-parametric estimation.

[0015] Furthermore, using the formula δ(x,v)={1-p (1) (x,v)}-{1-p (0) The causal parameters of the drug cure rate are calculated in the formula (x,v); where p (1) (x,v) represents the potential incurability rate of the treatment group under condition (x,v), p (0) (x,v) represents the potential incurability rate of the control group under the condition (x,v), δ(x,v) represents the causal parameter of the drug cure rate, x represents the first covariate, and v represents the proxy variable.

[0016] Furthermore, based on the potential incurability rate of the treatment and control groups and the survival function of the uncured individuals, the survival function of the incurable master layer was calculated, including:

[0017] Calculate the proportion and sample weighting function of each principal layer based on the potential incurability rate of the treatment and control groups:

[0018]

[0019] π uu (x,v)=ρmin{p (1) (x,v),p (0) (x,v)}+(1-ρ)p (1) (x,v)p (0) (x,v),

[0020] π uc (x,v)=p (1) (x,v)-π uu (x,v),

[0021] π cu (x,v)=p (0) (x,v)-π uu (x,v),

[0022] π cc (x,v)=1-π uu (x,v)-π uc (x,v)-π cu (x,v);

[0023] Where z represents the treatment plan, z=1 represents the treatment group, z=0 represents the control group, and z i Let x represent the processing plan for the i-th sample, v represent the proxy variable, and h represent the processing plan for the i-th sample.z (x,v) represents the sample weight function of scheme group z, p (z) (x,v) represents the probability that a sample in scheme z is potentially incurable under condition (x,v), p (z) (x) represents the probability that a sample in scheme z is potentially incurable under condition x, I(·) represents the indicator function, and π uu (x,v) represents the probability that the sample is in the incurable main layer under the condition (x,v), π uc (x,v) represents the probability that the sample is in the damaged group under condition (x,v), π cu (x,v) represents the probability that the sample is in the protection group under condition (x,v), π cc (x,v) represents the probability that a sample is in the overall cure group under condition (x,v), and ρ represents the correlation parameter of potential cure status;

[0024] The survival function of the incurable main layer is calculated based on the proportion of each main layer and the sample weight function.

[0025] Furthermore, the survival function of the incurable primary layer is calculated according to the following formula:

[0026]

[0027]

[0028] Among them, v i Let represent the proxy variable for the i-th sample, w represent the second covariate, t represent the time parameter, h1(·) represent the sample weight function for the treatment group, h0(·) represent the sample weight function for the control group, and p (z) (x,v i ) indicates that the samples in scheme group z are under the condition (x, v) i The probability of a potential incurable disease under π, where I(·) represents the characteristic function, and π uu (x,v i ) indicates that the sample is under condition (x, v) i The probability of being in an incurable primary layer, π uc (x,v i ) indicates that the sample is under condition (x, v) i The probability of being in the damaged group, π cu (x,v i ) indicates that the sample is under condition (x, v) i The probability of being in the protection group, π cc (x,v i ) indicates that the sample is under condition (x, v) i The probability of being in the overall cure group. This represents the survival function in the treatment group that cannot be cured in the main layer. Let |·| represent the survival function of the incurable main layer in the control group, and |·| represent the number of samples in the set.

[0029] Furthermore, the effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer, including:

[0030] If the causal parameter δ(x,v) for drug cure rate is positive, it means that under the condition of covariate (x,v), the treatment regimen will improve the cure rate compared to the control regimen; when δ(x,v) is negative, it means that under the condition of covariate (x,v), the treatment regimen will reduce the cure rate compared to the control regimen.

[0031] Furthermore, the effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer, including:

[0032] According to the formula Calculate the difference in survival probability between the treatment regimen and the control regimen in the incurable main layer when the covariate is (x, w), where, This represents the survival function in the treatment group that cannot be cured in the main layer. denoted as the survival function of the incurable main layer in the control group, x represents the first covariate, and w represents the second covariate;

[0033] If τ at time t s A positive value for (t|x,w) indicates that the treatment regimen will increase the survival probability at time t when the covariate is (x,w) in the population that cannot be cured of the main layer; a negative value indicates that the treatment regimen will decrease the survival probability at time t compared to the control regimen when the covariate is (x,w) in the population that cannot be completely cured of the main layer.

[0034] According to the formula Calculate the average survival time of the incurable primary layer, where t * Indicates the end time of integration;

[0035] τ m A positive value for (x,w) indicates the extended survival time of the treatment when the covariate is (x,w) in the incurable primary disease population; a negative value indicates the reduced survival time of the treatment when the covariate is (x,w) in the incurable primary disease population.

[0036] Furthermore, evaluating the effectiveness of the drug based on the causal parameters of the drug's cure rate and the survival function of the incurable principal layer also includes:

[0037] Calculate the difference in survival probability between the treatment regimen and the control regimen in the target population. Where n represents the number of the target population;

[0038] If τ at time t s A positive value for (t) indicates that the treatment regimen improves the survival probability at time t in the target population compared to the control regimen; a negative value indicates that the experimental drug reduces the survival probability at time t in the target population compared to the control regimen. i ,w i () represents the first and second covariates of the i-th sample;

[0039] According to the formula Calculate the average survival time of the target population;

[0040] If τ m A positive value indicates that the treatment regimen extends the survival time of the target population compared to the control regimen; a negative value indicates that the treatment regimen reduces the survival time of the target population compared to the control regimen.

[0041] On the other hand, embodiments of the present invention provide a drug efficacy evaluation system for a partially cured population, comprising the following modules:

[0042] The sample acquisition module is used to acquire sample data for observational studies, determine proxy variables and covariates, and divide the samples into treatment and control groups according to the treatment plan.

[0043] The model parameter estimation module is used to perform parameter estimation using a hybrid cure model on the treatment group and the control group, respectively, to obtain the potential incurability rate and survival function of the uncured individuals in the treatment group and the control group.

