CN105975790A

CN105975790A - Individualized medicine recommending method based on probability

Info

Publication number: CN105975790A
Application number: CN201610333846.6A
Authority: CN
Inventors: 袁伟伟; 何康亚; 王绚; 关东海; 周丽
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2016-05-17
Filing date: 2016-05-17
Publication date: 2016-09-28

Abstract

The invention relates to a personalized drug recommendation method for a specific group of people, and belongs to the technical field of drug evaluation in pharmacoeconomics. The present invention obtains the average effectiveness and cost distribution of the medicine through the expenditure of the whole population on the medicine and the response to the medicine; through the effectiveness and cost modeling analysis of each medicine, the effectiveness distribution and cost distribution of each medicine are obtained. cost distribution. On this basis, the present invention first calculates the incremental distribution of the cost and effectiveness of each drug relative to the overall population, and then calculates the probability value of each drug under the premise that a specific group of people is willing to increase the cost to obtain an increase in effectiveness , and finally give personalized drug recommendation results for specific groups of people according to the size of the probability value.

Description

A probability-based personalized drug recommendation method

技术领域technical field

本发明涉及一种基于概率的个性化药物推荐方法，属于药物经济学领域。The invention relates to a probability-based personalized drug recommendation method, which belongs to the field of pharmacoeconomics.

背景技术Background technique

医药技术是保证人类健康的重要技术手段，研究表明随着经济发展和消费水平的提高，人们消费结构中医疗支出所占比重逐渐增大。医药资源的合理配置成为越来越重要的问题。药物经济学是人类为应对医药资源配置而兴起的交叉学科。药物经济学以经济学理论为基础，全面的分析医药技术的成本和收益，进而形成最优的方案，使得药物资源使用合理化。Medical technology is an important technical means to ensure human health. Studies have shown that with the development of the economy and the improvement of consumption levels, the proportion of medical expenditure in people's consumption structure is gradually increasing. The rational allocation of medical resources has become an increasingly important issue. Pharmacoeconomics is an interdisciplinary subject developed by human beings to deal with the allocation of medical resources. Based on economic theory, pharmacoeconomics comprehensively analyzes the cost and benefits of medical technology, and then forms the optimal plan to rationalize the use of drug resources.

文献[1]使用马尔可夫模型模拟疾病的发展周期过程中消耗的卫生资源以及产生的医疗效果，从而估算出治疗方案消耗的总成本和疾病发展的结果来决策出最优的方案。文献[2]使用决策树模型将问题分类，通过计算每种分类的收益和成本期望来决策最优的方案。国内许多研究[3，4]通过计算成本、收益的均值来分析决策出最优治疗方案。Literature [1] uses the Markov model to simulate the health resources consumed and the medical effects produced during the development cycle of the disease, so as to estimate the total cost of the treatment plan and the results of the disease development to determine the optimal plan. Literature [2] uses the decision tree model to classify the problems, and determines the optimal solution by calculating the income and cost expectations of each classification. Many domestic studies [3, 4] analyze and decide the optimal treatment plan by calculating the mean value of cost and benefit.

以上方法并没有考虑到不同人群经济能力和对药物反应的差异，以及不同人群的特殊要求。为解决以上方法的不足，本发明从概率的角度用概率模型来描述成本以及有效性，使得我们的方法能适用于多种药物的分析，并且能根据人群的经济能力以及要求做出个性化的决策方案。The above methods did not take into account the differences in the economic capacity and response to drugs of different groups of people, as well as the special requirements of different groups of people. In order to solve the shortcomings of the above methods, the present invention uses a probability model to describe the cost and effectiveness from the perspective of probability, so that our method can be applied to the analysis of various drugs, and can make personalized medicine according to the economic capacity and requirements of the population. decision-making options.

上文中提到的文献来源于如下的期刊：The literature mentioned above comes from the following journals:

[1].Krasnova，L.，P.Vorobiev and M.Holownia，Real-World Data on theEpidemiology and Treatment ofHER2-Advanced Breast Cancer in PostmenopausalPatients in Different Regions of Russia for Forming Markov Models ofManagment of Patients.Value in Health，2014.17(7)：p.A618-.[1].Krasnova, L., P.Vorobiev and M.Hownia, Real-World Data on the Epidemiology and Treatment of HER2-Advanced Breast Cancer in Postmenopausal Patients in Different Regions of Russia for Forming Markov Models of Managment of Patients. Value in Health, 2014.17 (7): p.A618-.

[2].Parienti，J.J.，et al.，Empirical therapies among adultshospitalized for community-acquired upper urinary tract infections：Adecision-tree analysis of mortality，costs，and resistance.American Journal ofInfection Control，2015.43(9)：p.e53-e59.[2]. Parienti, J.J., et al., Empirical therapies among adultshospitalized for community-acquired upper urinary tract infections: Adecision-tree analysis of mortality, costs, and resistance. American Journal of Infection Control, 2015.43(9): p.e53 -e59.

[3].王志亮与李新娥，3种磺脲类药用于2型糖尿病初始治疗的成本-效果分析.中国药房，2014(22)：第2019-2021页.[3]. Wang Zhiliang and Li Xin'e, Cost-effectiveness analysis of three sulfonylureas for the initial treatment of type 2 diabetes. China Pharmacy, 2014(22): pp. 2019-2021.

