A method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito ovitrap index

Abstract

The present invention discloses a method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index, comprising the following steps: obtaining case data and serial interval distribution data; wherein the serial interval distribution data comprises human serial interval distribution and mosquito-borne serial interval distribution; obtaining the risk distribution by calculating the joint distribution of the human serial interval distribution and the mosquito-borne serial interval distribution; calculating the effective reproduction number at each moment according to the case data and the risk distribution, realizing real-time monitoring and analysis of the transmission risk, quantifying the transmission risk of mosquito-borne infectious diseases based on the reproduction number, directly reflecting the real-time transmission risk of mosquito-borne infectious diseases, and contributing to a more intuitive understanding of the development trend of infectious diseases, and timely predicting and responding to the outbreak of infectious disease transmission.

Description

Technical Field

[0001] The present invention relates to the technical field of infectious disease risk monitoring, and more specifically to a method for analyzing the transmission risk of mosquito-borne infectious diseases based on a mosquito-borne ovitrap index. Background Art

[0002] At present, mosquito-borne infectious diseases are infectious diseases transmitted by mosquitoes, such as malaria, yellow fever, Zika virus disease, dengue fever, etc. Mosquito-borne infectious diseases are transmitted in a "human-mosquito-human" mode, that is, female mosquitoes bite humans to transmit pathogens from one host to another. With the increase in urbanization and international travel, the risk of transmission of mosquito-borne infectious diseases has increased significantly, and the scope and frequency of transmission have continued to expand. The risk of transmission is affected by many factors, including pathogen characteristics, mosquito-borne ecological characteristics, climatic conditions, and socioeconomic factors.

[0003] However, in existing technologies, the number of cases is often used to reflect the risk of transmission, and people are only recorded as cases when they are infected and diagnosed, which often means that the transmission has occurred for some time. Therefore, the number of cases often lags behind the actual transmission situation and can only serve as an indirect indicator.

[0004] Therefore, how to accurately and intuitively analyze transmission risks and achieve real-time monitoring is an urgent problem that technical personnel in this field need to solve. Summary of the invention

[0005] In view of this, the present invention provides a mosquito-borne infectious disease transmission risk analysis method based on the mosquito-borne ovitrap index, which quantifies the transmission risk of mosquito-borne infectious diseases based on the reproduction number, directly reflects the real-time transmission risk of mosquito-borne infectious diseases, and helps to more intuitively understand the development trend of infectious diseases and timely predict and respond to infectious disease transmission outbreaks.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index comprises the following steps:

[0008] Acquire case data and serial interval distribution data; wherein the serial interval distribution data includes human serial interval distribution and mosquito-borne serial interval distribution;

[0009] Obtaining a risk distribution by calculating a joint distribution of the human serial interval distribution and the mosquito-borne serial interval distribution;

[0010] Based on the case data and the risk distribution, the effective reproduction number at each moment is calculated to achieve real-time monitoring and analysis of transmission risks.

[0011] Preferably, the effective reproduction number is expressed as:

[0012] ;

[0013] Where is the number of new cases at time , represents the maximum time span of the serial interval, and is the variable weight of the span for the serial interval distribution.

[0014] Preferably, the generation interval distribution is a combined generation interval distribution of infection of humans and infection of mosquito vectors.

[0015] Preferably, the generation interval distribution is:

[0016] ;

[0017] where is the generation interval distribution of humans, is the generation interval distribution of mosquito vectors, represents the random variable of the sum of the generation intervals of infected humans and infected mosquito vectors, and represents the random variable of the generation interval of infected humans.

[0018] Preferably, the generation interval distribution of the mosquito vector is:

[0019] ;

[0020] in, is the distribution of the generations of infected mosquito vectors, A generation-interval random variable representing infected mosquito vectors.