[0044] The causal effect parameter calculation module is used to calculate the causal effect parameter of drug cure rate based on the potential incurability of the treatment group and the control group.

[0045] The module for calculating the incurable primary layer survival function is used to calculate the survival function of the incurable primary layer based on the potential incurability rate of the treatment group and the control group and the survival function of the uncured individuals.

[0046] The drug efficacy evaluation module is used to evaluate the efficacy of the drug based on the causal parameters of the cure rate and the survival function of the incurable master layer.

[0047] Based on further improvements to the above system, the incurable primary layer survival function calculation module calculates the incurable primary layer survival function using the following process:

[0048] Calculate the proportion and sample weighting function of each principal layer based on the potential incurability rate of the treatment and control groups:

[0049]

[0050] π uu (x,v)=ρmin{p (1) (x,v),p (0) (x,v)}+(1-ρ)p (1) (x,v)p (0) (x,v),

[0051] π uc (x,v)=p (1) (x,v)-π uu (x,v),

[0052] π cu (x,v)=p (0) (x,v)-π uu (x,v),

[0053] π cc (x,v)=1-π uu (x,v)-π uc (x,v)-π cu (x,v);

[0054] Where z represents the treatment plan, z=1 represents the treatment group, z=0 represents the control group, and z i Let x represent the processing plan for the i-th sample, v represent the proxy variable, and h represent the processing plan for the i-th sample. z (x,v) represents the sample weight function of scheme group z, p (z) (x,v) represents the probability that a sample in scheme z is potentially incurable under condition (x,v), p (z) (x) represents the probability that a sample in scheme z is potentially incurable under condition x, I(·) represents the indicator function, and π uu (x,v) represents the probability that the sample is in the incurable main layer under the condition (x,v), π uc (x,v) represents the probability that the sample is in the damaged group under condition (x,v), π cu (x,v) represents the probability that the sample is in the protection group under condition (x,v), π cc (x,v) represents the probability that a sample is in the overall cure group under condition (x,v), and ρ represents the correlation parameter of potential cure status;

[0055] The survival function of the incurable main layer is calculated based on the proportion of each main layer and the sample weight function.

[0056] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0057] 1. In view of the problem that existing technologies can only use randomized controlled trials to evaluate drug efficacy, this invention proposes a technology to evaluate drug efficacy using observational (retrospective) study data, thereby improving the utilization value of real-world data.

[0058] 2. In view of the problem that existing technologies and methods only focus on the estimation of model parameters and the obtained parameters cannot accurately reflect the effectiveness of drugs, this invention needs to propose drug effectiveness evaluation indicators with practical significance, including the causal effect of cure rate and the causal effect of survival time in the case of incurability, in order to reflect drug effectiveness.

[0059] 3. To address the problem that existing technologies cannot eliminate the influence of the cured population on the primary outcome when evaluating drug efficacy in the presence of a partially cured population, this invention proposes a method that combines the characteristics of the cure model to reflect the occurrence of potential cure outcomes, thereby obtaining the direct causal effect of the drug on the primary outcome, and thus evaluating the drug's efficacy.

[0060] 4. In view of the problem that traditional master stratification methods use the limited monotonicity assumption in the process of evaluating drug efficacy, this invention needs to use more general correlation assumptions of potential cure outcomes to avoid the impact of unreasonable assumptions on drug efficacy evaluation, thereby improving the accuracy of drug efficacy evaluation.

[0061] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0062] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0063] Figure 1 This is a flowchart illustrating a method for evaluating drug efficacy in a partially cured population, as described in an embodiment of the present invention.

[0064] Figure 2 This is a block diagram of a drug efficacy evaluation system for a partially cured population, as described in an embodiment of the present invention.

[0065] Figure 3 This is a comparison diagram of the effects of the embodiments of the present invention and the prior art. Detailed Implementation

[0066] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0067] First, the terms / variables used in this invention will be explained:

[0068] X is a covariate (optional), which is usually a series of physical characteristics of the subject collected before the use of the drug. These indicators may have a certain impact on the patient's treatment plan, the potential outcome of a cure, and the potential primary outcome. For ease of distinction, it is referred to as the first covariate in this invention.

[0069] W is a covariate (optional), similar to X, and is usually a series of physical characteristics of the subject collected before the use of the drug. However, these indicators can only affect the potential primary outcome, not the potential cure, except for the treatment plan; for ease of distinction, it is referred to as the second covariate in this invention.

[0070] V is a proxy variable (required). In addition to affecting the treatment plan, it is a variable that is only related to the potential cure outcome and does not affect the potential primary outcome. It is generally a risk factor related to whether the patient can be cured.

[0071] Z represents the treatment regimen (required), which is usually a binary variable. Generally, Z=1 indicates that the treatment regimen is the drug regimen to be evaluated, and Z=0 indicates that the treatment regimen is the control regimen. The control regimen can be placebo, other drug regimens, or no treatment.

[0072] D represents the occurrence of censoring (required), which is usually a binary variable. D=1 indicates that no censoring occurred, meaning the primary outcome was observed. D=0 indicates that censoring occurred, meaning the subject was lost to follow-up for some reason, and the primary outcome was not observed.

[0073] Y represents the time of the event (which is mandatory). It is usually a continuous variable representing the time of the main outcome. When D = 1, Y represents the time of the main outcome. When D = 0, Y represents the time of censoring.

[0074] One specific embodiment of the present invention discloses a method for evaluating the effectiveness of a drug in a partially cured population, such as... Figure 1 As shown, it includes the following steps:

[0075] S1. Obtain observational study sample data, determine proxy variables and covariates, and divide the samples into treatment and control groups according to the treatment plan;

[0076] S2. Parameter estimation was performed using a mixed cure model in both the treatment and control groups to obtain the cure rate and survival function of the uncured individuals in both groups.