[4].姚尧，盐酸氨溴索治疗小儿支气管炎的疗效评价.临床医药文献电子杂志，2015(13)：第2529-2532页.[4]. Yao Yao, Evaluation of the efficacy of ambroxol hydrochloride in the treatment of children with bronchitis. Electronic Journal of Clinical Medicine Literature, 2015(13): pp. 2529-2532.

发明内容Contents of the invention

本发明为解决的技术问题：The technical problem that the present invention is to solve:

本发明的目的是提出一种基于概率的个性化药物推荐方法，以解决在药物经济学中传统方法无法根据人群的经济能力以及自身特征做出个性化决策的问题。The purpose of the present invention is to propose a probability-based personalized drug recommendation method to solve the problem that traditional methods in pharmacoeconomics cannot make personalized decisions based on the economic capabilities of the population and their own characteristics.

本发明为解决其技术问题采用如下技术方案：The present invention adopts following technical scheme for solving its technical problem:

本发明为解决其技术问题采用如下技术方案，包括如下步骤：The present invention adopts following technical scheme for solving its technical problem, comprises the steps:

A)分析单位人群和总体人群的成本数据，用概率模型表示单位人群成本分布情况和总体人群成本分布情况；A) Analyze the cost data of the unit population and the overall population, and use the probability model to represent the cost distribution of the unit population and the overall population cost distribution;

B)分析单位人群和总体人群的治疗情况，用概率模型来表示单位有效性和总体有效性；B) Analyze the treatment situation of the unit population and the overall population, and use the probability model to represent the unit effectiveness and overall effectiveness;

C)根据单位成本概率分布和总体成本概率分布计算单位群体相对于总体的成本增量分布，根据单位有效性概率分布和总体有效性概率分布计算单位群体相对于总体有效性增量分布；C) Calculate the incremental cost distribution of the unit population relative to the overall according to the unit cost probability distribution and the overall cost probability distribution, and calculate the incremental distribution of the unit population relative to the overall effectiveness based on the unit effectiveness probability distribution and the overall effectiveness probability distribution;

D)利用成本增量和有效性增量计算成本有效性增量比的概率分布；D) Calculate the probability distribution of the cost-effectiveness increment ratio by using the cost increment and the effectiveness increment;

E)根据增量比概率分布计算在人群要求在整体水平上提高单位有效性愿意增加医疗费用的情况下每种药物能满足要求的概率，最后根据每种药物的概率值大小来决定哪种药物是最佳选择。E) According to the probability distribution of the incremental ratio, calculate the probability that each drug can meet the requirements under the condition that the crowd demands to improve the unit effectiveness at the overall level and is willing to increase medical expenses, and finally decide which drug to use according to the probability value of each drug is the best choice.

其中为成本建立概率模型，步骤A具体包括：Where a probability model is established for the cost, step A specifically includes:

A1、用向量C_i[1，2....m]表示使用药物i的单元人群花费的原始成本数据，m表示该单元总共有m个人，将原始成本数据归一化，C_i′[1，2....m]表示归一化处理后的成本数据；向量C[1，2....n]表示整体实验人群的原始成本数据，n表示实验人群总数为n，C′[1，2....n]表示归一化处理后的数据，即：A1. Use the vector C _i [1, 2....m] to represent the original cost data of the unit population using drug i, m means that there are m people in the unit, and normalize the original cost data, C _i ′[ 1, 2....m] represents the cost data after normalization processing; the vector C[1, 2....n] represents the original cost data of the overall experimental population, n represents the total number of experimental population is n, C' [1, 2....n] represents the normalized data, namely:

${C C}_{i i}^{' '} [[j j]] = = \frac{{C C}_{i i} [[j j]]}{M m I I N N ((C C)) + + M m A A X x ((C C))}$

${C C}^{' '} [[j j]] = = \frac{C C [[j j]]}{M m I I N N ((C C)) + + M m A A X x ((C C))}$

其中，C_i[j]表示使用药物i的编号为j的患者所花费的原始成本，C′_i[j]则表示对应归一化处理后的成本；C[j]表示总体试验人群中编号为j的人花费成本原始数据，C′[j]则表示对应归一化处理后的成本；MIN(C)表示整体实验人群原始成本数据最小值，MAX(C)表示整体实验人群原始成本数据最大值；Among them, C _i [j] represents the original cost spent by patient j who uses drug i, and C′ _i [j] represents the cost after normalization processing; C[j] represents the number in the overall trial population is the original cost data of person j, and C′[j] represents the corresponding normalized cost; MIN(C) represents the minimum value of the original cost data of the overall experimental population, and MAX(C) represents the original cost data of the overall experimental population maximum value;

A2、(计算均值、方差)根据单元成本数据集C_i′[1，2....m]和总体成本数据集C′[1，2....n]计算对应均值E(C)和标准差s；计算对数正态分布的参数μ和σ；A2. (Calculation of mean and variance) Calculate the corresponding mean value E(C) according to the unit cost data set C _i '[1, 2....m] and the overall cost data set C'[1, 2....n] and standard deviation s; calculate the parameters μ and σ of the lognormal distribution;