[0021] Preferably, the steps further include:

[0022] Acquire mosquito-borne ovitrap index data, and construct a first regression model based on the mosquito-borne ovitrap index data and the effective live number;

[0023] Early warning can be achieved by continuously monitoring the changes in the mosquito ovitrap index and combining it with the first regression model.

[0024] Preferably, the first regression model is:

[0025] ;

[0026] in, is the regression model function, is the intercept term, is the regression coefficient, It's time The error term, is the time variable, is a lagged term, and MOI is the monthly mosquito ovitrap index.

[0027] Preferably, the steps further include: setting an effective regeneration baseline value, and comparing it with the effective regeneration value, and performing a one-sided test based on the comparison result.

[0028] Preferably, the effective regeneration baseline value is:

[0029] ;

[0030] in, is the effective regeneration baseline, and are the intercept parameter and regression coefficient parameter of the maximum likelihood estimation of the first regression model respectively.

[0031] Preferably, the one-sided inspection step includes:

[0032] Setting a profile pseudo-likelihood framework for local sampling, constructing a second regression model based on the local sampling data, and obtaining a local regression coefficient; confirming the overall regression coefficient by the first regression model, and calculating the significance of the local regression coefficient compared with the overall regression coefficient;

[0033] When the significance meets the preset threshold, the corresponding risk surge time point is output according to the current profile pseudo-likelihood framework.

[0034] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index, which quantifies the transmission risk of mosquito-borne infectious diseases based on the reproduction number, directly reflects the real-time transmission risk of mosquito-borne infectious diseases, and directly and in real time calculates the transmission capacity of mosquito-borne infectious diseases (e.g., dengue fever), rather than just the current number of cases. Reduce the type of data that needs to be collected and processed, simplify the data collection and processing process, and make the estimation process more efficient. Analyze the long-term dynamic trend of the transmission risk of mosquito-borne infectious diseases, and find the time point of the surge in transmission risk based on the profile (pseudo) likelihood estimation framework to further analyze the potential mechanism of the change in transmission risk; in addition, the reproduction number provided by the present invention can be quickly adjusted according to different pathogenic biological characteristics and intervention measures, and the reproduction number estimation process has been verified by sensitivity analysis. Changes in epidemiological parameters within a reasonable range will not affect the main estimation results. This technology has good adaptability and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0036] Figure 1 A schematic diagram of a method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index provided by the present invention.

[0037] Figure 2 A schematic diagram of the distribution of sequence intervals provided in an embodiment of the present invention.

[0038] Figure 3 Schematic diagram of the effective reproduction number function curve in an embodiment of the present invention.

[0039] Figure 4 Schematic diagram of a one-sided hypothesis test in an embodiment of the present invention.

[0040] Figure 5 It is a schematic diagram of the surge time point obtained based on the one-sided hypothesis test traversal in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] The embodiment of the present invention discloses a method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index, comprising the following steps:

[0043] S1: Obtain case data and serial interval distribution data; wherein the serial interval distribution data includes human serial interval distribution and mosquito-borne serial interval distribution.

[0044] S2: The risk distribution is obtained by calculating the joint distribution of the human serial interval distribution and the mosquito-borne serial interval distribution.

[0045] S3: Based on case data and risk distribution, calculate the effective reproduction number at each moment to achieve real-time monitoring and analysis of transmission risks.

[0046] Among them, the effective reproduction number ( ), also known as the time-varying reproduction number, refers to the (For example: The average number of new infections caused by a typical case, taking into account factors such as the actual population immunity level, prevention and control measures, and changes in social behavior, is used to describe the spread of an infectious disease at a specific point in time. The real-time transmission risk of When >1, infectious diseases will spread rapidly among the population, causing an outbreak of the disease; When it is less than 1, the spread of infectious diseases tends to stop and the disease is gradually relieved. This indicator is a dynamic value that changes over time. The effective reproduction numbers on the 2000-kilometer scale are arranged in chronological order to form a time series, which reveals the actual transmission dynamics of infectious diseases. Therefore, the time series of effective reproduction numbers is used to analyze the changes in the transmission risk of mosquito-borne infectious diseases.

