阅读说明：本技术 一种基于累积和控制图的流行疾病监控方法 (Epidemic disease monitoring method based on accumulation and control chart ) 是由 吴苍 王名亮 侯慧娟 刘增辉 杨宝琦 于 2021-08-06 设计创作，主要内容包括：本发明涉及医疗数据监控技术领域,具体为一种基于累积和控制图的流行疾病监控方法,提出的基本假设如下：假设某种疾病的感染人数服从泊松分布,每隔相同时间间隔进行采样和统计；观测值存在一阶自相关；基于上述假设,本发明提出一种基于累积和控制图的流行疾病监控方法,其本发明具有以下有益效果：1、本发明解决具有时间关联性的离散型时间序列建模和监控问题；2、本发明对非线性数据依然适用；3、本发明控制图的监控过程可视,异常出现会及时报警。(The invention relates to the technical field of medical data monitoring, in particular to a popular disease monitoring method based on accumulation and control charts, which proposes the following basic assumptions: the number of infected people of a certain disease is assumed to obey Poisson distribution, and sampling and statistics are carried out at the same time interval; the observation value has first-order autocorrelation; based on the hypothesis, the invention provides a epidemic disease monitoring method based on accumulation and control chart, and the invention has the following beneficial effects: 1. the invention solves the problems of discrete time sequence modeling and monitoring with time correlation; 2. the invention is still applicable to non-linear data; 3. the monitoring process of the control chart is visible, and an alarm can be given in time when an abnormality occurs.)

1. A epidemic disease monitoring method based on accumulation and control chart proposes the following basic assumptions: the number of infected people of a certain disease is assumed to obey Poisson distribution, and sampling and statistics are carried out at the same time interval; the observation value has first-order autocorrelation;

based on the hypothesis, the invention provides a epidemic disease monitoring method based on accumulation and control chart, which is characterized by comprising the following steps:

the method comprises the following steps: the number of infected persons is a time series of counts, denoted d₁，...，d_t，...，d_TObserved value d_tThe density function and the distribution function of (d) are denoted as F, F.

Step two: the first-order autocorrelation exists among variables, a binary copula function is selected to describe the first-order autocorrelation, and the joint distribution among adjacent variables is

H(d_t，d_t+1)＝C(F(d_t)，F(d_t+1)；α)

Wherein C (,; α) represents a binary copula function with a parameter α; for discrete data, the joint density function is

h(d_t，d_t+1)＝C(F(d_t)，F(d_t+1)；α)-C(F(d_t-1)，F(d_t+1)；α)-C(F(d_t)，F(d_t+1-1)；α)+C(F(d_t-1)，F(d_t+1-1)；α)；

Step three: two-stage maximum likelihood method for estimating process parameters

The first stage is as follows: the maximum likelihood method estimates the parameters of the poisson distribution,

and a second stage: estimating copula function parameters

Step four: generating homologous discrete data d ═ d₁，...，d_T}

(1) Random variable U is randomly generated from uniformly distributed U (0, 1)₁And setting t 2;

(2) in addition, random variable q is randomly generated from uniformly distributed U (0, 1)_tSolving equation C_t(u_t；u_t-1)＝q_tTo give u_t；

(3) If T ═ T, the procedure terminates; otherwise, setting i to i +1 and executing the previous step;

(4) calculating d_t＝F^-1(u_t) Wherein i 1.. t. wherein F^-1Is the inverse function of the poisson distribution;

step five: assuming a point-change model, i.e. the mean of the poisson process after time τ is from λ₀Change to lambda₁Time series d₁，...，d_t(τ < t) a combined density of

Due to the characteristics of disease monitoring, the increase of the number of infected people is more concerned, and a unilateral control chart is constructed to monitor the upward drift of the mean value; for ease of use, the statistics S are approximated in a recursive fashion_t

Setting an initial value S₀Is equal to 0, and

step six: comparison statistic S_tWhen the control limit is exceeded, the disease infection process is determined to be abnormal, and attention should be paid to further investigate the cause.

Technical Field

The invention relates to the technical field of medical data monitoring, in particular to a popular disease monitoring method based on accumulation and control charts.

Background

The spread of epidemic diseases is influenced by numerous factors such as the level of medical hygiene, season, and population mobility. Concern about the development of prevalent diseases has a significant impact on medical resource allocation and personal health protection. At present, various medical and health organizations establish a complete medical data collection and disclosure mechanism. How to accurately and efficiently analyze and monitor epidemic disease data becomes a considerable problem to be studied.

Statistical Process Control (SPC) methods are common process monitoring and quality management tools used in manufacturing, service, and medical fields. The number of people infected due to epidemic diseases often presents discrete, non-independent characteristics. There are two main approaches to SPC existing for monitoring such data. The first method directly adopts a c diagram and a u diagram facing discrete data for monitoring, but the two control diagrams assume that observed values are independent from each other, and correlation among data is ignored. Another method transforms discrete data into continuous variables approximately complying with normal distribution, models the continuous variables by adopting a time sequence, and then carries out monitoring by adopting a houttte diagram, a cumulative sum (CUSUM) diagram and an Exponential Weighted Moving Average (EWMA) diagram. However, this conversion method only works well for discrete processes with large mean values, and has a large error for small mean values. These methods have difficulty meeting the problem of modeling and monitoring epidemic infected population.

