### 统计代写|广义线性模型代写generalized linear model代考|MAST30025

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|广义线性模型代写generalized linear model代考|Repeated measures design

Let $y_{i j}$ denote the primary response variable for the $i$ th subject at the $j$ th time $t_{i j}$. An ordinary situation of repeated measures design adopted in RCTs or animal experiments is when the primary response variable is measured once at baseline period (before randomization) and $T$ times during the treatment period (after randomization) where measurements are scheduled to be made at the same times for all subjects $t_{i j}=t_j$ in the sampling design. We call this design the Basic 1: $T$ repeated measures design throughout the book, where the response profile vector $\boldsymbol{y}i$ for the $i$ th subject is expressed as $$\boldsymbol{y}_i=(\underbrace{y{i 0}}{\text {baseline data }}, \underbrace{y{i 1}, \ldots, y_{i T}}_{\text {data after randomization }})^t .$$
In exploratory trials in the early phases of drug development, statistical analyses of interest will be to estimate the time-dependent mean profile for each treatment group and to test whether there is any treatment-by-time interaction. In confirmatory trials in the later phases of drug development, on the other hand, we need a simple and clinically meaningful effect size of the new treatment. So, many RCTs tend to try to narrow the evaluation period down to one time point (ex., the last $T$ th measurement), leading to the so-called pre-post design or the 1:1 design:
$$\boldsymbol{y}i=(\underbrace{y{i 0}}{\text {baseline data }}, y{i 1}, \ldots, y_{i(T-1)}, \underbrace{y_{i T}}{\text {data to be analyzed }})^t .$$ Some other RCTs define a summary statistic such as the mean $\bar{y}_i$ of repeated measures during the evaluation period (ex., mean of $y{i(T-1)}$ and $y_{i T}$ ), which also leads to a $1: 1$ design. In these simple $1: 1$ designs, traditional analysis methods such as analysis of covariance (ANCOVA) have been used to analyze data where the baseline measurement is used as a covariate. In the 1:1 design, ANCOVA is preferred over the mixed-effects model when the covariance matrix over time is homogeneous across groups (Winkens et al., 2007; Crager, 1987; Chen, 2006) although the difference is small in practice. However, ANCOVA cannot be applied when the covariance matrices over time are heterogeneous across groups. Since the ANCOVA-type method is easily influenced by missing data, some kind of imputation method such as LOCF (last observation carried forward) are inevitably needed for ITT (intention-to-treat) analysis (Winkens et al., 2007; Crager, 1987; Chen, 2006).

## 统计代写|广义线性模型代写generalized linear model代考|Generalized linear mixed models

In this book, we shall consider mainly a parallel group randomized controlled trial or an animal experiment of two treatment groups where the primary response variable is either a continuous, count or binary response and that the first $n_1$ subjects belong to the control treatment (group 1) and the latter $n_2$ subjects to the new treatment (group 2). Needless to say, the following arguments are applicable when multiple treatment groups are compared. To a $S: T$ repeated measures design, we shall introduce here the following practical and important three types of statistical analysis plans or statistical models that you frequently encounter in many randomized controlled trials:
Model for the treatment effect at each scheduled visit
$\diamond$ Model for the average treatment effect
$\diamond$ Model for the treatment by linear time interaction
All of these models are based on the repeated measures models or generalized linear mixed models (GLMM), which are also called generalized linear mixedeffects models

## 统计代写|广义线性模型代写generalized linear model代考|Repeated measures design

$$\boldsymbol{y}i=(\underbrace{y i 0}{\text {data after randomization }} \text { baseline data }, \underbrace{t} .$$

$$\boldsymbol{y} i=(\underbrace{y i 0} \text { baseline data }, y i 1, \ldots, y_{i(T-1)}, \underbrace{y_{i T}} \text { data to be analyzed })^t .$$

⋄平均治疗效果模型
⋄线性时间交互作用治疗模型

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。