[0047] In one embodiment, the effective reproduction number is expressed as The number of new cases at the time of The ratio of the total transmission risk accumulated at each moment can be estimated by updating the equation, and its 95% credible interval can be estimated by the Bayesian method. The specific formula is as follows:

[0048] (1)

[0049] in, yes Number of new cases at time, weighted average is as of The total cumulative transmission risk at all times, n represents the maximum time span for successful transmission (i.e. the maximum time span between generations), and the weight Determined by the generation interval distribution, which describes the distribution of transmission risk during an infection.

[0050] In this example, mosquito-borne infectious diseases use mosquitoes as the medium of transmission of pathogens. Mosquitoes carrying pathogens transmit pathogens to human hosts by biting them (transmitted by mosquitoes, i.e., "human-mosquito-human"). We distribute the infection sequence interval (SI) Modeled as the joint generation interval distribution of infected humans and infected mosquito vectors, Can be distributed through the generation interval of infection in humans and the distribution of intergenerational intervals of infected mosquito vectors The specific formula is as follows:

[0051] (2)

[0052] Where k is a random variable representing the sum of the intervals between generations of infected humans and infected mosquito vectors; is a random variable representing the interval between generations of infection in humans. In formula (2) and The specific explanation is as follows: Set to a fixed probability distribution, such as the gamma distribution. Since mosquito vectors can continue to spread pathogens (to humans) until they die after infection, the generation interval distribution of mosquito vectors It is necessary to consider the distribution of the intergenerational interval of infected mosquito vectors. The distribution of the time points of mosquito-borne infection is derived by the “convolution” of the distribution of the infected mosquito-borne intergenerational intervals and the distribution of the time points of mosquito-borne infection. .in, Usually set to a fixed probability distribution, the variable A generation-interval random variable representing infected mosquito vectors.

[0053] The time point of mosquito infection (denoted as ) is modeled as a uniform distribution, with the range being the life span of female mosquito vectors, thus obtaining the distribution of mosquito vector infection time points (using ). Considering the sequence interval is For each possible mosquito infection time point , calculate the value of the corresponding infection time point distribution in the remaining time of the mosquito life. and Carry out (from 0 to ) can be integrated to obtain the complete generation interval distribution of mosquito vectors. As follows:

[0054] .

[0055] Pay special attention to: is the integrand variable inside the convolution integral. When the convolution integral is completed, the result is the same as Not relevant.

[0056] In another embodiment, after obtaining the effective reproduction number sequence, a regression model can be constructed based on the effective reproduction number sequence combined with the mosquito ovitrap index to estimate the effective reproduction value baseline.

[0057] The effective reproduction number baseline value ( ), reflects the seasonal fluctuations in transmission risk, which is driven by local mosquito abundance and mosquito activity, and is indirectly affected by other factors that affect mosquito populations. Specifically, the vector of mosquito-borne infectious diseases is mosquitoes. Mosquito growth is affected by meteorological factors such as temperature, rainfall, and humidity. High temperature, high humidity, and high rainfall will create a good habitat for mosquitoes. Guangzhou, my country, has a subtropical monsoon climate with high temperature, high humidity, and heavy rain in summer. Its summer climate characteristics provide favorable conditions for the reproduction of dengue vectors. The effective reproduction number baseline is determined by local mosquito activity. The activity conditions of local mosquitoes such as reproduction, survival, and biting frequency constitute the basic conditions for the transmission of dengue virus. The effective reproduction number baseline can quantify these effects and reflect the virus transmission capacity of mosquito activities under natural conditions (without special prevention and control or other major interference factors). The effective reproduction number is a moment level. By comparing the effective reproduction number with its corresponding baseline value, it can be judged whether the change in the risk of transmission of mosquito-borne infectious diseases is due to seasonal fluctuations or other factors. The comparison process between the two is: if the effective reproduction number is greater than the baseline value of the effective reproduction number, it indicates that the virus transmission is relatively active at that time point, and there may be other factors that promote transmission; otherwise, it means that the transmission is relatively suppressed, which may benefit from prevention and control measures or other unfavorable transmission conditions. Therefore, the steps also include:

[0058] S4: Obtain mosquito-borne ovitrap index data, and construct a first regression model based on the mosquito-borne ovitrap index data and the effective number of live births.