Disclosure of Invention

The invention aims to provide a popular disease monitoring method based on a cumulative sum control chart, which mainly solves the problem that the existing control chart cannot adapt to medical data with self-correlation, non-linear and discrete attributes.

In order to achieve the purpose, the invention provides the following technical scheme:

a epidemic disease monitoring method based on accumulation and control chart proposes the following basic assumptions: the number of infected people of a certain disease is assumed to obey Poisson distribution, and sampling and statistics are carried out at the same time interval; the observation value has first-order autocorrelation;

based on the hypothesis, the invention provides a epidemic disease monitoring method based on accumulation and control chart, which is characterized by comprising the following steps:

step one, the number of infected persons is a counting time sequence and is marked as d₁，...，d_t，...，d_TObserved value d_tThe density function and the distribution function of (d) are denoted as F, F.

Step two: the first-order autocorrelation exists among variables, a binary copula function is selected to describe the first-order autocorrelation, and the joint distribution among adjacent variables is

H(d_t，d_t+1)＝C(F(d_t)，F(d_t+1)；α)

Wherein C (,; α) represents a binary copula function with a parameter α; for discrete data, the joint density function is

h(d_t，d_t+1)＝C(F(d_t)，F(d_t+1)；α)-C(F(d_t-1)，F(d_t+1)；α)-C(F(d_t)，F(d_t+1-1)；α)+C(F(d_t-1)，F(d_t+1-1)；α)

Step three: two-stage maximum likelihood method for estimating process parameters

The first stage is as follows: the maximum likelihood method estimates the parameters of the poisson distribution,

and a second stage: estimating copula function parameters

Step four: generating homologous discrete data d ═ d₁，...，d_T}

(1) Random variable U1 is randomly generated from a uniform distribution U (0, 1)_.And setting t to 2;

(2) in addition, random variable q is randomly generated from uniformly distributed U (0, 1)_tSolving equation C_t(u_t；u_t-1)＝q_tTo give u_t；

(3) If T ═ T, the procedure terminates; otherwise, setting i to i +1 and executing the previous step;

(4) calculating d_t＝F^-1(u_t) Wherein i 1.. t. wherein F^-1Is the inverse function of the poisson distribution;

step five: assuming a point-change model, i.e. the mean of the poisson process after time τ is from λ₀Change to lambda₁Time series d₁，...，d_t(τ < t) a combined density of

Due to the characteristics of disease monitoring, the increase of the number of infected people is more concerned, and a unilateral control chart is constructed to monitor the upward drift of the mean value; for ease of use, the statistics S are approximated in a recursive fashion_t

Setting an initial value S₀Is equal to 0, and

step six: comparison statistic S_tWhen the control limit is exceeded, the disease infection process is determined to be abnormal, and attention should be paid to further investigate the cause.

The invention has the following beneficial effects: 1. the invention solves the problems of discrete time sequence modeling and monitoring with time correlation; 2. the invention is still applicable to non-linear data; 3. the monitoring process of the control chart is visible, and an alarm can be given in time when an abnormality occurs.

Drawings

For a more clear understanding of the present invention, the present disclosure will be further described by reference to the drawings and illustrative embodiments which are provided for illustration and are not to be construed as limiting the disclosure.

FIG. 1 is an observation and control chart of the invention as applied to German cholera data.

Detailed Description

The present invention will be described in further detail below. The principles of the proposed algorithms and strategies, as well as advantages and disadvantages, will be described more clearly below by way of examples, and these principles are not limited to the examples given, but rather are more consistent with the problems encountered in actual production.

Examples

The invention is further described in connection with data published by the world health organization, taking the number of cholera infections reported each year in 1971-2016, Germany. Referring to fig. 1, the implementation steps of the invention are as follows:

the method comprises the following steps: table 1 lists the number of people infected with cholera annually in Germany from 1971 to 2016. Since the number of infected persons is very small compared to the general population in germany, it is naturally assumed that these 46 samples obey a poisson distribution with parameter λ;

TABLE 1 number of cholera infections reported in 1971-2016

Step two: estimating process parameters using a two-stage maximum likelihood methodcopula parameter

Step three: generating homologous data according to a parameter estimation result and a copula-based Poisson data generation method; under the condition that the average running chain length ARL of the controlled state is given to be 200, the control limits are respectively 2.8 and 3.26 through simulation when the target offset amplitude theta is 1.5 and theta is 2;

step four: combining the original data, respectively generating two groups of abnormal samples with the same number of abnormal offset amplitudes of 1.5 and 2, calculating CUSUM statistic and dotting in a control chart;

as shown in fig. 1, fig. 1(a) is a combination of the number of true infections and a sample with an abnormal offset amplitude of 1.5; FIG. 1(b) is a combination of the true infection number and a sample with an abnormal offset amplitude of 2; FIG. 1(c) is the CUSUM statistic corresponding to FIG. 1 (a); FIG. 1(d) is the CUSUM statistic corresponding to FIG. 1 (b);

step five: from the monitoring effect of fig. 1, in both cases, no false alarm has occurred in the first half, and after stepping into the abnormal phase, the control map with the abnormal offset amplitude of 1.5 exceeds the control limit at the 11 th point, and the control map with the abnormal offset amplitude of 2 exceeds the control limit at the 6 th point.

Step six: the results show that the CUSUM control chart provided by the invention can effectively monitor small and medium amplitude deviation in the process.

The basic principles and the main features of the present invention as well as the advantages of the present invention have been shown and described. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.