Clinical multi-state model causal inference and prediction method and system containing time-dependent covariable

Abstract

The invention relates to a clinical multi-state model causal inference and prediction method and system containing time-dependent covariables, belongs to the technical field of state prediction, and solves the problem of low reliability of causal inference and prediction in the prior art. The method comprises the steps of obtaining state data of an observed patient; determining an instantaneous transfer risk function based on the observed patient's state data; based on the instantaneous transfer risk function, constructing a cumulative generation function of health state transfer, and determining asymptotic unbiased estimation of the cumulative generation function by adopting an effective influence function method; based on the asymptotic unbiased estimation, calculating the cumulative incidence rate of the target health state under different treatment schemes to obtain the causal effect of the treatment schemes on the target state; and obtaining state data of the to-be-predicted patient at the initial moment, and calculating the cumulative occurrence rate of the to-be-predicted patient in different clinical health states at the target moment based on the cumulative occurrence function to obtain a clinical health state prediction result of the to-be-predicted patient. And accurate clinical health state causal inference and prediction are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of state prediction, and in particular to a causal inference and prediction method and system for a clinical multi-state model including time-dependent covariates. Background Art

[0002] The multi-state process refers to the dynamic process of an individual developing from one state to another, which includes multiple intermediate state evolution scenarios. For example, patients with cardiovascular and cerebrovascular diseases generally go through multiple transformation processes, from a healthy state to a low-risk, medium-high-risk and coronary artery disease state, during which there is recovery, disease risk reduction or deterioration to death.

[0003] Traditional multi-state models focus on correlation analysis and cannot accurately estimate the causal effect of interventions on state transitions. When it comes to time-dependent covariates, a strict Markov assumption is usually used, which assumes that the current state depends only on the state at the previous moment without considering earlier historical information. This strong Markov assumption is too limited in complex scenarios such as medical scenarios and does not match the actual scenario, thus affecting the reliability of predictions, confusing medical mechanisms, and not conducive to studying the real principles behind disease interventions, making it difficult to provide guidance for actual treatment / disease prevention scenarios. Summary of the invention

[0004] In view of the above analysis, an embodiment of the present invention aims to provide a causal inference and prediction method and system for a clinical multi-state model including time-dependent covariates, so as to solve the problem that the existing strong assumptions affect the reliability of causal inference and prediction.

[0005] On the one hand, an embodiment of the present invention provides a causal inference and prediction method of a clinical multi-state model including time-dependent covariates. The method comprises the following steps:

[0006] Obtaining status data of each observed patient at the baseline time and at each observation time; the status data includes clinical health status, covariate status and censoring status; the covariate status is a status constructed by the covariate at time;

[0007] Determining an instantaneous transition risk function based on the baseline data of each observed patient and the status data at each observed time;

[0008] Based on the instantaneous transfer risk function, a cumulative occurrence function of health state transfer is constructed, and an effective influence function method is used to determine an asymptotically unbiased estimate of the cumulative occurrence function of health state transfer; based on the asymptotically unbiased estimate of the cumulative occurrence function, the cumulative incidence of the target health state under different treatment plans is calculated to obtain the causal effect of the treatment plan on the target health state;

[0009] The status data of the patient to be predicted at the initial moment is obtained, and the cumulative incidence rate of the patient to be predicted in different clinical health states at the target moment is calculated based on the cumulative occurrence function of the health state transfer, and the clinical health state prediction result of the patient to be predicted is obtained based on the cumulative incidence rate.

[0010] Based on the further improvement of the above method, the asymptotically unbiased estimate of the cumulative occurrence function of health state transition is:

[0011]

[0012] in, represents the asymptotically unbiased estimator of the cumulative occurrence function of the clinical health state transition to r when the treatment method is a, l is a variable representing the baseline covariate, Q r represents the set of all clinical health state transition paths ending at clinical health state r, and m1 represents path q x The number of state transitions, m2 represents the number of covariate state transitions, represents the set of all covariate state transition paths with a state transition number of m2, is a variable representing the time of the m1th clinical health status transition, t x,1 is a variable indicating the time of the first clinical health status transition, t x,j is a variable representing the jth clinical health status transition time, is the variable representing the time of the m2th covariate state transition, t l,j is a variable representing the jth covariate state transition time, t l,1 is a variable representing the first covariate state transition time, X represents the set of all clinical health states, represents the set of all covariate health states, Represents the path q x Whether it is in clinical health state g at time u, Represents the path q l Whether it is in the covariate state g′ at time u, represents the baseline covariate of the ith observed patient, represents the indicator function, z(u) represents the clinical health status transition path q x , the covariate state transition path is q l , when the baseline covariate is l, historical information at time u, represents the probability estimate of historical information z(·), indicates whether the i-th observed patient has transferred from clinical health state g to clinical health state h at time u, indicates whether the i-th observed patient transfers from covariate state g′ to covariate state h′ at time u, xj-1 represents the clinical health status transition path q x The j-1th clinical health status in j represents the clinical health status transition path q x The jth clinical health state in k-1 represents the clinical health status transition path q x The k-1th clinical health status in k represents the clinical health status transition path q x The kth clinical health state in represents the i-th observed patient at t x,k Is the moment from clinical health status x k-1 Transfer to clinical health status x k ,l j-1 Represents the covariate state transition path q l The j-1th covariate state in j Represents the covariate state transition path q l The j-th covariate state in l k-1 Represents the covariate state transition path q l The k-1th covariate state in k Represents the covariate state transition path q l The kth covariate state in , represents the i-th observed patient at t l,k Whether the moment is from the covariate state l k-1 Transfer to covariate state l k , denoting the estimated function of the probability distribution function of the baseline covariate, represents an estimate of the probability density of the integration path, Represents the estimation function of the instantaneous transition risk function of health status, represents the estimation function of the instantaneous transition hazard function of the covariate state, and n represents the number of observed patients.