[0077] S3. Calculate the causal parameters of drug cure rate based on the cure rates of the treatment group and the control group;

[0078] S4. Calculate the survival function of the incurable principal layer based on the cure rate of the treatment group and the control group and the survival function of the uncured individuals;

[0079] S5. Evaluate the effectiveness of the drug based on the causal parameters of the drug cure rate and the survival function of the incurable principal layer.

[0080] Compared with existing technologies, this invention utilizes observational (retrospective) study data and employs a mixed cure model in the presence of partially cured individuals. It assesses the causal effect of the drug on the primary outcome by evaluating the occurrence of potential cures, thereby evaluating drug efficacy. For incurable individuals, a survival function is used to assess the drug's ability to prolong survival, thus evaluating drug efficacy. The evaluation indicators are practically meaningful and more accurate and reasonable.

[0081] This technology can be used to assess the long-term efficacy or safety of drugs after they have been marketed. Previous trials have demonstrated the short-term efficacy of a drug, and the aim is now to explore its long-term effects or safety. No new randomized trials need to be designed; the task can be accomplished using only retrospective data from post-marketing studies. Because the amount of retrospective data is far greater than that of randomized trials, this technology can more accurately assess drug efficacy in cases where a partial cure exists.

[0082] In implementation, step S1 first collects observational study sample data and determines the proxy variables and covariates based on the meanings of the aforementioned proxy variables and covariates. The samples are then divided into a treatment group and a control group according to their treatment protocols. The treatment group receives the medication to be evaluated, while the control group may receive no treatment, a placebo, or other medications.

[0083] Taking a study on transplantation methods for leukemia treatment as an example. Fully matched transplantation was used as the control group, and haploidentical transplantation as the treatment group. If a patient underwent fully matched transplantation, Z=0; otherwise, Z=1. If a patient relapsed or died during the follow-up period, the time Y was recorded, and the event occurrence was recorded as D=1. If a patient was discontinued during the study, the discontinuation time Y was recorded, and the event non-occurrence was recorded as D=0. At baseline, the patient's various physical characteristics were (X, W) (e.g., whether the patient's disease stage was CR1, and whether the diagnosis was B-cell acute leukemia; these indicators also have a certain impact on the patient's treatment plan, potential cure rate, and potential major outcomes, therefore they are classified as the first covariate X). V is a variable only related to the potential cure outcome, such as whether the patient's minimum residual disease (MRD) was positive.

[0084] For example, in Alzheimer's disease research, when the primary outcome is the time to MCI conversion, age accelerates the conversion time but has no effect on whether MCI is converted, so it is used as a covariate W; learning scores only reduce the MCI conversion rate but have no effect on the conversion time, so they can be used as a proxy variable V; while abstract thinking ability affects both the probability of MCI conversion and the time required for MCI conversion, so it can be used as a covariate X.

[0085] To better assess drug efficacy in the presence of cured individuals, within the potential outcome framework, B(z) is defined as a binary variable representing the potential cure status of a subject at treatment z, where z = 0, 1. z = 1 indicates treatment with the drug regimen being evaluated, and z = 0 indicates treatment with the control regimen. If B(z) = 1, it means the potential cure status of a subject at treatment z is incurable; if B(z) = 0, it means the potential cure status is complete cure. T(z) is defined as the time to occurrence of the potential primary outcome at treatment z. When B(z) = 0, the potential cure status of a subject at treatment z is complete cure, therefore T(z) = ∞. In practice, clinical trials do not continue indefinitely, so some individuals will inevitably be lost to observation. Therefore, defining C(z) as the potential censoring time, the variable representing whether censoring is potential can be expressed as D(z) = I{T(z)≤C(z)}, where I(·) is the indicator function, D(z) = 1 indicates that the potential observable major outcome is present, and D(z) = 0 indicates that potential censoring has occurred. Similarly, the potential event occurrence time can be expressed as Y(z) = min{T(z),C(z)}. Then the actual observed outcome variables are Y = Z*Y(1) + (1-Z)*Y(0) and D = Z*D(1) + (1-Z)*D(0).

[0086] Since the primary outcome of interest is the time of occurrence of the primary outcome with respect to the treatment regimen, i.e., T(z), it is necessary to introduce the concept of a survival function from survival analysis. Define S... (z) (t) = P(T(z)>t) represents the probability that the potential survival time of a subject is greater than t when treated with z. Since some subjects can be completely cured, we have lim t→∞ S (z) D(t) > 0, and this limit represents the potential cure rate of the subject when treated as z. Due to censoring, it is impossible to know definitively whether each subject can be cured. However, D(z) = 1 indicates that the subject must have experienced the primary outcome when treated as z, i.e., the subject must not have been cured. However, a subject with D(z) = 0 may be cured when treated as z, or their potential survival time may be greater than the potential censoring time.

[0087] In implementation, a principal stratification method was adopted, defining G = (B(1), B(0)) as the principal stratum, i.e., the potential cure status under different treatment plans is the principal stratum. The principal stratum is divided into: B(1) = B(0) = 0 is the overall cure group, indicating that the patient can be completely cured regardless of the treatment plan, denoted as CC; B(0) = 1, B(1) = 0 is the protection group, indicating that the patient can be cured with the treatment plan (i.e., the drug to be evaluated) but cannot be cured with the control plan, denoted as CU; B(0) = 0, B(1) = 1 is the damage group, indicating that the patient cannot be cured with the treatment plan (i.e., the drug to be evaluated) but can be cured with the control plan, denoted as UC; B(1) = B(0) = 1 is the incurable group, indicating that the patient cannot be completely cured regardless of the treatment plan, denoted as UU, as shown in Table 1. Obviously, if the patient can be cured regardless of the treatment plan (i.e., CC group), the recommended treatment drug can be any one of them. If a patient can only be cured by one of the treatment options (i.e., the CU group and the UC group), then the treatment that can cure the patient should be recommended. However, for patients who cannot be cured by either treatment (i.e., the UU group), further research is needed to evaluate the effectiveness of the drug. In such cases, the effectiveness of the drug is usually defined as its ability to prolong the patient's survival time. That is, to prolong the patient's survival time as much as possible when a cure is not possible.