$σ σ = = \sqrt{L L n no ((11 + + \frac{{s the s}^{22}}{E E. {((c c))}^{22}}))}$

$μ μ = = L L n no [[E E. ((c c))]] - - \frac{11}{22} {σ σ}^{22}$

A3、用对数正态分布模型表示成本分布情况，单元人群i的成本分布为 A3. Use the lognormal distribution model to represent the cost distribution, and the cost distribution of unit population i is

${f f}_{{C C}_{i i}} (({c c}_{i i};; {μ μ}_{i i},, {σ σ}_{i i})) = = \frac{11}{\sqrt{22 π π} {σ σ}_{i i} {c c}_{i i}} {e e}^{- - \frac{{(({lnc lnc}_{i i} - - {μ μ}_{i i}))}^{22}}{22 {σ σ}_{i i}^{22}}}$

其中c_i表示单元人群i的成本变量，μ_i，σ_i为对应对数正态分布的参数；Where c _i represents the cost variable of unit population i, μ _i and σ _i are parameters corresponding to lognormal distribution;

总体人群成本分布为f_C(c；μ，σ)The overall population cost distribution is f _C (c; μ, σ)

${f f}_{C C} ((c c;; μ μ,, σ σ)) = = \frac{11}{\sqrt{22 π π} σ σ c c} {e e}^{- - \frac{{((ln ln c c - - μ μ))}^{22}}{22 {σ σ}^{22}}}$

上式中c表示整体成本变量，μ，σ表示对应的参数。In the above formula, c represents the overall cost variable, and μ, σ represent the corresponding parameters.

其中为有效性建立概率模型，步骤B包括：Where a probabilistic model is established for effectiveness, step B includes:

B1、统计单元人群i中治愈和未治愈的人数，分别记为α_i和β_i；统计总体人群中治愈和未治愈的人数，分别记为α和β；B1, the number of cured and uncured people in statistical unit population i is recorded as α _i and β _i respectively; the number of cured and uncured in the statistics of the overall population is recorded as α and β respectively;

B2、药物i针对单元人群的有效性 B2. The effectiveness of drug i targeting the unit population

${f f}_{{E E.}_{i i}} (({e e}_{i i})) = = \frac{11}{B B (({α α}_{i i},, {β β}_{i i}))} {e e}_{i i}^{{α α}_{i i} - - 11} {((11 - - {e e}_{i i}))}^{{β β}_{i i} - - 11}$

其中e_i为有效性变量，B(α_i，β_i)表示贝塔函数，α_i和β_i为对应参数；Where e _i is the validity variable, B(α _i , β _i ) represents the beta function, and α _i and β _i are the corresponding parameters;

所有药物针对总体人群的有效性f_E(e)，The effectiveness of all drugs against the overall population f _E (e),

${f f}_{E E.} ((e e)) = = \frac{11}{B B ((α α,, β β))} {e e}^{α α - - 11} {((11 - - e e))}^{β β - - 11}$

其中e为变量，α和β表示对应参数。Where e is a variable, and α and β represent corresponding parameters.

进行增量分析的步骤C包括：Step C of performing incremental analysis includes:

C1、根据联合概率密度，求出增量ΔX的分布函数：C1. Calculate the distribution function of the increment ΔX according to the joint probability density:

$\begin{matrix} {F f}_{Δ Δ X x} ((Δ Δ x x)) = = P P {{Δ Δ X x \leq \leq Δ Δ x x}} = = P P {{X x i i - - X x \leq \leq Δ Δ x x}} \\ = = {&Integral; &Integral;}_{00}^{b b - - Δ Δ x x} d d x x {&Integral; &Integral;}_{00}^{x x + + Δ Δ x x} {f f}_{Δ Δ X x} ((x x,, {x x}_{i i})) {dx dx}_{i i} + + {&Integral; &Integral;}_{b b - - Δ Δ x x}^{a a} d d x x {&Integral; &Integral;}_{00}^{b b} {f f}_{Δ Δ X x} ((x x,, {x x}_{i i})) {dx dx}_{i i} \\ = = {&Integral; &Integral;}_{00}^{a a} d d x x {&Integral; &Integral;}_{00}^{x x + + Δ Δ x x} {f f}_{Δ Δ X x} ((x x,, {x x}_{i i})) {dx dx}_{i i} - - {&Integral; &Integral;}_{b b - - Δ Δ x x}^{a a} d d x x {&Integral; &Integral;}_{b b}^{x x + + Δ Δ x x} {f f}_{Δ Δ X x} ((x x,, {x x}_{i i})) {dx dx}_{i i} \end{matrix}$

$\underset{&OverBar; &OverBar;}{\underset{&OverBar; &OverBar;}{{x x}_{i i} = = x x + + u u}} {&Integral; &Integral;}_{00}^{a a} d d x x {&Integral; &Integral;}_{- - x x}^{Δ Δ x x} {f f}_{Δ Δ X x} ((x x,, x x + + u u)) d d u u - - {&Integral; &Integral;}_{b b - - Δ Δ x x}^{a a} d d x x {&Integral; &Integral;}_{b b - - x x}^{Δ Δ x x} {f f}_{Δ Δ X x} ((x x,, x x + + u u)) d d u u$

C2、对分布函数求导可得概率密度函数：C2. The probability density function can be obtained by deriving the distribution function:

$\begin{matrix} {f f}_{Δ Δ X x} ((Δ Δ x x)) = = {F f}^{' '}_{Δ Δ X x} ((Δ Δ x x)) = = {&Integral; &Integral;}_{00}^{a a} {f f}_{Δ Δ X x} ((x x,, x x + + u u)) d d x x + + 00 - - {&Integral; &Integral;}_{a a - - Δ Δ x x}^{a a} {f f}_{Δ Δ X x} ((x x,, x x + + Δ Δ x x)) d d x x \\ = = {&Integral; &Integral;}_{00}^{a a - - Δ Δ x x} {f f}_{Δ Δ X x} ((x x,, x x + + Δ Δ x x)) d d x x \end{matrix}$

C3、同理可得，当ΔX≤0时：C3. In the same way, when ΔX≤0:

${f f}_{Δ Δ X x} ((Δ Δ x x)) = = {&Integral; &Integral;}_{00}^{b b + + Δ Δ x x} {f f}_{Δ Δ X x} (({x x}_{i i} - - Δ Δ x x,, {x x}_{i i})) {dx dx}_{i i}$

计算成本有效性增量比的开率模型，步骤D具体包括：Calculating the opening rate model of the cost-effectiveness incremental ratio, step D specifically includes:

若Δe_i＞0且Δc_i＞0，计算成本有效性增量比f₁(Δe_i，Δc_i)If Δe _i >0 and Δc _i >0, calculate cost-effectiveness incremental ratio f ₁ (Δe _i , Δc _i )

${f f}_{11} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} ((c c,, c c + + {Δc Δ c}_{i i})) d d c c * * {&Integral; &Integral;}_{00}^{11 - - Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} ((e e,, e e + + {Δe Δ e}_{i i})) d d e e$

若Δe_i＜0且Δc_i＞0，计算成本有效性增量比f₂(Δe_i，Δc_i)If Δe _i <0 and Δc _i >0, calculate cost-effectiveness incremental ratio f ₂ (Δe _i , Δc _i )

${f f}_{22} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{11 + + Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} (({e e}_{i i} - - {Δe Δe}_{i i},, {e e}_{i i})) {de de}_{i i} * * {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} ((c c,, c c + + {Δc Δ c}_{i i})) d d c c$

若Δe_i＜0且Δc_i＜0，计算成本有效性增量比f₃(Δe_i，Δc_i)If Δe _i <0 and Δc _i <0, calculate the cost-effectiveness incremental ratio f ₃ (Δe _i , Δc _i )

${f f}_{33} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{11 + + Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} (({e e}_{i i} - - {Δe Δe}_{i i},, {e e}_{i i})) {de de}_{i i} * * {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} (({c c}_{i i} - - {Δc Δ c}_{i i},, {c c}_{i i})) {dc dc}_{i i}$

若Δe_i＜0且Δc_i＜0，计算成本有效性增量比f₄(Δe_i，Δc_i)If Δe _i <0 and Δc _i <0, calculate cost-effectiveness incremental ratio f ₄ (Δe _i , Δc _i )

${f f}_{44} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{11 - - Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} ((e e,, e e + + {Δe Δe}_{i i})) d d e e * * {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} (({c c}_{i i} - - {Δc Δ c}_{i i},, {c c}_{i i})) {dc dc}_{i i}$

根据增量比的概率密度以及对于每个象限的权值，计算每种药物在符合人群要求的阈值icer(人群要求在整体水平上提高单位有效性愿意增加医疗费用)的概率值：According to the probability density of the incremental ratio and the weight for each quadrant, calculate the probability value of each drug at the threshold icer that meets the population requirements (the population requires that the unit effectiveness be increased at the overall level and is willing to increase medical expenses):

若icer≤1，If icer≤1,

$\begin{matrix} {F f}_{{ICER ICER}_{i i}} (({icer icer}_{i i})) = = {w w}_{11} * * {&Integral; &Integral;}_{00}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{00}^{{Δe Δe}_{i i} * * {icer icer}_{i i}} {f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} + + {w w}_{33} * * {&Integral; &Integral;}_{- - 11}^{00} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{{Δe Δ e}_{i i} * * {icer icer}_{i i}} {f f}_{33} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} \\ + + {w w}_{44} * * {&Integral; &Integral;}_{00}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{00} {f f}_{44} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} \end{matrix}$

若icer＞1，If icer>1,

$\begin{matrix} {F f}_{{ICER ICER}_{i i}} (({icer icer}_{i i})) = = {w w}_{11} * * (({&Integral; &Integral;}_{00}^{\frac{11}{{icer icer}_{i i}}} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{00}^{{Δe Δ e}_{i i} * * {icer icer}_{i i}} {f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} + + {&Integral; &Integral;}_{\frac{11}{{icer icer}_{i i}}}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{00}^{11} {f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i})) \\ + + {w w}_{33} * * {&Integral; &Integral;}_{\frac{- - 11}{{icer icer}_{i i}}}^{00} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{{Δe Δe}_{i i} * * {icer icer}_{i i}} {f f}_{33} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} + + {w w}_{44} * * {&Integral; &Integral;}_{00}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{00} {f f}_{44} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} \end{matrix}$

其中w₁，w₂，w₃，w₄为根据成本有效性增量比的意义而赋予的权值；Among them, w ₁ , w ₂ , w ₃ , and w ₄ are the weights given according to the significance of cost-effectiveness incremental ratio;

本发明采用以上技术方案与现有技术相比，具有以下有益效果：Compared with the prior art by adopting the above technical scheme, the present invention has the following beneficial effects:

(1)本发明从概率的角度分析药物的成本以及有效性，使得该方法更具有普遍性，更加适用于多种药物的分析。(1) The present invention analyzes the cost and effectiveness of drugs from the perspective of probability, making the method more universal and more applicable to the analysis of multiple drugs.