[0013] Based on a further improvement of the above method, an instantaneous transfer risk function is determined based on the status data of each observed patient at the baseline moment and at each observation moment, including:

[0014] The clinical health status instantaneous transition risk function, the covariate status instantaneous transition risk function and the censored status instantaneous transition risk function were constructed respectively;

[0015] Determine the state transition path of each observed patient based on the state data at the baseline moment and each observation moment of each observed patient, and obtain the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process, and the likelihood function of the censored state transition process of each observed patient based on the state transition path of each observed patient and the clinical health state instantaneous transition risk function, the covariate state instantaneous transition risk, and the censored state instantaneous transition risk function;

[0016] Based on the likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process are solved to obtain the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk function and the estimation function of the censored state instantaneous transition risk function.

[0017] Based on the further improvement of the above method, the constructed clinical health status instantaneous transition risk function is:

[0018]

[0019] in, represents the basic risk function for instantaneous transition of clinical health status, represents the regression coefficient of the instantaneous transition risk function from clinical health state g to clinical health state h, Z(t) represents the historical state before time t, represents the instantaneous transition risk function from clinical health state g to clinical health state h, and the superscript T represents the transposition.

[0020] Based on the further improvement of the above method, the likelihood function of the clinical health state transition process of each observed patient is obtained based on the state transition path of each observed patient and the instantaneous transition risk function of the clinical health state:

[0021]

[0022] in, represents the likelihood function of the clinical health state transition process of the i-th observed patient, represents the number of state transitions in the clinical health state transition path of the i-th observed patient; represents the time of the j-1th state transition in the clinical health state transition path of the i-th observed patient, represents the time of the jth state transition in the clinical health state transition path of the i-th observed patient, Indicates clinical health status The instantaneous transition risk function to clinical health state s, χ represents the set of all clinical health states, Indicates clinical health status Transfer to clinical health status The instantaneous transfer risk function is represents the j-1th clinical health state in the clinical health state transition path of the i-th observed patient, represents the jth clinical health state in the clinical health state transition path of the i-th observed patient, Z i (u) represents the historical information of the i-th observed patient before time u, C i represents the censoring time of the i-th observed patient, T Di represents the death time of the ith patient, and τ represents the total observation time.

[0023] Based on the further improvement of the above method, the constructed covariate state instantaneous transition risk function is:

[0024]

[0025] in, represents the basic hazard function for instantaneous transitions in the covariate state, represents the regression coefficient of the instantaneous transition risk function from the covariate state g′ to the covariate state h′, Z(t) represents the historical state before time t, represents the instantaneous transition hazard function from the covariate state g′ to the covariate state h′, and the superscript T represents the transposition.

[0026] Based on the further improvement of the above method, the likelihood function of the covariate state transition process of each observed patient is obtained based on the state transition path of each observed patient and the instantaneous transition risk of the covariate state:

[0027]

[0028] in, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the number of state transitions in the covariate state transition path of the i-th observed patient; represents the time of the j-1th state transition in the covariate state transition path of the i-th observed patient, represents the time of the jth state transition in the covariate state transition path of the i-th observed patient, Indicates that from the covariate state The instantaneous transition hazard function to a covariate state s is, represents the set of all covariate states, Indicates that from the covariate state Transfer to covariate state The instantaneous transfer risk function is represents the j-1th state in the covariate state transition path of the i-th observed patient, represents the jth state in the covariate state transition path of the i-th observed patient.

[0029] Based on the further improvement of the above method, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process are solved based on the likelihood function to obtain the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk function and the estimation function of the censored state instantaneous transition risk function, including:

[0030] Based on the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process, a total likelihood function is constructed;

[0031] Based on the total likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process are solved to obtain the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk and the estimation function of the censored state instantaneous transition risk function.

[0032] Based on the further improvement of the above method, the total likelihood function is:

[0033]

[0034] in, represents the probability distribution function of the baseline covariate; π A (·) represents the propensity score function of the observed patient, represents the baseline covariate of the i-th observed patient, n represents the number of observed patients, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the likelihood function of the censored state transition process of the i-th observed patient, and n represents the number of observed patients.

[0035] On the other hand, an embodiment of the present invention provides a clinical multi-state model causal inference and prediction system including time-dependent covariates, comprising:

[0036] A data collection module is used to obtain the status data of each observed patient at the baseline time and at each observation time; the status data includes clinical health status, covariate status and censoring status; the covariate status is a status constructed by the covariate at time;

[0037] An instantaneous transfer risk function determination module, used to determine an instantaneous transfer risk function based on the baseline moment of each observed patient and the state data at each observation moment;

[0038] A causal effect inference module is used to construct a cumulative occurrence function of health state transfer based on the instantaneous transfer risk function, and determine an asymptotic unbiased estimate of the cumulative occurrence function of health state transfer using an effective influence function method; based on the asymptotic unbiased estimate of the cumulative occurrence function, calculate the cumulative incidence of the target health state under different treatment plans, and obtain the causal effect of the treatment plan on the transfer to the target health state;

[0039] The prediction module is used to obtain the status data of the patient to be predicted at the initial moment, calculate the cumulative incidence of the patient to be predicted in different clinical health states at the target moment based on the cumulative occurrence function of the health state transfer, and obtain the clinical health state prediction result of the patient to be predicted based on the cumulative incidence.