[0059] S5: Early warning can be achieved by continuously monitoring the changes in the mosquito ovitrap index and combining it with the first regression model.

[0060] S6: Confirm the effective regeneration baseline value, compare it with the effective regeneration value, and perform a one-sided test based on the comparison result.

[0061] In this embodiment, by performing maximum likelihood estimation on the first regression model confirmed by the previous overall situation, the effective regeneration baseline value is confirmed as the stable state of the effective regeneration number. Combined with the actual effective regeneration value, the significance of the actual effective regeneration number compared with the stable state is judged. When the significance reaches the significance requirement of the one-sided test, it is judged to be a surge point.

[0062] In this example, the mosquito index (e.g., monthly mosquito ovitrap index) reflects the overall status of mosquito activity and population abundance in a certain area. The exponential function of the monthly mosquito ovitrap index (with a lag of 2.5 days) and the regression model of the effective reproduction number are constructed. The specific formula is as follows:

[0063] (3)

[0064] in, is the intercept term, is the regression coefficient, It's time The error term of . yes The continuous form of , where z is the time variation being integrated, and z vanishes after integration. MOI( ) indicates time The monthly mosquito ovitrap index is . The lag term x is set according to the period of mosquitoes changing from larvae to adults. It is expressed as:

[0065] (4)

[0066] and Represents the parameter point estimate of the regression model, calculated using the classical maximum likelihood function method (or least squares method). Assume that at a specific time , Greater than (or less than) , conduct a one-sided hypothesis test.

[0067] In order to further implement the above technical solution, the one-sided inspection steps include:

[0068] A profile pseudo-likelihood framework is set up for local sampling, and a second regression model is constructed based on the local sampling data to obtain the local regression coefficient. The overall regression coefficient is confirmed by the first regression model, and the significance of the local regression coefficient compared with the overall regression coefficient is calculated. When the significance meets the preset threshold, the corresponding risk surge time point is output according to the current profile pseudo-likelihood framework.

[0069] Specifically, the time point of the surge in transmission risk reflects the occurrence of a certain emergency or condition at a certain point in time, which causes the risk to spread rapidly in a short period of time. Further analysis of the driving factors of the surge in transmission risk, such as genetic variation of pathogens, changes in meteorological conditions, population migration patterns, etc., can provide a basis for exploring the potential mechanisms of infectious disease outbreaks and help predict and respond to future infectious disease outbreaks. In the real world, we cannot obtain the exact time of the surge in transmission risk through infectious disease monitoring, so we need to use statistical model tools to calculate this time point. In this profile (pseudo) likelihood framework, we can estimate the unknown parameters by constructing a likelihood function related to the research problem (here is the pseudo-likelihood function) and finding the parameter value that makes the likelihood function reach the maximum value. The unknown parameter here is the time point of the surge in transmission risk.

[0070] By comparing the heterogeneity between the overall regression of formula (3) and the local regression using only part of the data, it is possible to estimate the time when the transmission risk surges. The overall regression is fitted using all the data during the study period, using The local regression is limited to using data within a 1-year period, that is, the time window length is 1 year. Represents local regression Estimated values. Comparisons were made using one-sided t-tests and , get each The corresponding significance level The value is used to determine the maximum (pseudo) likelihood estimate, which is a measure of the likelihood of a surge in transmission risk. This process is called determining the pseudo-likelihood framework. When the transmission risk increases, the local regression coefficient is significantly higher than the overall regression coefficient, that is, > , assuming that > ”.