[0088] Table 1. Definition of principal stratification under the cure model.

[0089]

[0090] Therefore, the evaluation of drug effectiveness consists of two parts. First, the cure rate of the drug is assessed. Second, for those who cannot be cured by the drug, survival time needs to be compared.

[0091] Define π g (x,v)=P(G=g|X=x,V=v) represents the probability of a subject in each principal layer G=g, p (z) (x,v)=P(B(z)=1|X=x,V=v) represents the potential incurability of the subject.

[0092] The efficacy of a drug in potentially curing a patient is assessed using the causal parameter of the drug's cure rate, expressed as:

[0093] δ(x,v)={1-p (1) (x,v)}-{1-p (0) (x,v)}

[0094] Where, p (1) (x,v) represents the potential incurability rate of the treatment group under condition (x,v), p (0)(x,v) represents the potential incurability rate of the control group under the condition (x,v), δ(x,v) represents the causal parameter of the drug cure rate, x represents the first covariate, and v represents the proxy variable.

[0095] When δ(x,v)>0, it means that the cure rate of the drug to be evaluated is higher than that of the control drug under the condition of (x,v).

[0096] For individuals with incurable conditions, two causal parameters can be defined to assess the effectiveness of the drug:

[0097] (1) Poor survival probability (RDU) in patients who cannot be completely cured.

[0098] τ s (t|x,w)=S (1) (t|G=UU,X=x,W=w)-S (0) (t|G=UU,X=x,W=w)

[0099] τ s (t|x,w) is used to represent the difference in survival probability of a drug over time. If τ s If (t|x,w)>0, it means that in the population that cannot be completely cured, when the covariate is (x,w), the survival probability of the drug to be evaluated at time t is higher than that of the control group.

[0100] (2) Time to complete survival (TDU) of patients who cannot be completely cured

[0101]

[0102] This is used to assess the average survival time extended by a drug. The integration interval is typically limited to [0, t]. * ], where t * The maximum censoring time is greater than the minimum of the two treatment options. If τ m If (x,w)>0, it means that in people who cannot be completely cured, when the covariate (x,w) is less than 0, the drug to be evaluated can prolong survival time.

[0103] To ensure the identifiability of these causal parameters, we need the following assumptions (where P represents probability, E represents expectation, and ⊥ represents statistical independence):

[0104] Condition 1: Negligibility: Z⊥(G,T(z),C(z))|X,V,W;

[0105] Condition 1 means that, given the baseline covariates (including X, V, W) and principal layers of the subjects, the treatment assignments are independent of the potential outcomes. This assumption is a common one in causal inference.

[0106] Condition 2: Positivity: 0 < P(Z = 1|X, V, W) < 1, and 0 < P(B(z) = 1|X, V, W) < 1

[0107] This condition means that it guarantees the existence of the UU group. The subjects always have a certain probability of being cured, and whether a subject can be cured is not absolute but occurs with a certain probability.

[0108] Condition 3: Random censoring: C(z) ⊥ (B(z), T(z))|Z = z, X, V, W;

[0109] This condition means that the potential censoring is independent of the events of the primary outcome. Such an assumption is common in survival analysis.

[0110] Condition 4: Sufficiently long censoring time: inf{t: S (z) (t|B(z) = 1, X, V, W) = 0} < inf{t: H (z) (t|B(z) = 1, X, V, W) = 1}, where H (z) is the cumulative density function of the potential censoring time C(z);

[0111] This condition means that there will always be a relatively large censoring time to ensure that the patients who cannot be cured can observe the occurrence of their primary outcome. This condition ensures that the cured population can be observed in the trial and is also a common assumption for the identifiability of the cure model.

[0112] Condition 5: Exclusion restriction: V ⊥ T(z)|Z = z, G, X, W;

[0113] This condition means that V does not directly affect the potential survival time T(z), but only affects the survival time T(z) through G.

[0114] Condition 6: Surrogate correlation: V ⊥ G|X, W;

[0115] This condition means that V is an influencing factor of the main stratum G, that is, it affects the cure rate. At this time, V can be regarded as an instrumental variable of G.

[0116] Condition 7: Random monotonicity: Define

[0117]

[0118] to represent the correlation between the potential cure results B(1) and B(0). Assume that ρ(X, V) = ρ and 0 ≤ ρ ≤ 1 is a known constant.

[0119] This condition means a relaxation of individual monotonicity, thus ensuring the rationality of the principal stratification method in the cure model and the accuracy of drug efficacy assessment. The principal stratification is distinguished by the correlation of potential outcomes, with ρ being the corresponding correlation parameter. When ρ = 1, it indicates that the UC or CU layer does not exist given the covariates (X, V). This assumption is reasonable because if a drug has a high cure rate, it means that the drug is more suitable for the patient; if treatments with lower cure rates can cure the patient, treatments with higher cure rates should be able to cure the patient even more. When ρ = 0, the potential cure outcomes B(1) and B(0) are completely independent given the covariates (X, V). When 0 < ρ < 1, the situation is somewhere in between. Generally, different ρ values ​​can be selected based on the actual situation in practical applications. Simulations show that different ρ values ​​result in smaller biases, while ρ = 1 usually has smaller variance, so ρ = 1 is preferred for analysis.

[0120] To address the limitation of traditional master stratification methods that rely on monotonicity assumptions in assessing drug efficacy, this invention employs more general correlation assumptions regarding potential cure outcomes. This avoids the impact of unreasonable assumptions on drug efficacy assessment, thereby improving the accuracy of drug efficacy evaluation.

