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Mathematical and Statistical Modelling to Optimise Paediatric Medicines Research

优化儿科药物研究的数学和统计模型

基本信息

批准号：
MR/M008665/1
负责人：
Joseph Frank Standing
金额：
$ 84.87万
依托单位：
University College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2015
资助国家：
英国
起止时间：
2015 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=MR%2FM008665%2F1
关键词：
Mathematical Statistical Modelling Optimise Paediatric

项目摘要

This project will improve the methods used in mathematical and statistical modelling to help us make best use of medicines in children. Mathematical modelling uses equations to describe observations made during an experiment. For example, suppose we measure the number of bacteria in the lung of a child with a chest infection at a few time points. A simple model is a straight line given by the equation: y = mx + c, where y is the number of bacteria for each value of x (the time that the measurement was taken), m is the slope of the line, and c is the number of bacteria when time is 0. In this case, m and c are model parameters and we estimate their values from our observations. With these values of m and c, we can use the model to predict what the number of bacteria would be at values of x (time points) that were not measured in our experiment. We can also look at the values of m and c to learn about the system, e.g. m tells us how quickly the number of bacteria decreases with time. If we collected information like this from children receiving different doses or types of antibiotics, then we could see what effect antibiotic dose and type has on the rate that bacterial numbers decrease. Because each child is an individual, the value of m and c might be different in different children. Also our mathematical model is a simple representation of the system. For these reasons, we add a statistical part to the model. This explains the variability between individuals, and the unexplained variability from the model. By adding this statistical part, we can judge how much confidence we should have in the predictions from the model. The models used will be more complex than the example above, and the technique is called nonlinear mixed effects modelling.The reason that mathematical and statistical modelling is important is that fewer patients are needed than for traditional controlled trials, which involve comparing outcomes amongst large groups of subjects. By intensively studying a small number of children, we can work out the optimum treatment regime more efficiently. The models that will be used will be a system of equations to link three things: the dose of a medicine administered, its concentration in the body, and the effect. Research over the last 10-15 years has meant we now understand what kinds of models to use to link dose and concentration in children. This project will seek to improve our methods for linking concentration with effect. This will be done by designing new types of laboratory experiment and using new statistical methods. Three different scenarios have been identified where improvements in modelling the link between concentration and effect are required:1. Situations where the effect is difficult or impossible to measure. An example of this is in bacterial infections, where we know the child is ill, but it is very difficult to measure the bacterial count. This problem will be addressed by doing laboratory experiments to mimic the site of bacterial infection, and then using mathematical and statistical modelling to link the results of these experiments with dose-concentration results obtained in clinical studies of children.2. The effect is measured as a score or number of different responses. An example of this is in intensive care where the level of sedation is measured by combining scores for things like breathing rate, alertness, and tension in the face. A statistical technique called Item Response Theory will be used to model these scores and link them to the dose and concentration of sedative drugs.3. Medicines are affecting a marker that we can readily measure. An example of this is the concentration of immune cells in the blood after a transplant where children receive drugs called immunosuppressants. Mathematical models that have parameters relating to birth and death rates of these cells will be used to understand the optimum immunosuppressant dose and how these rates change with age

该项目将改进数学和统计建模中使用的方法，以帮助我们最好地利用儿童药物。数学模型使用方程来描述实验中观察到的结果。例如，假设我们在几个时间点测量患有胸部感染的儿童肺部的细菌数量。一个简单的模型是由方程给出的直线：y = mx + c，其中y是每个x值（测量的时间）的细菌数量，m是直线的斜率，c是时间为0时的细菌数量。在这种情况下，m和c是模型参数，我们从观测中估计它们的值。有了这些m和c的值，我们可以用这个模型来预测在实验中没有测量到的x（时间点）值下的细菌数量。我们还可以通过观察m和c的值来了解系统，例如，m告诉我们细菌数量随时间减少的速度。如果我们从接受不同剂量或类型抗生素的儿童身上收集这样的信息，那么我们就可以看到抗生素的剂量和类型对细菌数量减少的速度有什么影响。因为每个孩子都是一个个体，所以m和c的值在不同的孩子中可能是不同的。此外，我们的数学模型是系统的简单表示。由于这些原因，我们在模型中添加了统计部分。这解释了个体之间的差异，以及模型中无法解释的差异。通过添加这个统计部分，我们可以判断我们应该对模型的预测有多大的信心。使用的模型将比上面的例子更复杂，这种技术被称为非线性混合效果建模。数学和统计建模很重要的原因是，与传统的对照试验相比，需要的患者更少，而传统的对照试验涉及在大量受试者中比较结果。通过对少数儿童的深入研究，我们可以更有效地制定出最佳的治疗方案。将使用的模型将是一个连接三件事的方程式系统：药物剂量，体内浓度和效果。过去10-15年的研究意味着我们现在了解了使用什么样的模型来将儿童的剂量和浓度联系起来。这个项目将设法改进我们把集中与效果联系起来的方法。这将通过设计新型的实验室实验和使用新的统计方法来实现。已经确定了三种不同的情景，其中需要改进浓度与效应之间联系的建模：影响难以或不可能测量的情况。这方面的一个例子是细菌感染，我们知道孩子生病了，但很难测量细菌数量。这个问题将通过实验室实验来模拟细菌感染部位，然后使用数学和统计模型将这些实验结果与儿童临床研究中获得的剂量-浓度结果联系起来来解决。效果是通过得分或不同回答的数量来衡量的。这方面的一个例子是在重症监护中，镇静水平是通过结合呼吸频率、警觉性和面部紧张等评分来衡量的。一种叫做项目反应理论的统计技术将被用来模拟这些分数，并将它们与镇静药物的剂量和浓度联系起来。药物正在影响一个我们可以轻易测量的标记。这方面的一个例子是，儿童接受免疫抑制剂药物后，移植后血液中免疫细胞的浓度。具有与这些细胞的出生和死亡率有关的参数的数学模型将用于了解最佳免疫抑制剂剂量以及这些剂量如何随年龄变化