[0040] Compared with the prior art, the causal inference and prediction method of the clinical multi-state model including time-dependent covariates provided by the embodiment of the present invention obtains the non-time-dependent covariates of each observed patient, the status data at the baseline moment and each observation moment, determines the instantaneous transition risk function based on the status data at the baseline moment and each observation moment, thereby relaxing the Markov assumption, determines the instantaneous transition risk function based on key historical information, and then constructs the cumulative occurrence function of health state transition based on the instantaneous transition risk function, adopts the effective influence method to determine the asymptotic unbiased estimate of the cumulative occurrence function of health state transition, and calculates the cumulative incidence of target health state transition under different treatment schemes based on the asymptotic unbiased estimate of the cumulative occurrence function, thereby more accurately obtaining the causal effect of the treatment scheme on the transition to the target state, and more accurately predicts the clinical health state prediction result of the patient to be predicted based on the cumulative occurrence function.

[0041] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components;

[0043] Figure 1A flowchart of a method for causal inference and prediction of a clinical multi-state model based on time-dependent covariates according to an embodiment of the present invention;

[0044] Figure 2 1 is a block diagram of a clinical multi-state model causal inference and prediction system including time-dependent covariates according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a 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 used to limit the scope of the present invention.

[0046] A specific embodiment of the present invention discloses a causal inference and prediction method of a clinical multi-state model including time-dependent covariates, such as Figure 1 As shown, the following steps are included:

[0047] S1. Obtain the status data of each observed patient at the baseline time and at each observation time; the status data includes clinical health status, covariate status and censoring status; the covariate status is a status constructed by the covariate at time;

[0048] S2, determining an instantaneous transfer risk function based on the baseline data of each observed patient and the status data at each observation time;

[0049] S3. Based on the instantaneous transfer risk function, construct a cumulative occurrence function of health state transfer, and use the effective influence function method to determine the asymptotic unbiased estimate of the cumulative occurrence function of health state transfer; based on the asymptotic unbiased estimate of the cumulative occurrence function, calculate the cumulative incidence of the target health state under different treatment plans, and obtain the causal effect of the treatment plan on the transfer to the target health state;

[0050] S4. Obtain the status data of the patient to be predicted at the initial moment, calculate the cumulative incidence of the patient to be predicted in different clinical health states at the target moment based on the cumulative occurrence function of the health state transfer, and obtain the clinical health state prediction result of the patient to be predicted based on the cumulative incidence.

[0051] It should be noted that time-dependent covariates are covariates that change with time, such as whether the patient smokes or how often they exercise. Time-independent covariates are covariates that do not change with time, such as the patient's gender, blood type, etc.

[0052] It is assumed that the patient has a total of r clinical health states, and the patient's clinical health state before time τ is a discrete random variable sequence that changes over time. Taking cardiovascular and cerebrovascular patients as an example, it is assumed that during the course of the disease, there are: healthy state (state 0), low risk (state 1), medium and high risk (state 2), coronary artery disease state (state 3), and death (state 4). Under this disease background setting, the number of clinical health states is 5.

[0053] The initial moment is the baseline moment. At this time, the clinical health status of the i-th observed patient is expressed as All covariates at baseline, including both time-dependent and non-time-dependent covariates, that is, baseline covariates are expressed as

[0054] The covariate state is the state obtained by combining different values ​​of the time-dependent covariate. For example, the observed time-dependent covariates include whether to smoke and exercise frequency. The smoking covariate includes two values: smoking and not smoking; the exercise frequency covariate includes three values: no, occasionally, and often. The different values ​​of the two covariates are combined to obtain 6 situations, and the number of time-dependent covariate states is 6.

[0055] The censoring status refers to whether the observed patient is censored. The censoring status transition of each observed patient occurs at most once.

[0056] During implementation, it is assumed that there are n patients followed up in the data set, that is, there are n observed patients. The observation time is a fixed time period [0, τ], that is, the clinical health status and covariate status of the observed patients at each observation time before time τ are observed and recorded. The treatment plan of the observed patient is represented by A, A = 1 means that the observed patient is in the treatment group, and A = 0 means that the observed patient is in the control group.

[0057] Compared with the prior art, the causal inference and prediction method of the clinical multi-state model including time-dependent covariates provided by the embodiment of the present invention obtains the non-time-dependent covariates of each observed patient, the status data at the baseline moment and each observation moment, determines the instantaneous transition risk function based on the status data at the baseline moment and each observation moment, thereby relaxing the Markov assumption, determines the instantaneous transition risk function based on key historical information, and then constructs the cumulative occurrence function of health state transition based on the instantaneous transition risk function, adopts the effective influence method to determine the asymptotic unbiased estimate of the cumulative occurrence function of health state transition, and calculates the cumulative incidence of target health state transition under different treatment schemes based on the asymptotic unbiased estimate of the cumulative occurrence function, thereby more accurately obtaining the causal effect of the treatment scheme on the transition to the target state, and more accurately predicts the clinical health state prediction result of the patient to be predicted based on the cumulative occurrence function.