[0121] Under conditions 1-4 above, the causal parameters for the cure rate can be identified. Under conditions 1-7, the causal parameters RDU and TDU can be identified.

[0122] Based on the above definitions, a mixed cure model was used for parameter estimation in both the treatment and control groups to obtain the potential incurability rate and survival function of uncured individuals in both groups. In the mixed cure model, (X,V,W) affects the survival function sub-model, and (X,V) affects the cure rate sub-model. Therefore, step S2 specifically includes:

[0123] S21. Using the proxy variables and covariates as explanatory variables and the potential cure status of the samples as the response variable, semi-parametric estimation is used to estimate the potential incurability rate p of the treatment group and the control group. (z) (x,v).

[0124] S22. Using the proxy variables and covariates as explanatory variables and the latent survival function of the samples as the response variable, semi-parametric estimation is used to estimate the survival functions of the treatment group and the control group (untreated individuals) to obtain the survival functions.

[0125] For example, using a logistic model, with the proxy variables and covariates as explanatory variables and the potential cure status of the samples as the response variable, and employing a semi-parametric estimation method to estimate the model parameters, the potential incurability rate p of the treatment group and the control group can be obtained. (z) (x,v).

[0126]

[0127] in, For the intercept term, and It is the model coefficient vector corresponding to the covariate x and the proxy variable v, and the superscript T indicates transpose.

[0128] For example, using the Cox proportional hazards model, with the proxy variables and covariates as explanatory variables and the latent survival function of the sample as the response variable, semi-parametric estimation is used to estimate the parameters and obtain the latent survival functions of the treatment group and the control group of untreated patients.

[0129]

[0130] in, and It is the model coefficient vector corresponding to the first covariate x, the proxy variable v, and the second covariate w, with the superscript T indicating transpose.

[0131] The semi-parametric estimation method uses the EM algorithm for iterative estimation. Assume the parameters obtained in the (m-1)th iteration are... Then, in the E-step of the m-th iteration of the EM algorithm, we have:

[0132]

[0133] in,

[0134] The samples are sorted according to the main outcome time, so that Y (1) ≤…≤Y (n) It is Y1,…,Y n The ranking statistics were then used to obtain... Perform M steps to maximize the partial likelihood function:

[0135]

[0136]

[0137] Among them, R i It is in Y (i) Individuals who are still at risk at all times, namely R iThis represents the set of samples whose primary outcome occurs at a time greater than that of the i-th sample. Maximization and It can be obtained and The estimate is then obtained using a nonparametric method.

[0138]

[0139] in

[0140] Repeat the EM iterations described above until the parameter γ is reached. (z) and β (z) Convergence. The final parameters are... Substitute these values ​​into the model to obtain the potential incurable rate p for the treatment and control groups. (z) (x,v) and the survival functions of uncured individuals in the treatment and control groups.

[0141] Furthermore, based on the potential incurability rates of the treatment and control groups, the causal parameter of the drug cure rate is calculated, i.e., according to the formula δ(x,v)={1-p (1) (x,v)}-{1-p (0) Calculate the causal coefficient of the drug to be evaluated on the cure rate (x,v)}.

[0142] Based on the potential incurability rate of the treatment and control groups and the survival function of the incurable patients, the survival function of the incurable master layer is calculated. Specifically, step S4 includes:

[0143] S41. Calculate the proportion and sample weighting function of each principal layer based on the potential incurability rate of the treatment group and the control group:

[0144]

[0145] π uu (x,v)=ρmin{p (1) (x,v),p (0) (x,v)}+(1-ρ)p (1) (x,v)p (0) (x,v),

[0146] π uc (x,v)=p (1) (x,v)-π uu (x,v),

[0147] π cu (x,v)=p (0) (x,v)-π uu (x,v),

[0148] π cc (x,v)=1-π uu (x,v)-π uc (x,v)-π cu (x,v);

[0149] Where z represents the treatment plan, z=1 represents the treatment group, z=0 represents the control group, and z i Let x represent the processing plan for the i-th sample, v represent the proxy variable, and h represent the processing plan for the i-th sample. z (x,v) represents the weight function of the z-scheme group, p (z) (x,v) represents the probability that a sample in scheme z is potentially incurable under condition (x,v), p (z) (x) represents the probability that a sample in scheme z is potentially incurable under condition x, I(·) represents the indicator function, and π uu (x,v) represents the probability that the sample is in the incurable main layer under the condition (x,v), π uc (x,v) represents the probability that the sample is in the damaged group under condition (x,v), π cu (x,v) represents the probability that the sample is in the protection group under condition (x,v), π cc (x,v) represents the probability that a sample is in the overall cure group under condition (x,v), and ρ represents the correlation parameter of potential cure status.

[0150] S42. Based on the proportion of each principal layer and the sample weight function, eliminate the influence of other principal layers on the incurable principal layer, and calculate the survival function of the incurable principal layer.

[0151] h z (x,v) satisfies the following conditions:

[0152] ∫ V h z (x,v)dv=0,

[0153]

[0154]

[0155] Using function h z (x,v) can eliminate the influence of the remaining main layers on the UU layer.

[0156] According to the main layer definition, the survival function of the healers in the treatment group is...

[0157]

[0158] When P(π) uc (x,V)>0)=1, then π uc(x,v)>0 is almost true for any It is true, where P(π) uc (x,V)>0) represents π given x. uc The probability of (x,V)>0 with respect to V is given by:

[0159]

[0160] For a given x, when P(π) uc When (x,V)>0)<1, for Then we have π uc (x,v)=0. Then for have Therefore, it can be calculated. exist Calculated using the weighted average in Right now

[0161]

[0162] Where p1(v) represents the density function of V in group z=1, i.e., the treatment group.

[0163] Similarly, according to the definition of the principal layer, the survival function of the cured patients in the control group is...