(2)本发明基于概率，考虑不同人群的需求以及特性，使得该方法能针对特定人群推荐个性化治疗方案。(2) The present invention is based on probability and considers the needs and characteristics of different groups of people, so that the method can recommend personalized treatment plans for specific groups of people.

附图说明Description of drawings

图1是本发明的体系结构图。整个模型分为单元分析、总体分析、增量分析、增量比分析四个部分如图1所示。单元分析是针对使用同种药物的人群的治愈情况和成本的观测值求出用该种药的有效性以及成本分布情况。由于该模型后面用到增量，故需要一个比较的基准。考虑到人群对药物反应的差异性，将整个试验人群的有效性以及成本作为比较的基准。故总体分析是分析整个人群的有效性以及成本分布。增量分析主要包括成本增量以及有效性增量，是对某种药物与总体成本以及有效性的差异量化表示。增量比分析，在增量分析的基础上从概率的角度考虑药物有效性增量随成本增量变化的关系。最后从概率的角度来分析针对特定人群提出最优的治疗药物。Fig. 1 is a system structure diagram of the present invention. The whole model is divided into four parts: unit analysis, overall analysis, incremental analysis, and incremental ratio analysis, as shown in Figure 1. Unit analysis is to find out the effectiveness and cost distribution of using the same drug based on the observed value of the cure and cost of the population using the same drug. Since increments are used later in the model, a benchmark for comparison is needed. Taking into account the differences in the population's response to the drug, the effectiveness and cost of the entire trial population are used as a benchmark for comparison. Therefore, the overall analysis is to analyze the effectiveness and cost distribution of the entire population. Incremental analysis mainly includes cost increment and effectiveness increment, which is a quantitative representation of the difference between a certain drug and the overall cost and effectiveness. Increment ratio analysis, on the basis of incremental analysis, considers the relationship between drug effectiveness increment and cost increment from the perspective of probability. Finally, from the perspective of probability, the optimal treatment drugs are proposed for specific groups of people.

图2是增量分析示意图。计算增量的概率密度，其中a，b分别表示X，Xi的上限，阴影部分表示积分区间。Figure 2 is a schematic diagram of incremental analysis. Calculate the probability density of the increment, where a and b represent the upper limit of X and Xi respectively, and the shaded part represents the integration interval.

图3是成本有效性增量比分析示意图。f₁(Δe_i，Δc_i)，f₂(Δe_i，Δc_i)，f₃(Δe_i，Δc_i)，f₄(Δe_i，Δc_i)，表示ΔC_i与ΔE_i在四个象限的联合概率密度，四条虚线围成的矩形是ΔC_i和ΔE_i的取值区间。过原点的斜线反应阈值(愿意为提高单位有效性所增加相应的费用)，阴影部分表示积分区间。Figure 3 is a schematic diagram of cost-effectiveness incremental ratio analysis. f ₁ (Δe _i , Δc _i ), f ₂ (Δe _i , Δc _i ), f ₃ (Δe _i , Δc _i ), f ₄ (Δe _i , Δc _i ), indicating that ΔC _i and ΔE _i are in four quadrants The joint probability density of , the rectangle surrounded by four dotted lines is the value range of ΔC _i and ΔE _i . The response threshold of the slash passing through the origin (willing to increase the corresponding cost to improve the effectiveness of the unit), the shaded part indicates the integral interval.

具体实施方式detailed description

下面结对本发明创造做进一步详细说明。Below the present invention is described in further detail.

在药物经济学研究中，药物评价是一门关键的技术。对于多种药物的经济性比较中，如何选取一个一个比较对象是至关重要的。传统方法采用成本最低的方案(或药物)作为比较对象或者设置标准的对照组。前者无法反应整个人群的经济水平以及整体药物的有效性，而后者在操作上有较大的难度；对于成本以及有效性，传统方法仅仅从统计学角度计算均值和方差，忽略了不同人群的经济水平以及对药物反应的差异性。本发明从概率模型的角度考虑，用对数正态分布来描述人群对于每种药物以及总体人群的成本分布情况，用贝塔分布来描述药物的有效性情况，利用联合概率求出每种药物的有效性、成本情况相对于总体的有效性、成本增量。最后根据人群的特定需求(愿意为提高单位有效性所增加相应的费用)来计算每种药物的概率值，根据概率值大小来决策出最优的方案。Drug evaluation is a key technique in pharmacoeconomics research. For the economical comparison of multiple drugs, how to select a comparison object is very important. Traditional approaches use the least costly regimen (or drug) as a comparator or control group that sets the standard. The former cannot reflect the economic level of the entire population and the effectiveness of the overall drug, while the latter is more difficult to operate; for cost and effectiveness, the traditional method only calculates the mean and variance from a statistical point of view, ignoring the economics of different populations. levels and variability in response to drugs. Considering from the perspective of probability model, the present invention uses lognormal distribution to describe the cost distribution of the population for each drug and the overall population, uses Beta distribution to describe the effectiveness of the drug, and uses the joint probability to obtain the cost of each drug. Effectiveness, cost situation relative to the overall effectiveness, cost increment. Finally, the probability value of each drug is calculated according to the specific needs of the population (willing to increase the corresponding cost to improve the unit effectiveness), and the optimal plan is determined according to the probability value.