[0071]

[0072] Therefore, the time when the risk of transmission surges can be estimated based on the profile (pseudo) likelihood framework. The maximum (pseudo) likelihood estimate and its 95% confidence interval. The 95% confidence interval is a method for interval estimation of a population parameter (dengue virus strain invasion time) based on sample data. It means that in the process of repeated sampling and parameter estimation, in 95% of cases the interval obtained will contain the true transmission risk surge point t0 parameter value. The invasion time of the new virus strain estimated in this study is not a single point time estimate (such as the maximum likelihood estimate of April 2014), which takes into account the inaccurate estimates caused by sampling errors and data uncertainty. Simply put, the profile (pseudo) likelihood framework is the process of finding the time point when the transmission risk surges, and the maximum likelihood estimate is the time point when the transmission risk surges that we want to determine.

[0073] In order to prove the beneficial effects of the present invention, the present invention is verified by using actual data, and the specific verification process is as follows:

[0074] First, the monitoring data can be used to obtain the time series of the number of dengue cases and mosquito index (monthly mosquito ovitrap index, MOI) in a certain area over the past few years. Before data analysis, the data were preprocessed, and the seasonal autoregressive moving average model (SARIMA model) was used to interpolate missing or incomplete historical data. All data were scaled to "daily" units, and the locally weighted regression smoothing method (LOESS) was used to generate a smooth curve.

[0075] Secondly, based on the epidemiological characteristics of dengue virus infection, the human generation interval distribution was set to a gamma distribution with a mean of 8 days and a standard deviation of 1 day (see Figure 2 The distribution of mosquito vector generation intervals was set to a cumulative gamma distribution with a mean of 7 days and a standard deviation of 1.5 days (see Figure 2 Part b) of the above. Based on the life span of female mosquitoes ranging from 5 to 8 weeks, the probability distribution of the time of mosquito-borne infection is The distribution of the combined sequence intervals is set to be evenly distributed in the range of 5 to 8 weeks. Formula (2) is used to further determine the distribution of the combined sequence intervals (see Figure 2 Part c). Figure 2 In the figure, the horizontal axis is the time after dengue infection. The endogenous and exogenous incubation periods are indicated by indigo and green, respectively.

[0076] In addition, the time series of the effective reproduction number is estimated based on the number of cases using formula (1), and the results are as follows: Figure 3 Then, the effective reproduction number and the monthly mosquito-borne ovitrap index were fitted using formula (3). The monthly mosquito-borne ovitrap index used for regression fitting was lagged by 15 days, and the parameter value was estimated using the least squares method to obtain the baseline value of the effective reproduction number. The results are shown in Figure 4 Part a in the figure. The estimated effective reproduction number is a red dotted curve, the 95% confidence interval is a pink vertical bar, and the effective reproduction value baseline is a black curve.

[0077] Compare the effective reproduction number with its corresponding baseline value, assuming that at a specific time , the effective reproduction number is greater than ( / less than) the effective reproduction baseline value, and a one-sided hypothesis test is performed. The results are shown in Figure 4 Part b.

[0078] Among them, the estimated value of the effective reproduction number is a red dot curve, the 95% confidence interval is a pink vertical bar, and the effective reproduction value baseline is a black curve.

[0079] “ Greater than (red vertical bar) or less than (blue vertical bar) the regression fit baseline The significance level of the one-sided test of value) (b).

[0080] Figure 4 In part c, the colored curves are the local regression fitting results for each year from 2012 to 2015. The values ​​are the significance levels of the hypothesis test "If the transmission risk surges in January every year from 2012 to 2015". The significance level of the one-sided test "The regression coefficient (i.e. slope) of the local regression from 2011 to 2016 (the colored curve in part c) is greater than the regression coefficient of the overall regression from 2008 to 2018 (the black curves in a and c)" in part d.