[0164]

[0165] When P(π) cu (x,V)>0)=1, then π cu (x,v)>0 is almost true for any It is true, where P(π) cu (x,V)>0) represents π given x. cu The probability of (x,V)>0 with respect to V is given by:

[0166]

[0167] For a given x, when P(π) cu When (x,V)>0)<1, for Then we have π cu (x,v)=0. Then for have Therefore, it can be calculated. exist Calculated using the weighted average in Right now

[0168]

[0169] Where p0(v) represents the density function of V in the group z=0, i.e., the control group.

[0170] Therefore, the survival function of the treatment group that cannot cure the primary layer is calculated according to the following formula:

[0171]

[0172]

[0173] Where z represents the treatment plan, z=1 represents the treatment group, z=0 represents the control group, and z i Let x represent the processing plan for the i-th sample, and v represent the first covariate. i Let represent the proxy variable for the i-th sample, w represent the second covariate, t represent the time parameter, h1(·) represent the sample weight function for the treatment group, h0(·) represent the sample weight function for the control group, and p (z) (x,v i ) indicates that the samples in scheme group z are under the condition (x, v) i The probability of a potential incurable disease under π, where I(·) represents the characteristic function, and π uu (x,v i ) indicates that the sample is under the condition (x, v) i The probability of being in an incurable primary layer, π uc (x,v i ) indicates that the sample is under the condition (x, v) i The probability of being in the damaged group, π cu (x,v i ) indicates that the sample is under condition (x, v) i The probability of being in the protection group, π cc (x,v i ) indicates that the sample is under condition (x, v) i The probability of being in the overall cure group is given by ρ, which represents the correlation parameter of potential cure status. This represents the survival function in the treatment group that cannot be cured in the main layer. Let |·| represent the survival function of the incurable main layer in the control group, and |·| represent the number of samples in the set.

[0174] After calculating the causal parameters of the cure rate and the survival function of the incurable principal layer, the effectiveness of the drug is evaluated based on these parameters.

[0175] Specifically, in step S5, the effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer, including:

[0176] If the causal parameter δ(x,v) for drug cure rate is positive, it means that under the condition of covariate (x,v), the treatment regimen will improve the cure rate compared to the control regimen; when δ(x,v) is negative, it means that under the condition of covariate (x,v), the treatment regimen will reduce the cure rate compared to the control regimen.

[0177] When δ(x,v) is positive, the larger the value of δ(x,v), the more significant the improvement in cure rate of the treatment group drug compared to the control group drug when covariates X=x and V=v.

[0178] Specifically, step S5, which assesses the effectiveness of the drug based on the causal parameters of the drug cure rate and the survival function of the incurable principal layer, includes:

[0179] According to the formula Calculate the difference in survival probability between the treatment regimen and the control regimen in the incurable main layer when the covariate is (x, w), where, This represents the survival function in the treatment group that cannot be cured in the main layer. denoted as the survival function of the incurable main layer in the control group, x represents the first covariate, and w represents the second covariate;

[0180] If τ at time t s A positive value for (t|x,w) indicates that in the incurable population with covariate (x,w), the treatment regimen increases the survival probability at time t; a negative value indicates that in the incurable population with covariate (x,w), the treatment regimen decreases the survival probability at time t compared to the control regimen. τ s When (t|x,w) is positive, the larger the value, the more significant the improvement in the survival probability of the drug under evaluation at time t compared to the control group when covariates X=x and W=w in the incurable population, that is, the more effective the drug is.

[0181] According to the formula Calculate the average survival time of the incurable primary layer, where t * Indicates the end time of integration;

[0182] τ m A positive value for (x, w) indicates the increased survival time of the treatment regimen when the covariate is (x, w) in patients with an incurable primary disease layer; a negative value indicates the decreased survival time of the treatment regimen when the covariate is (x, w) in patients with an incurable primary disease layer. τ m When (x,w) is positive, the larger the value, the longer the survival time extended by the drug to be evaluated in the incurable population when covariates X=x and W=w, that is, the more effective the drug is.

[0183] Furthermore, the effectiveness of the drug in the target population can be evaluated. Therefore, step S5, which assesses the effectiveness of the drug based on the causal parameters of the cure rate and the survival function of the incurable principal layer, also includes:

[0184] Calculate the difference in survival probability between the treatment regimen and the control regimen in the target population. Where n represents the number of the target population; where (x i ,w i ) represents the first and second covariates of the i-th sample.

[0185] If τ at time t s A positive value for (t) indicates that the treatment regimen improves the survival probability at time t in the target population compared to the control regimen; a negative value indicates that the experimental drug reduces the survival probability at time t in the target population compared to the control regimen.

[0186] τ s When (t) is positive, the larger the value, the more significant the improvement in the survival probability of the experimental drug at time t in the target population compared to the control group, that is, the more effective the drug is.

[0187] According to the formula Calculate the average survival time of the target population;

[0188] If τ m A positive value indicates that the treatment regimen extends the survival time of the target population compared to the control regimen; a negative value indicates that the treatment regimen reduces the survival time of the target population compared to the control regimen.

[0189] τ m When positive, a larger value indicates that the drug extends the survival time of the target population, meaning the drug is more effective.

[0190] To demonstrate the effectiveness of this invention, a simulation study example is given below.

[0191] Let the baseline covariate X follow a Bernoulli distribution with a mean of 0.5, W and V follow a standard normal distribution, and the treatment Z follow a Bernoulli distribution with a mean of 0.5. Define the exponential link function expit(x) = 1 / exp(-x). The latent variable indicating whether a person can be cured in the treatment and control groups follows a probability expit((1,X,V)γ) z The two-point distribution of γ1, where γ1 = (2, -1, -1) T and γ0=(0,1,1) T Assuming ρ is 0 or 1, calculate the probabilities of different principal layers. This leads to the conclusion that the principal layer G follows a multinomial distribution (π). uu (X,V),πcu (X,V),π uc (X,V),π cc (X,V)). Y and D are generated based on the main hierarchy G and the processing scheme Z.