下面通过说明书附图以及实施例对本发明进行说明。The present invention will be described below through the accompanying drawings and embodiments.

1)实施例一1) Embodiment one

本发明的实施例一介绍了一种基于概率的增量分析方法，如图2所示，展示了增量大于0时的积分区域，计算增量概率模型的具体步骤如下所示：Embodiment 1 of the present invention introduces a probability-based incremental analysis method, as shown in Figure 2, which shows the integral area when the increment is greater than 0, and the specific steps for calculating the incremental probability model are as follows:

根据联合概率密度，求出增量ΔX的分布函数：According to the joint probability density, the distribution function of the increment ΔX is obtained:

对分布函数求导可得概率密度函数：Deriving the distribution function gives the probability density function:

同理可得，当ΔX≤0时：Similarly, when ΔX≤0:

2)实施例二2) Embodiment two

本发明的实施例二介绍介绍了基于概率的成效比增量分析方法，如图3所示展示了阈值小于1时的积分区域，对每种药物的成本有效性增量比分析具体步骤如下所示：The second embodiment of the present invention introduces the probabilistic-based effectiveness ratio incremental analysis method. As shown in Figure 3, the integral area when the threshold is less than 1 is shown. The specific steps of the cost-effectiveness incremental ratio analysis of each drug are as follows Show:

根据成本增量的概率密度和有效性增量的概率密度计算成本有效性增量比的概率密度：Calculate the probability density of the cost-effectiveness increment ratio according to the probability density of the cost increment and the probability density of the effectiveness increment:

${f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} ((c c,, c c + + {Δc Δ c}_{i i})) d d c c * * {&Integral; &Integral;}_{00}^{11 - - Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} ((e e,, e e + + {Δe Δ e}_{i i})) d d e e$

${f f}_{22} (({Δe Δ e}_{i i},, {Δc Δc}_{i i})) = = {&Integral; &Integral;}_{00}^{11 + + Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} (({e e}_{i i} - - {Δe Δ e}_{i i},, {e e}_{i i})) {de de}_{i i} * * {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} ((c c,, c c + + {Δc Δ c}_{i i})) d d c c$

${f f}_{33} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{11 + + Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} (({e e}_{i i} - - {Δe Δe}_{i i},, {e e}_{i i})) {de de}_{i i} * * {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} (({c c}_{i i} - - {Δc Δ c}_{i i},, {c c}_{i i})) {dc dc}_{i i}$

${f f}_{44} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) = = {&Integral; &Integral;}_{00}^{11 - - Δ Δ e e} {f f}_{{ΔE ΔE}_{i i}} ((e e,, e e + + {Δe Δe}_{i i})) d d e e * * {&Integral; &Integral;}_{00}^{+ + ∞ ∞} {f f}_{{ΔC ΔC}_{i i}} (({c c}_{i i} - - {Δc Δ c}_{i i},, {c c}_{i i})) {dc dc}_{i i}$

根据增量比的概率密度以及对于每个象限的权值，计算每种药物在符合人群要求的阈值T(人群要求在整体水平上提高单位有效性愿意增加医疗费用)的概率值 According to the probability density of the incremental ratio and the weights for each quadrant, calculate the probability value of each drug at the threshold T that meets the requirements of the population (the population requires an increase in unit effectiveness at the overall level and is willing to increase medical expenses)

根据图3中的积分区域计算当icer≤1时，According to the integral area calculation in Figure 3, when icer≤1,

$\begin{matrix} {F f}_{{ICER ICER}_{i i}} (({icer icer}_{i i})) = = {w w}_{11} * * {&Integral; &Integral;}_{00}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{00}^{{Δe Δe}_{i i} * * {icer icer}_{i i}} {f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} + + {w w}_{33} * * {&Integral; &Integral;}_{- - 11}^{00} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{{Δe Δ e}_{i i} * * {icer icer}_{i i}} {f f}_{33} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} \\ + + {w w}_{44} * * {&Integral; &Integral;}_{00}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{00} {f f}_{44} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} \end{matrix}$

同理可计算当icer＞1时，In the same way, it can be calculated that when icer>1,

$\begin{matrix} {F f}_{{ICER ICER}_{i i}} (({icer icer}_{i i})) = = {w w}_{11} * * (({&Integral; &Integral;}_{00}^{\frac{11}{{icer icer}_{i i}}} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{00}^{{Δe Δe}_{i i} * * {icer icer}_{i i}} {f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} + + {&Integral; &Integral;}_{\frac{11}{{icer icer}_{i i}}}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{00}^{11} {f f}_{11} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i})) \\ + + {w w}_{33} * * {&Integral; &Integral;}_{\frac{- - 11}{{icer icer}_{i i}}}^{00} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{{Δe Δe}_{i i} * * {icer icer}_{i i}} {f f}_{33} (({Δe Δ e}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} + + {w w}_{44} * * {&Integral; &Integral;}_{00}^{11} {dΔe dΔe}_{i i} {&Integral; &Integral;}_{- - 11}^{00} {f f}_{44} (({Δe Δe}_{i i},, {Δc Δ c}_{i i})) {dΔc dΔc}_{i i} \end{matrix}$

C、根据药物的概率值大小来决策出最优的治疗药物。C. Determine the optimal treatment drug according to the probability value of the drug.