[0058] The present invention considers part of the historical information, relaxes the Markov assumption, and considers the key historical information Z(t) in the state transfer, so that it can be used without tracking the complete history. On the premise of accurate prediction of health status, it contains key information in the complete historical information that has a significant impact on the status, so that it is more in line with the actual scenario, achieves a balance between algorithm complexity and the degree of matching with the actual scenario, takes into account both model accuracy and wide applicability, ensures the reliability and practicality of inference, and realizes accurate prediction of health status.

[0059] Partial Markovian Assumption:

[0060]

[0061] In particular, it is assumed that when Z(t) contains all states and covariate state information experienced by the individual at time t and before (regardless of the time sequence), the partial Markov assumption holds.

[0062] N c (t) represents the missing status at time t, X(t) represents the clinical health status at time t, and L(t) represents the covariate status at time t.

[0063] Specifically, the instantaneous transfer risk function is determined based on the status data of each observed patient at the baseline moment and at each observation moment, including:

[0064] S21, construct the clinical health status instantaneous transition risk function, the covariate status instantaneous transition risk function and the censored status instantaneous transition risk function respectively;

[0065] S22, determining the state transition path of each observed patient based on the state data at the baseline moment and each observation moment of each observed patient, and obtaining the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process, and the likelihood function of the censored state transition process of each observed patient based on the state transition path of each observed patient and the clinical health state instantaneous transition risk function, the covariate state instantaneous transition risk, and the censored state instantaneous transition risk function;

[0066] S23. Based on the likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process are solved to obtain the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk function and the estimation function of the censored state instantaneous transition risk function.

[0067] Specifically, the instantaneous transition risk function includes a clinical health state instantaneous transition risk function, a covariate state instantaneous transition risk function and a censored state instantaneous transition risk function; the state transition path of each observed patient includes a clinical health state transition path and a covariate state transition path.

[0068] During implementation, the instantaneous transition risk function may be constructed using an existing survival analysis framework, for example, using a Cox regression framework to construct an instantaneous transition risk function.

[0069] Specifically, the constructed clinical health status instantaneous transition risk function is:

[0070]

[0071] in, represents the basic risk function for instantaneous transition of clinical health status, represents the regression coefficient of the instantaneous transition risk function from clinical health state g to clinical health state h, Z(t) represents the historical state before time t, represents the instantaneous transition risk function from clinical health state g to clinical health state h, and the superscript T represents the transposition.

[0072] During implementation, the historical information Z(t) includes whether the observed patient has reached each clinical health state and each covariate state before time t, as well as the clinical health state and time-dependent covariate state at the current moment, and the non-time-dependent covariates at baseline. It should be noted that the baseline non-time-dependent covariates include the observed patient's treatment plan A, which is also a variable that researchers pay close attention to in clinical practice.

[0073] The traditional Markov assumption assumes that the current state of the system depends only on the previous state without referring to earlier historical information. This memoryless assumption may be too limiting in some complex situations. Although non-parametric models that do not set up clear statistical assumptions can cover a wider range of potential scenarios, they are often too flexible and result in high computational complexity, which limits efficiency and operability in practical applications. The present invention relaxes the traditional Markov assumption and considers the impact of multi-step historical information on the current state, thereby estimating the instantaneous transfer risk function. At the same time, the historical information of the present invention only considers whether the observation has reached a certain state without considering the time to reach the state, that is, considering the key influencing information in the historical information, forming a partial Markov model, thereby enhancing the adaptability of the algorithm in actual scenarios. A balance is achieved between the complexity of the algorithm and the degree of matching the actual scenario, taking into account both the accuracy of the model and its wide applicability, ensuring the reliability and practicality of the inference.

[0074] During implementation, the Breslow estimator is used to obtain the basic risk function for instantaneous transition of clinical health status:

[0075]

[0076] in, indicates whether the i-th observed patient transfers from clinical health state g to clinical health state h at time t, Indicates whether the i-th observed patient is in clinical health state g at time t, Z i (t) represents the historical information of the i-th observed patient before time t, represents the regression coefficient.

[0077] By using the Breslow estimator, the parameters to be solved for the basic risk function of instantaneous transition of clinical health status are only

[0078] The i-th observed patient is in clinical health state g at time t, otherwise

[0079] The i-th observed patient has transitioned from clinical health state g to clinical health state h at time t, then otherwise,

[0080] Specifically, the constructed covariate state instantaneous transition risk function is:

[0081]

[0082] in, represents the basic hazard function for instantaneous transitions in the covariate state, represents the regression coefficient of the instantaneous transition risk function from the covariate state g′ to the covariate state h′, Z(t) represents the historical state before time t, represents the instantaneous transition hazard function from the covariate state g′ to the covariate state h′, and the superscript T represents the transposition.

[0083] Similarly, the Breslow estimator is used to obtain the basic risk function of the instantaneous transition of the covariate state:

[0084]

[0085] in, indicates whether the i-th observed patient transfers from covariate state g′ to covariate state h′ at time t, Indicates whether the i-th observed patient is still in the covariate state g′ at time t, Z i (t) represents the historical information of the i-th observed patient before time t, represents the regression coefficient.