[0192] Assume that the survival functions in each group satisfy the proportional hazards model, and the baseline survival function is 0.5exp(-t / 2). For the covariate (X,W) treatment group, the parameters at the UU and UC levels are β1 = (-1,1). T and β uc =(0,1) T The parameters for the control group in the UU and CU layers were β0 = (1,1). T and β cu =(1,2) T Assume that the censoring time in the treatment group follows a uniform distribution U(5,12), while the censoring time in the control group follows a uniform distribution U(5,8).

[0193] The existing technology involves directly integrating the survival function obtained from the cure model into the target population to obtain the corresponding average mixed cure model, as shown in the following expression:

[0194]

[0195] Figure 3 This figure illustrates the difference between the survival function obtained by the present invention and existing technologies in the target population and the actual results. The solid lines in the figure represent the true survival curves of the treatment and control groups in the main layer; the long dashed lines represent the mean of 500 simulations estimated by the present invention and existing methods; and the dotted lines represent the 2.5%–97.5% quantiles obtained by the present invention and existing technologies based on 500 simulations. It is clearly visible that the existing technology exhibits significant systematic bias, with the true value sometimes even exceeding its 97.5% quantile curve. In contrast, the present invention can effectively estimate causality coefficients and further utilize these results to make reasonable evaluations of drug efficacy.

[0196] On the other hand, embodiments of the present invention provide a drug efficacy evaluation system for a population with a partial cure, such as... Figure 2 As shown, the system includes the following modules:

[0197] The sample acquisition module is used to acquire sample data for observational studies, determine proxy variables and covariates, and divide the samples into treatment and control groups according to the treatment plan.

[0198] The model parameter estimation module is used to perform parameter estimation using a hybrid cure model on the treatment group and the control group, respectively, to obtain the potential incurability rate and survival function of the uncured individuals in the treatment group and the control group.

[0199] The causal effect parameter calculation module is used to calculate the causal effect parameter of drug cure rate based on the potential incurability of the treatment group and the control group.

[0200] The module for calculating the incurable primary layer survival function is used to calculate the survival function of the incurable primary layer based on the potential incurability rate of the treatment group and the control group and the survival function of the uncured individuals.

[0201] The drug efficacy evaluation module is used to evaluate the efficacy of the drug based on the causal parameters of the cure rate and the survival function of the incurable master layer.

[0202] Preferably, the uncurable primary layer survival function calculation module calculates the uncurable primary layer survival function using the following process:

[0203] Calculate the proportion and sample weighting function of each principal layer based on the potential incurability rate of the treatment and control groups:

[0204]

[0205] π uu (x,v)=ρmin{p (1) (x,v),p (0) (x,v)}+(1-ρ)p (1) (x,v)p (0) (x,v),

[0206] π uc (x,v)=p (1) (x,v)-π uu (x,v),

[0207] π cu (x,v)=p (0) (x,v)-π uu (x,v),

[0208] π cc (x,v)=1-π uu (x,v)-π uc (x,v)-π cu (x,v);

[0209] Where z represents the treatment plan, z=1 represents the treatment group, z=0 represents the control group, and z i Let x represent the processing plan for the i-th sample, v represent the proxy variable, and h represent the processing plan for the i-th sample. z (x,v) represents the sample weight function of scheme group z, p (z) (x,v) represents the probability that a sample in scheme z is potentially incurable under condition (x,v), p (z)(x) represents the probability that a sample in scheme z is potentially incurable under condition x, I(·) represents the indicator function, and π uu (x,v) represents the probability that the sample is in the incurable main layer under the condition (x,v), π uc (x,v) represents the probability that the sample is in the damaged group under condition (x,v), π cu (x,v) represents the probability that the sample is in the protection group under condition (x,v), π cc (x,v) represents the probability that a sample is in the overall cure group under condition (x,v), and ρ represents the correlation parameter of potential cure status;

[0210] The survival function of the incurable main layer is calculated based on the proportion of each main layer and the sample weight function.

[0211] The above-described method and system embodiments are based on the same principles, and their related aspects can be referenced from each other to achieve the same technical effects. For specific implementation processes, please refer to the foregoing embodiments, which will not be repeated here.

[0212] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0213] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for evaluating drug efficacy in a partially cured population, characterized in that, Includes the following steps: Obtain observational study sample data, identify proxy variables and covariates, and divide the samples into treatment and control groups according to the treatment plan; The mixed cure model was used to estimate parameters in the treatment group and the control group to obtain the potential incurability rate and survival function of the uncured individuals in the treatment group and the control group. Calculate the causal parameters of drug cure rate based on the potential incurability of the treatment and control groups; The survival function of the incurable principal layer was calculated based on the potential incurability rate of the treatment and control groups and the survival function of the incurable individuals. The effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer; The survival function of the incurable principal layer was calculated based on the potential incurability rate of the treatment and control groups and the survival function of the incurable individuals, including: Calculate the proportion and sample weighting function of each principal layer based on the potential incurability rate of the treatment and control groups: ， ， ， ； in, Indicate the solution. Indicates the processing group. This represents the control group. Indicates the first The processing plan for each sample Denotes the first covariate. Represents a proxy variable. express The sample weighting function of the scheme group express Samples in the scheme group under the conditions The probability of it being potentially incurable. express Samples in the scheme group under the conditions The probability of it being potentially incurable. , Indicates that the sample is under the condition The probability of being in an incurable primary layer. Indicates that the sample is under the condition The probability of being in the damage group. Indicates that the sample is under the condition The probability of being in the protection group Indicates that the sample is under the condition The probability of being in the overall cure group. Correlation parameters indicating potential cure status; The survival function of the incurable main layer is calculated based on the proportion of each main layer and the sample weight function.

