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，以帮助我们充分利用儿童药物。数学建模使用方程来描述实验过程中的观察结果。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以下方程给出的直线：y = mx + c，其中 y 是每个 x 值（进行测量的时间）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，我们根据观察估计它们的值。有了 m 和 c 的这些值，我们可以使用模型来预测在我们的实验中未测量的 x 值（时间点）时的细菌数量。我们还可以查看 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那里收集这样的信息，那么我们就可以了解抗生素剂量和类型对细菌数量减少速度的影响。因为每个孩子都是一个个体，所以不同孩子的m和c值可能不同。我们的数学模型也是系统的简单表示。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变异性，以及模型中无法解释的变异性。通过添加这个统计部分，我们可以判断我们对模型的预测应该有多大的信心。使用的模型将比上面的示例更复杂，该技术称为非线性混合效应建模。数学和统计建模之所以重要，是因为与传统对照试验相比，需要更少的患者，传统对照试验涉及比较大组之间的结果的科目。通过深入研究少数儿童，我们可以更有效地制定最佳治疗方案。将使用的模型将是一个将三件事联系起来的方程组：给药剂量、药物在体内的浓度以及效果。过去 10-15 年的研究意味着我们现在了解了可以使用哪些模型来将儿童的剂量和浓度联系起来。该项目将寻求改进我们将注意力与效果联系起来的方法。这将通过设计新型实验室实验和使用新的统计方法来完成。已经确定了三种不同的场景，需要改进浓度和效果之间联系的建模：1。影响难以或无法衡量的情况。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。这个问题将通过进行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的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。2．效果以不同反应的分数或数量来衡量。一个例子是在重症监护中，镇静水平是通过综合呼吸频率、警觉性和面部紧张度等指标来衡量的。一种称为项目反应理论的统计技术将用于对这些分数进行建模，并将它们与镇静药物的剂量和浓度联系起来。3．药物正在影响我们可以轻松测量的标志物。一个例子是移植后血液中免疫细胞的浓度，其中儿童接受称为免疫抑制剂的药物。具有与这些细胞的出生率和死亡率相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比率如何随年龄变化