[0086] The i-th observed patient is in the covariate state g′ at time t, otherwise

[0087] The i-th observed patient transfers from covariate state g′ to covariate state h′ at time t, then otherwise,

[0088] By using the Breslow estimator, the parameters to be solved for the basic risk function of the instantaneous transition of the covariate state, that is, the regression parameters, are only

[0089] The instantaneous transition hazard function of the censored state is:

[0090] dΛ c (t||Z(t))=dΛ c (t||Z(t))exp(Z(t) T β c )

[0091] The basic risk function of the instantaneous transfer of the censored state is obtained by using the Breslow estimator:

[0092]

[0093] Among them, Y i (t) indicates whether the i-th observed patient has not been censored at time t, and is an indicator of the censored state at time t. If the i-th observed patient has not been censored at time t, that is, is still at risk of state change, then Y i (t)=1, otherwise Y i (t) = 0; Indicates whether the i-th observed patient is censored at time t. If censored, then otherwise, β c represents the regression coefficient.

[0094] For each observed patient, the clinical health state transition path is expressed as:

[0095]

[0096] represents the clinical health status of the i-th observed patient at baseline, represents the clinical health status of the i-th observed patient after the first state transition, represents the time of the first state transition of the i-th observed patient, represents the number of patients observed Clinical health status after the secondary state transition, represents the number of patients observed The time of the next state transition. Represents the total number of clinical health status transitions of the i-th observed patient.

[0097] For each observed patient, the covariate state transition path is expressed as:

[0098]

[0099] represents the covariate status of the i-th observed patient at baseline, represents the covariate state of the i-th observed patient after the first state transition, represents the time of the first state transition of the i-th observed patient, represents the number of patients observed The covariate state after the state transition, represents the number of patients observed The time of the next state transition. represents the total number of covariate state transitions for the i-th observed patient.

[0100] Specifically, based on the state transition path of each observed patient and the clinical health state instantaneous transition risk function, the likelihood function of the clinical health state transition process of each observed patient is obtained:

[0101]

[0102] in, represents the likelihood function of the clinical health state transition process of the i-th observed patient, represents the number of state transitions in the clinical health state transition path of the i-th observed patient; represents the time of the j-1th state transition in the clinical health state transition path of the i-th observed patient, represents the time of the jth state transition in the clinical health state transition path of the i-th observed patient, Indicates clinical health status The instantaneous transition risk function to clinical health state s, represents the set of all clinical health states, Indicates clinical health status Transfer to clinical health status The instantaneous transfer risk function is represents the j-1th clinical health state in the clinical health state transition path of the i-th observed patient, represents the jth clinical health state in the clinical health state transition path of the i-th observed patient, Z i(u) represents the historical information of the i-th observed patient before time u, C i represents the censoring time of the i-th observed patient, T Di represents the death time of the ith patient, and τ represents the total observation time.

[0103] Specifically, based on the state transition path of each observed patient and the instantaneous transition risk of the covariate state, the likelihood function of the covariate state transition process of each observed patient is obtained as follows:

[0104]

[0105] in, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the number of state transitions in the covariate state transition path of the i-th observed patient; represents the time of the j-1th state transition in the covariate state transition path of the i-th observed patient, represents the time of the jth state transition in the covariate state transition path of the i-th observed patient, Indicates that from the covariate state The instantaneous transition hazard function to a covariate state s is, represents the set of all covariate states, Indicates that from the covariate state Transfer to covariate state The instantaneous transfer risk function is represents the j-1th state in the covariate state transition path of the i-th observed patient, represents the jth state in the covariate state transition path of the i-th observed patient.

[0106] Specifically, based on the state transition path of each observed patient and the risk of instantaneous transition of the censored state, the likelihood function of the censored state transition process of each observed patient is obtained as follows:

[0107]

[0108] Among them, C i represents the censoring time of the i-th observed patient, dΛ c (·) represents the instantaneous transition hazard function of the change of censoring status. represents the indicator function, represents the likelihood function of the censored state transition process for the i-th observed patient.

[0109] Based on the likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process, and the likelihood function of the censored state transition process are solved to obtain an estimation function of the clinical health state instantaneous transition risk function, an estimation function of the covariate state instantaneous transition risk function, and an estimation function of the censored state instantaneous transition risk function, including:

[0110] Based on the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process, a total likelihood function is constructed;

[0111] Based on the likelihood function of the total likelihood function for the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process, the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk and the estimation function of the censored state instantaneous transition risk function are obtained.

[0112] Specifically, the total likelihood function is:

[0113]

[0114] in, represents the probability distribution function of the baseline covariate; π A (·) represents the propensity score function of the observed patient, represents the baseline covariate of the ith observed patient, and n represents the number of observed patients.

[0115] After obtaining the total likelihood function, the maximum likelihood estimation can be performed based on the existing likelihood solution method, such as the Profile Likelihood algorithm, to obtain the regression coefficient of the instantaneous transition risk function of the clinical health status. Regression coefficients of the covariate state instantaneous transition hazard function The regression coefficient of the censored state instantaneous transition risk function β c , substitute the corresponding instantaneous transition risk function, and obtain the estimated function of the instantaneous transition risk function of the clinical health status at time t Estimation function of the instantaneous transition hazard function of the covariate state Estimation function of the hazard function for the instantaneous transition of the censored state

[0116] After obtaining the instantaneous transition risk function, the cumulative occurrence function of clinical health status transition is constructed based on the instantaneous transition risk function.

[0117] The constructed cumulative incidence function (CIF) of clinical health state transition can be expressed as:

[0118]

[0119] Among them, Z A＝a (u) represents the historical information of treatment plan a. It represents the cumulative incidence of clinical health status transitioning to r at time t when treatment plan is a.