2. The method for evaluating drug efficacy in a partially cured population according to claim 1, characterized in that, Parameter estimation was performed using a mixed cure model in both the treatment and control groups to obtain the potential incurability rate and survival functions for those not cured in both groups, including: Using the proxy variables and covariates as explanatory variables and the potential cure status of the samples as response variables, the semi-parametric estimation method was used to estimate the potential incurability rates of the treatment group and the control group. Using the proxy variables and covariates as explanatory variables and the latent survival function of the samples as the response variable, the survival function of the uncured subjects in the treatment group and the control group was obtained by semi-parametric estimation.

3. The method for evaluating drug efficacy in a partially cured population according to claim 1, characterized in that, Using formula Calculate the causal parameters of drug cure rate; among which, Indicates the processing group is in The potential incurable rate under certain conditions Indicating that the control group is in The potential incurable rate under certain conditions This parameter represents the causal relationship between drug cure rate and other parameters. Denotes the first covariate. This represents a proxy variable.

4. The method for evaluating drug efficacy in a partially cured population according to claim 1, characterized in that, Calculate the survival function of the uncurable primary layer using the following formula: in, Indicates the first proxy variables for each sample Indicates the second covariate. Indicates time parameter, The sample weight function represents the treatment group. The sample weighting function represents the control group. express Samples in the scheme group under the conditions The probability of it being potentially incurable. , Indicates that the sample is under the condition The probability of being in an incurable primary layer. Indicates that the sample is under the condition The probability of being in the damage group. Indicates that the sample is under the condition The probability of being in the protection group Indicates that the sample is under the condition The probability of being in the overall cure group. This represents the survival function in the treatment group that cannot be cured in the main layer. This represents the survival function of the main layer that cannot be cured in the control group. This indicates the number of samples in the set.

5. The method for evaluating drug efficacy in a partially cured population according to claim 1, characterized in that, The effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer, including: If the drug cure rate is a causal parameter A positive value indicates that in the covariate Under these conditions, the treatment regimen will improve the cure rate compared to the control regimen; when A negative value indicates that the value is in the covariate. Under these conditions, the treatment regimen will reduce the cure rate compared to the control regimen.

6. The method for evaluating drug efficacy in a partially cured population according to claim 1, characterized in that, The effectiveness of the drug is evaluated based on the causal parameters of the cure rate and the survival function of the incurable principal layer, including: According to the formula Calculate the covariates as When the treatment regimen in the primary layer cannot be cured, the survival probability is worse than that of the control regimen. This represents the survival function in the treatment group that cannot be cured in the main layer. This represents the survival function of the main layer that cannot be cured in the control group. Denotes the first covariate. Indicates the second covariate; like time A positive value indicates that in the population where the primary layer cannot be cured, the covariate is... At that time, the solution will improve The probability of survival at any given time; if negative, it indicates that the main layer of the population cannot be completely cured when the covariate is... The time-saving solution will reduce the time compared to the control solution. The probability of survival at any given moment; According to the formula Calculate the average survival time of the incurable primary layer, where, Indicates the end time of integration; If the value is positive, it indicates that in the population where the main layer cannot be cured, when the covariate is... When the treatment extends survival time, the value indicates that the covariate is negative; if it is negative, it indicates that the covariate is negative in the population that cannot be cured. At that time, the processing solution reduces the lifespan.

7. The method for evaluating drug efficacy in a partially cured population according to claim 6, characterized in that, The assessment of drug effectiveness based on the causal parameters of the cure rate and the survival function of the incurable principal layer also includes: Calculate the difference in survival probability between the treatment regimen and the control regimen in the target population. ,in, Indicates the size of the target audience; like time A positive value indicates that the treatment regimen is more effective than the control regimen in the target population. The probability of survival at a given time; a negative value indicates that the experimental drug will reduce the survival rate relative to the control regimen in the target population. The probability of survival at time t, where, ( Indicates the first The first and second covariates of each sample; According to the formula Calculate the average survival time of the target population; like A positive value indicates that the treatment regimen extends the survival time of the target population compared to the control regimen; a negative value indicates that the treatment regimen reduces the survival time of the target population compared to the control regimen.

8. A drug efficacy evaluation system for a portion of cured patients, characterized in that, Includes the following modules: The sample acquisition module is used to acquire sample data for observational studies, determine proxy variables and covariates, and divide the samples into treatment and control groups according to the treatment plan. The model parameter estimation module is used to perform parameter estimation using a hybrid cure model on the treatment group and the control group, respectively, to obtain the potential incurability rate and survival function of the uncured individuals in the treatment group and the control group. The causal effect parameter calculation module is used to calculate the causal effect parameter of drug cure rate based on the potential incurability of the treatment group and the control group. The module for calculating the incurable primary layer survival function is used to calculate the survival function of the incurable primary layer based on the potential incurability rate of the treatment group and the control group and the survival function of the uncured individuals. The drug efficacy evaluation module is used to evaluate the efficacy of the drug based on the causal effect parameters of the drug cure rate and the survival function of the incurable master layer; The uncurable primary layer survival function calculation module calculates the uncurable primary layer survival function using the following process: Calculate the proportion and sample weighting function of each principal layer based on the potential incurability rate of the treatment and control groups: ， ， ， ； in, Indicate the solution. Indicates the processing group. This represents the control group. Indicates the first i The processing plan for each sample Denotes the first covariate. Represents a proxy variable. express The sample weighting function of the scheme group express Samples in the scheme group under the conditions The probability of it being potentially incurable. express Samples in the scheme group under the conditions The probability of it being potentially incurable. , Indicates that the sample is under the condition The probability of being in an incurable primary layer. Indicates that the sample is under the condition The probability of being in the damage group. Indicates that the sample is under the condition The probability of being in the protection group Indicates that the sample is under the condition The probability of being in the overall cure group. Correlation parameters indicating potential cure status; The survival function of the incurable main layer is calculated based on the proportion of each main layer and the sample weight function.

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