[0081] Finally, the specific time point of the peak of transmission risk is estimated based on the profile (pseudo) likelihood framework. Formula (3) is used to fit the effective reproduction number and the monthly mosquito ovitrap index by overall regression and local regression, respectively, to estimate the overall regression coefficient and the local regression coefficient , the results are shown in Figure 4 c. And compare the overall regression coefficient with the local regression coefficient, assuming that " > " and conduct a one-sided hypothesis test. The results are shown in Figure 4 d. According to the significance level of hypothesis test (i.e.: The results showed that the maximum likelihood estimate of the time of the surge in transmission risk was April 2014 (two months before and after), see Figure 5 .

[0082] Previous genetic studies have found that a highly contagious new dengue pathogen strain was isolated from the large-scale dengue epidemic in 2014, and phylogenetic analysis also showed that the new pathogen strain was imported from abroad before the outbreak of the epidemic in 2014. These research results are consistent with the time point of the surge in transmission risk estimated by this technology, proving that the present invention can accurately determine the time point of the surge in transmission risk, accurately reflect the development trend of the epidemic, and timely predict and respond to the outbreak of the epidemic.

[0083] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0084] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index, characterized in that: The following steps are involved: Obtain case data and generational interval distribution data; wherein the generational interval distribution data includes human generational interval distribution and mosquito-borne generational interval distribution; The risk distribution is obtained by calculating the joint distribution of the human generation interval distribution and the mosquito-borne generation interval distribution; Calculate the effective reproduction number at each moment based on the case data and the risk distribution to achieve real-time monitoring and analysis of transmission risks; Wherein, the effective reproduction number is expressed as: Among them, I t is the number of new cases at time t, n represents the maximum time span of the sequence interval, k is the variable of span, and weight w(k) is the risk distribution; The risk distribution is: Among them, w h is the generation interval distribution of human beings, w v is the generation interval distribution of mosquito vectors, k is the random variable representing the sum of the generation intervals of infected humans and infected mosquito vectors; τ is the random variable representing the generation interval of infected humans; The mosquito vector generation interval distribution is: Among them, w v (τ|infected) is the distribution of the generation interval of infected mosquito vectors, and x represents the random variable of the generation interval of infected mosquito vectors.

2. The method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index according to claim 1, characterized in that: The steps also include: Obtaining mosquito-borne ovitrap index data, and constructing a first regression model based on the mosquito-borne ovitrap index data and the effective live number; Early warning can be achieved by continuously monitoring the changes in the mosquito ovitrap index and combining it with the first regression model.

3. The method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index according to claim 2, characterized in that: The first regression model is: Among them, R(t) is the regression model function, β0 is the intercept term, β is the regression coefficient, ε t is the error term at time t, t is the time variable, x is the lag term, and MOI is the monthly mosquito ovitrap index.

4. The method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index according to claim 3, characterized in that: The steps also include: confirming the effective regeneration baseline value, comparing it with the effective regeneration number, and performing a one-sided test based on the comparison result.

5. The method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index according to claim 4, characterized in that: The effective regeneration baseline value is: Among them, R base (t) is the effective regeneration baseline, and are the intercept parameter and regression coefficient parameter of the maximum likelihood estimation of the first regression model respectively.

6. The method for analyzing the transmission risk of mosquito-borne infectious diseases based on the mosquito-borne ovitrap index according to claim 4, characterized in that: The one-sided test step comprises: Setting a profile pseudo-likelihood framework for local sampling, constructing a second regression model based on the local sampling data, and obtaining a local regression coefficient; confirming the overall regression coefficient by the first regression model, and calculating the significance of the local regression coefficient compared with the overall regression coefficient; When the significance meets the preset threshold, the corresponding risk surge time point is output according to the current profile pseudo-likelihood framework.

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