[0120]

[0121] The probability density of the integral path, that is, the clinical health state transition trajectory is q x The time point at which the corresponding transfer occurs is The covariate state transition path is q l The time point at which the corresponding transfer occurs is The probability that the baseline covariate is l. l is a variable representing the baseline covariate, Q r represents the set of all clinical health state transition paths ending at clinical health state r, and m1 represents path q x The number of state transitions, m2 represents the number of covariate state transitions, represents the set of all covariate state transition paths with a state transition number of m2, is a variable representing the time of the m1th clinical health status transition, t x,1 is a variable indicating the time of the first clinical health status transition, t x,j is a variable representing the jth clinical health status transition time, is the variable representing the time of the m2th covariate state transition, t l,j is a variable representing the jth covariate state transition time, t l,1 is a variable indicating the time of the first covariate state transition.

[0122] Path q x The number of state transitions corresponds to The number of integral symbols in .

[0123] Similarly, path q l The number of state transitions corresponds to The number of integral symbols in .

[0124] Using the effective influence function method (Efficient Influence Function, referred to as EIF), the effective influence function of the cumulative occurrence function is:

[0125]

[0126]

[0127] in,

[0128]

[0129] L o represents the baseline covariate, z(·) represents historical information, and P(Z(·)=z(·)) represents the probability that the historical information is z(·). When calculating the probability of P(Z(u)=z(u)), it is necessary to consider the probability that no censoring occurs until time u. During implementation, the probability that no censoring occurs until time u is calculated based on the censoring state instantaneous transition risk function.

[0130] If the empirical expectation of EIF is set to 0, the asymptotically unbiased estimate of CIF is:

[0131]

[0132]

[0133] in, represents the asymptotically unbiased estimate of the cumulative occurrence function of the clinical health state changing to r when the treatment method is a, l is a variable representing the baseline covariate, and its range of variation is the range of values ​​of the baseline covariate, Q r represents the set of all clinical health state transition paths ending at clinical health state r, and m1 represents path q x The number of state transitions, m2 represents the number of covariate state transitions, represents the set of all covariate state transition paths with a state transition number of m2, is a variable representing the time of the m1th clinical health status transition, t x,1 is a variable indicating the time of the first clinical health status transition, t x,j is a variable representing the jth clinical health status transition time, is the variable representing the time of the m2th covariate state transition, t l,j is a variable representing the jth covariate state transition time, t l,1 is the variable representing the first covariate state transition time, represents the set of all clinical health states, represents the set of all covariate health states, Represents the path q x Whether it is in clinical health state g at time u, Represents the path q l Whether it is in the covariate state g′ at time u, represents the baseline covariate of the ith observed patient, represents the indicator function, z(u) represents the clinical health status transition path q x , the covariate state transition path is a l , when the baseline covariate is l, historical information at time u, represents the probability estimate of historical information z(·), indicates whether the i-th observed patient has transferred from clinical health state g to clinical health state h at time u, Indicates whether the i-th observed patient transfers from covariate state g′ to covariate state h, x′ at time u j-1 represents the clinical health status transition path q x The j-1th clinical health status in j represents the clinical health status transition path q x The jth clinical health state in k-1 represents the clinical health status transition path q x The k-1th clinical health status in k represents the clinical health status transition path q x The kth clinical health state in represents the i-th observed patient at t x,k Is the moment from clinical health status x k-1 Transfer to clinical health status x k ,l j-1 Represents the covariate state transition path q l The j-1th covariate state in j Represents the covariate state transition path q l The jth covariate state in k-1 Represents the covariate state transition path q l The k-1th covariate state in k Represents the covariate state transition path q l The kth covariate state in , represents the i-th observed patient at t l,k Whether the moment is from the covariate state l k-1 Transfer to covariate state l k , denoting the estimated function of the probability distribution function of the baseline covariate, represents an estimate of the probability density of the integration path, Represents the estimation function of the instantaneous transition risk function of health status, Represents the estimated function of the instantaneous transition hazard function of the covariate state.

[0134] It should be noted that The historical information is represented as the probability estimate of z(u). When calculating the probability, it is necessary to consider the probability that no deletion occurs until time u. During implementation, the probability that no deletion occurs until time u is calculated based on the instantaneous transition risk function of the deletion state.

[0135] Based on the asymptotically unbiased estimate of the cumulative occurrence function, the cumulative incidence of the target health state under different treatment regimens is calculated to obtain the causal effect of the treatment regimen on the transition to the target health state.

[0136] It is used to represent the cumulative probability of transitioning to state r by time t when all patients receive treatment a. The difference between is also an intuitive reflection of the causal effect of the treatment method. For example, in the observational data, there are two treatment methods: new therapy (a = 1) and conventional therapy (a = 0). The causal effect of the new therapy on the patient's state transition can be expressed as Calculated.

[0137] For the patient to be predicted, after obtaining its covariate information L0, when the level of treatment plan a is known, based on the cumulative occurrence function of health state transition, the cumulative incidence of the patient to be predicted in different clinical health states at the target time is calculated in the following way:

[0138]

[0139] Among them, CIF r,pred (t) represents the cumulative incidence of the patient's clinical health status changing to r at time t when the treatment plan a is used.

[0140] After the cumulative incidence rates of different clinical health states are obtained, the clinical state with the highest cumulative incidence rate is the predicted clinical health state of the patient to be predicted at the target time.