Claims

1. personalised drug based on probability recommend a method, including cost measuring, health outcome measure and model analysis its It is characterised by comprising the steps:

A. unit of analysis crowd and the cost data of general population, by probabilistic model representation unit crowd's cost distribution situation with total Body crowd's cost distribution situation；

B. the treatment situation of unit of analysis crowd and general population, carrys out representation unit effectiveness with probabilistic model effective with overall Property；

C. according to unit cost probability distribution and overall cost probability distribution unit of account colony relative to overall cost increase Distribution, increases relative to collective effectiveness according to unit effectiveness probability distribution and collective effectiveness probability distribution unit of account colony Amount distribution；

D. cost increase and the probability distribution of effectiveness incremental computations cost effectiveness incremental raio are utilized；

E. calculate according to incremental raio probability distribution and require that improving unit effectiveness in integral level is ready to increase medical treatment crowd In the case of expense, every kind of medicine can meet the probability required, which kind of medicine is the probit size finally according to every kind of medicine determine Thing is optimum selection.

2. recommend method according to a kind of based on probability the personalised drug described in right 1, it is characterised in that described step A has Body includes:

A1. with vector C_i[1,2....m] represents the original cost data using the unit crowd of medicine i to spend, and m represents this unit A total of m people, by original cost data normalization, C_i' [1,2....m] represents the cost data after normalized；Vector C [1,2....n] represents the original cost data of integral experiment crowd, and n represents that Subject Population's sum is n,Represent Data after normalized, it may be assumed that

{C_{i}}^{'} [j] = \frac{C_{i} [j]}{M I N (C) + M A X (C)}

C^{'} [j] = \frac{C [j]}{M I N (C) + M A X (C)}

Wherein, C_i[j] represents the original cost that the patient of the numbered j using medicine i is spent, C '_i[j] then represents that correspondence is returned Cost after one change process；C [j] represents that in bulk test crowd, the people of numbered j spends cost initial data,Then table Show the cost after corresponding normalized；MIN (C) represents integral experiment crowd's original cost data minima, and MAX (C) represents Integral experiment crowd's original cost data maximums；

A2. according to unit cost data set C_i' [1,2....m] and overall cost data collectionCalculate corresponding average E And standard deviation s (C)；Calculate parameter μ and the σ of logarithm normal distribution；

σ = \sqrt{L n (1 + \frac{s^{2}}{E {(c)}^{2}})}

μ = L n [E (c)] - \frac{1}{2} σ^{2}

A3. being expressed as this distribution situation with logarithm normal distribution model, the cost of unit crowd i is distributed as

f_{C_{i}} (c_{i}; μ_{i}, σ_{i}) = \frac{1}{\sqrt{2 π} σ_{i} c_{i}} e^{- \frac{{(l n c_{i} - μ_{i})}^{2}}{2 {σ_{i}}^{2}}}

Wherein c_iRepresent the cost variations of unit crowd i, μ_i, σ_iParameter for corresponding logarithm normal distribution；

General population's cost is distributed as f_C(c；μ, σ)

f_{C} (c; μ, σ) = \frac{1}{\sqrt{2 π} σ c} e^{- \frac{{(l n c - μ)}^{2}}{2 σ^{2}}}

Wherein c represents holistic cost variable, and μ, σ represent corresponding parameter.

3. recommend method according to a kind of based on probability the personalised drug described in right 1, it is characterised in that described step B has Body includes:

B1. the number cured in statistic unit crowd i and do not cure, is designated as α respectively_iAnd β_i；In statistical universe crowd cure and not The number cured, is designated as α and β respectively；

B2. medicine i is for the effectiveness of unit crowd

f_{E_{i}} (e_{i}) = \frac{1}{B (α_{i}, β_{i})} {e_{i}}^{α_{i} - 1} {(1 - e_{i})}^{β_{i} - 1}

Wherein e_iFor effectiveness variable, B (α_i, β_i) represent beta function, α_iAnd β_iFor corresponding parameter；

All medicines are for the effectiveness f of general population_E(e),

f_{E} (e) = \frac{1}{B (α, β)} e^{α - 1} {(1 - e)}^{β - 1}

Wherein e is variable, α and β represents corresponding parameter.

4. recommend method according to a kind of based on probability the personalised drug described in right 1, it is characterised in that described step C has Body includes:

C1. computing unit cost is relative to the increment probability density of holistic cost

f_{{ΔC}_{i}} ({Δc}_{i}) = \{\begin{matrix} {&Integral;}_{0}^{+ \infty} f_{{ΔC}_{i}} (c, c + {Δc}_{i}) d c ............ {Δc}_{i} > 0 \\ {&Integral;}_{0}^{+ \infty} f_{{ΔC}_{i}} (c_{i} - {Δc}_{i}, c_{i}) {dc}_{i} ............. {Δc}_{i} \leq 0 \end{matrix}