[0141] In the case of an undetermined treatment method, the type of target clinical outcome (i.e., state r) can also be fixed, and different values ​​of treatment plan a can be substituted for calculation, and the treatment method with the highest (lowest) corresponding cumulative incidence can be selected according to the specific state type. For example, when the clinical outcome of the study is death, the treatment method with the lowest cumulative incidence of low-risk outcomes can be selected; when the clinical outcome of the study is the conversion of a positive infection state to a negative state, the treatment method with the highest cumulative incidence of negative outcomes can be selected.

[0142] During implementation, the confidence interval of the cumulative occurrence function can be determined by existing parameter estimation or non-parametric estimation methods (such as the Bootstrap method).

[0143] A specific embodiment of the present invention discloses a causal inference and prediction system for a clinical multi-state model including time-dependent covariates, such as Figure 2 As shown, including:

[0144] A data collection module is used to obtain the status data of each observed patient at the baseline time and at each observation time; the status data includes clinical health status, covariate status and censoring status; the covariate status is a status constructed by the covariate at time;

[0145] An instantaneous transfer risk function determination module, used to determine an instantaneous transfer risk function based on the baseline moment of each observed patient and the state data at each observation moment;

[0146] A causal effect inference module is used to construct a cumulative occurrence function of health state transfer based on the instantaneous transfer risk function, and use the effective influence function method to determine the asymptotic unbiased estimate of the cumulative occurrence function of health state transfer; based on the asymptotic unbiased estimate of the cumulative occurrence function, calculate the cumulative incidence of the target health state under different treatment plans, and obtain the causal effect of the treatment plan on the transfer to the target health state;

[0147] The prediction module is used to obtain the status data of the patient to be predicted at the initial moment, calculate the cumulative incidence of the patient to be predicted in different clinical health states at the target moment based on the cumulative occurrence function of the health state transfer, and obtain the clinical health state prediction result of the patient to be predicted based on the cumulative incidence.

[0148] The above method embodiments and system embodiments are based on the same principle, and their related parts can be used for reference, and can achieve the same technical effect. The specific implementation process refers to the above embodiment, which will not be repeated here.

[0149] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0150] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A causal inference and prediction method for a clinical multi-state model including time-dependent covariates, characterized in that: The following steps are involved: Obtaining status data of each observed patient at the baseline time and at each observation time; the status data includes clinical health status, covariate status and censoring status; the covariate status is a status constructed by the covariate at time; Determining an instantaneous transition risk function based on the baseline data of each observed patient and the status data at each observed time; Based on the instantaneous transfer risk function, a cumulative occurrence function of health state transfer is constructed, and an effective influence function method is used to determine an asymptotically unbiased estimate of the cumulative occurrence function of health state transfer; based on the asymptotically unbiased estimate of the cumulative occurrence function, the cumulative incidence of the target health state under different treatment plans is calculated to obtain the causal effect of the treatment plan on the target health state; The status data of the patient to be predicted at the initial moment is obtained, and the cumulative incidence rate of the patient to be predicted in different clinical health states at the target moment is calculated based on the cumulative occurrence function of the health state transfer, and the clinical health state prediction result of the patient to be predicted is obtained based on the cumulative incidence rate.

2. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 1, characterized in that: The asymptotically unbiased estimate of the cumulative occurrence function of health state transitions is: in, represents the asymptotically unbiased estimator of the cumulative occurrence function of the clinical health state transition to r when the treatment method is a, l is a variable representing the baseline covariate, Q r represents the set of all clinical health state transition paths ending at clinical health state r, and m1 represents path q x The number of state transitions, m2 represents the number of covariate state transitions, represents the set of all covariate state transition paths with a state transition number of m2, is a variable representing the time of the m1th clinical health status transition, t x,1 is a variable indicating the time of the first clinical health status transition, t x,j is a variable representing the jth clinical health status transition time, is the variable representing the time of the m2th covariate state transition, t l,j is a variable representing the jth covariate state transition time, t l,1 is a variable representing the first covariate state transition time, x represents the set of all clinical health states, represents the set of all covariate health states, Represents the path q x Whether it is in clinical health state g at time u, Represents the path q l Whether it is in the covariate state g′ at time u, represents the baseline covariate of the ith observed patient, represents the indicator function, z(u) represents the clinical health status transition path q x , the covariate state transition path is q l , when the baseline covariate is l, historical information at time u, represents the probability estimate of historical information z(·), indicates whether the i-th observed patient has transferred from clinical health state g to clinical health state h at time u, indicates whether the i-th observed patient transfers from covariate state g′ to covariate state h′ at time u, x j-1 represents the clinical health status transition path q x The j-1th clinical health status in j represents the clinical health status transition path q x The jth clinical health state in k-1 represents the clinical health status transition path q x The k-1th clinical health status in k represents the clinical health status transition path q x The kth clinical health state in represents the i-th observed patient at t x,k Is the moment from clinical health status x k-1 Transfer to clinical health status x k ,l j-1 Represents the covariate state transition path q l The j-1th covariate state in j Represents the covariate state transition path q l The j-th covariate state in l k-1 Represents the covariate state transition path q l The k-1th covariate state in k Represents the covariate state transition path q l The kth covariate state in , represents the i-th observed patient at t l,k Whether the moment is from the covariate state l k-1 Transfer to covariate state l k , represents the estimated function of the probability distribution function of the baseline covariate, represents an estimate of the probability density of the integration path, Represents the estimation function of the instantaneous transition risk function of the health state, represents the estimation function of the instantaneous transition hazard function of the covariate state, and n represents the number of observed patients.

3. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 1, characterized in that: Determine an instantaneous transition risk function based on each observed patient's baseline time and status data at each observed time, including: The clinical health status instantaneous transition risk function, the covariate status instantaneous transition risk function and the censored status instantaneous transition risk function were constructed respectively; Determine the state transition path of each observed patient based on the state data at the baseline moment and each observation moment of each observed patient, and obtain the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process, and the likelihood function of the censored state transition process of each observed patient based on the state transition path of each observed patient and the clinical health state instantaneous transition risk function, the covariate state instantaneous transition risk, and the censored state instantaneous transition risk function; Based on the likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process are solved to obtain the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk function and the estimation function of the censored state instantaneous transition risk function.

4. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 3, characterized in that: The constructed clinical health status instantaneous transition risk function is: in, represents the basic risk function for instantaneous transition of clinical health status, represents the regression coefficient of the instantaneous transition risk function from clinical health state g to clinical health state h, Z(t) represents the historical state before time t, represents the instantaneous transition risk function from clinical health state g to clinical health state h, and the superscript T represents the transposition.

5. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 3, characterized in that: Based on the state transition path of each observed patient and the instantaneous transition risk function of the clinical health state, the likelihood function of the clinical health state transition process of each observed patient is obtained: in, represents the likelihood function of the clinical health state transition process of the i-th observed patient, represents the number of state transitions in the clinical health state transition path of the i-th observed patient; represents the time of the j-1th state transition in the clinical health state transition path of the i-th observed patient, represents the time of the jth state transition in the clinical health state transition path of the i-th observed patient, Indicates clinical health status The instantaneous transition risk function for transitioning to clinical health state s, x represents the set of all clinical health states, Indicates clinical health status Transfer to clinical health status The instantaneous transfer risk function is represents the j-1th clinical health state in the clinical health state transition path of the i-th observed patient, represents the jth clinical health state in the clinical health state transition path of the i-th observed patient, Z i (u) represents the historical information of the i-th observed patient before time u, C i represents the censoring time of the i-th observed patient, T Di represents the death time of the ith patient, and τ represents the total observation time.

6. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 3, characterized in that: The constructed covariate state instantaneous transition risk function is: in, represents the basic hazard function for instantaneous transitions in the covariate state, represents the regression coefficient of the instantaneous transition risk function from the covariate state g′ to the covariate state h′, Z(t) represents the historical state before time t, represents the instantaneous transition hazard function from the covariate state g′ to the covariate state h′, and the superscript T represents the transposition.

7. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 3, characterized in that: Based on the state transition path of each observed patient and the instantaneous transition risk of the covariate state, the likelihood function of the covariate state transition process of each observed patient is obtained as follows: in, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the number of state transitions in the covariate state transition path of the i-th observed patient; represents the time of the j-1th state transition in the covariate state transition path of the i-th observed patient, represents the time of the jth state transition in the covariate state transition path of the i-th observed patient, Indicates that from the covariate state The instantaneous transition hazard function to a covariate state s is, represents the set of all covariate states, Indicates that from the covariate state Transfer to covariate state The instantaneous transfer risk function is represents the j-1th state in the covariate state transition path of the i-th observed patient, represents the jth state in the covariate state transition path of the i-th observed patient.

8. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 3, characterized in that: Based on the likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process, and the likelihood function of the censored state transition process are solved to obtain an estimation function of the clinical health state instantaneous transition risk function, an estimation function of the covariate state instantaneous transition risk function, and an estimation function of the censored state instantaneous transition risk function, including: Based on the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process, a total likelihood function is constructed; Based on the total likelihood function, the regression coefficients of the likelihood function of the clinical health state transition process, the likelihood function of the covariate state transition process and the likelihood function of the censored state transition process are solved to obtain the estimation function of the clinical health state instantaneous transition risk function, the estimation function of the covariate state instantaneous transition risk and the estimation function of the censored state instantaneous transition risk function.

9. The method for causal inference and prediction of a clinical multi-state model including time-dependent covariates according to claim 2, characterized in that: The total likelihood function is: in, represents the probability distribution function of the baseline covariate; π A (·) represents the propensity score function of the observed patient, represents the baseline covariate of the i-th observed patient, n represents the number of observed patients, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the likelihood function of the covariate state transition process for the i-th observed patient, represents the likelihood function of the censored state transition process of the i-th observed patient, and n represents the number of observed patients.

10. A causal inference and prediction system for a clinical multi-state model including time-dependent covariates, characterized in that: include: A data collection module is used to obtain the status data of each observed patient at the baseline time and at each observation time; the status data includes clinical health status, covariate status and censoring status; the covariate status is a status constructed by the covariate at time; An instantaneous transfer risk function determination module, used to determine an instantaneous transfer risk function based on the baseline moment of each observed patient and the state data at each observation moment; A causal effect inference module is used to construct a cumulative occurrence function of health state transfer based on the instantaneous transfer risk function, and determine an asymptotic unbiased estimate of the cumulative occurrence function of health state transfer using an effective influence function method; based on the asymptotic unbiased estimate of the cumulative occurrence function, calculate the cumulative incidence of the target health state under different treatment plans, and obtain the causal effect of the treatment plan on the transfer to the target health state; The prediction module is used to obtain the status data of the patient to be predicted at the initial moment, calculate the cumulative incidence of the patient to be predicted in different clinical health states at the target moment based on the cumulative occurrence function of the health state transfer, and obtain the clinical health state prediction result of the patient to be predicted based on the cumulative incidence.

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