Wherein Δ c_iFor cost increase,

f_{{ΔC}_{i}} (c, c_{i}) = \frac{1}{2 {πσσ}_{i} {cc}_{j}} e^{(- \frac{{(l n c - μ)}^{2}}{2 σ^{2}} - \frac{{(l n c_{i} - μ_{i})}^{2}}{2 {σ_{i}}^{2}})}

C2. computing unit effectiveness is relative to the probability density of the increment of overall effectiveness

f_{{ΔE}_{i}} ({Δe}_{i}) = \{\begin{matrix} {&Integral;}_{0}^{1 - Δ e} f_{{ΔE}_{i}} (e, e + {Δe}_{i}) d e ............ {Δe}_{i} > 0 \\ {&Integral;}_{0}^{1 + Δ e} f_{{ΔE}_{i}} (e_{i} - {Δe}_{i}, e_{i}) {de}_{i} ............. {Δe}_{i} \leq 0 \end{matrix}

Wherein Δ e_iFor effectiveness increment,

f_{{ΔE}_{i}} (e, e_{i}) = \frac{1}{B (α, β) B (α_{i}, β_{i})} e^{α - 1} {(1 - e)}^{β - 1} {e_{i}}^{α_{i} - 1} {(1 - e_{i})}^{β_{i} - 1}

5. recommend method according to a kind of based on probability the personalised drug described in right 1, it is characterised in that described step D has Body includes:

According to effectiveness increment and cost increase probabilistic model

If Δ e_i＞ 0 and Δ c_i＞ 0, calculates cost effectiveness incremental raio f₁(Δe_i, Δ c_i)

f_{1} ({Δe}_{i}, {Δc}_{i}) = {&Integral;}_{0}^{+ \infty} f_{{ΔC}_{i}} (c, c + {Δc}_{i}) d c * {&Integral;}_{0}^{1 - Δ c} f_{{ΔE}_{i}} (e, e + {Δe}_{i}) d e

If Δ e_i＜ 0 and Δ c_i＞ 0, calculates cost effectiveness incremental raio f₂(Δe_i, Δ c_i)

f_{2} ({Δe}_{i}, {Δc}_{i}) = {&Integral;}_{0}^{1 + Δ c} f_{{ΔE}_{i}} (e_{i} - {Δe}_{i}, e_{i}) {de}_{i} * {&Integral;}_{0}^{+ \infty} f_{{ΔC}_{i}} (c, c + {Δc}_{i}) d c

If Δ e_i＜ 0 and Δ c_i＜ 0, calculates cost effectiveness incremental raio f₃(Δe_i, Δ c_i)

f_{3} ({Δe}_{i}, {Δc}_{i}) = {&Integral;}_{0}^{1 + Δ e} f_{{ΔE}_{i}} (e_{i} - {Δe}_{i}, e_{i}) {de}_{i} * {&Integral;}_{0}^{+ \infty} f_{{ΔC}_{i}} (c_{i} - {Δc}_{i}, c_{i}) {dc}_{i}

If Δ e_i＜ 0 and Δ c_i＜ 0, calculates cost effectiveness incremental raio f₄(Δe_i, Δ c_i)

f_{4} ({Δe}_{i}, {Δc}_{i}) = {&Integral;}_{0}^{1 - Δ e} f_{{ΔE}_{i}} (e, e + {Δe}_{i}) d e * {&Integral;}_{0}^{+ \infty} f_{{ΔC}_{i}} (c_{i} - {Δc}_{i}, c_{i}) {dc}_{i}

6. recommend method according to a kind of based on probability the personalised drug described in right 1, it is characterised in that described step E has Body includes:

E1. according to cost effectiveness incremental raio ICER_iCalculate every kind of medicine and meet threshold value icer (crowd's requirement that crowd requires In integral level improve unit effectiveness be ready increase medical expense) probit

If icer≤1,

\begin{matrix} F_{{ICER}_{i}} ({icer}_{i}) = w_{1} * {&Integral;}_{0}^{1} {dΔe}_{i} {&Integral;}_{0}^{{Δe}_{i} * {icer}_{i}} f_{1} ({Δe}_{i}, {Δc}_{i}) {dΔc}_{i} w_{3} * {&Integral;}_{- 1}^{0} {dΔe}_{i} {&Integral;}_{- 1}^{{Δe}_{i} * {icer}_{i}} f_{3} ({Δe}_{i}, {Δc}_{i}) {dΔc}_{i} \\ + w_{4} * {&Integral;}_{0}^{1} {dΔe}_{i} {&Integral;}_{- 1}^{0} f_{4} ({Δe}_{i}, {Δc}_{i}) {dΔc}_{i} \end{matrix}

If icer ＞ 1,

Wherein w₁, w₂, w₃, w₄The weights given for the meaning according to cost effectiveness incremental raio；

E2. according to probit size, every kind of medicine is sorted.

7. a personalised drug based on probability recommends method, it is characterised in that comprise the following steps:

The present invention, from the point of view of probabilistic model, describes crowd for every kind of medicine and overall people by logarithm normal distribution The cost distribution situation of group, describes the effectiveness situation of medicine, utilizes joint probability to obtain every kind of medicine with beta distribution Effectiveness, cost situation are relative to overall effectiveness, cost increase.Finally according to the particular demands of crowd, (hope means raising Unit effectiveness is increased corresponding expense) calculate the probit of every kind of medicine, carry out decision-making according to probit size and go out optimum Scheme.