### 统计代写|广义线性模型代写generalized linear model代考|STAT7608

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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|Superiority and non-inferiority

In all the application of the generalized linear mixed models and their related models, we mainly use the statistical analysis system called SAS. In any outputs of SAS programs you can see several $p$-values (two-tailed) for fixedeffects parameters of interest. It should be noted, however, that any $p$-value (two-tailed) for the parameter $\beta_3\left(=\mu_2-\mu_1\right)$ of the primary interest shown in the SAS outputs is implicitly the result of a test for a set of hypotheses
$H_0: \beta_3=0$, versus $H_1: \beta_3 \neq 0$,
which is also called a test for superiority. In more detail, the definition of superiority hypotheses is as follows:

Test for superiority
If a negative $\beta_3$ indicates benefits, the superiority hypotheses are interpreted as
$$H_0: \beta_3 \geq 0 \text {, versus } H_1: \beta_3<0 \text {. }$$ If a positive $\beta_3$ indicates benefits, then they are $$H_0: \beta_3 \leq 0 \text {, versus } H_1: \beta_3>0 \text {. }$$
These hypotheses imply that investigators are interested in establishing whether there is evidence of a statistical difference in the comparison of interest between two treatment groups. However, it is debatable whether the terminology superiority can be used or not in this situation. Although the set of hypotheses defined in (1.16) was adopted as those for superiority tests in regulatory guidelines such as FDA draft guidance (2010), I do not think this is appropriate.

The non-inferiority hypotheses of the new treatment over the control treatment, on the other hand, take the following form:
Test for non-inferiority
If a positive $\beta_3$ indicates benefits, the hypotheses are
$$H_0: \beta_3 \leq-\Delta \text {, versus } H_1: \beta_3>-\Delta \text {, }$$
where $\Delta(>0)$ denotes the so-called non-inferiority margin. If a negative $\beta_3$ indicates benefits, the hypotheses should be
$$H_0: \beta_3 \geq \Delta \text {, versus } H_1: \beta_3<\Delta \text {. }$$

## 统计代写|广义线性模型代写generalized linear model代考|Analysis of variance model

Consider a clinical trial or an animal experiment to evaluate a treatment effect, such as data shown in Table 2.1, where subjects are randomly assigned to one treatment group, and measurements are made at equally spaced times on each subject. Then, the basic design will be the following:

1. Purpose: Comparison of $G$ treatment groups including the control group.
2. Trial design: Parallel group randomized controlled trial and suppose that $n_k$ subjects are allocated to treatment group $k(=1,2, \ldots, G), n_1+$ $n_2+\cdots n_G-N$, where the first treatment group $(k-1)$ is defined as the control group.
1. Repeated Measure Design: Basic 1:T repeated measures design described in Chapter $1 .$

A typical statistical model or analysis of variance model for the basic design will be
\begin{aligned} \text { Response }=& \text { Grand mean }+\text { Treatment group }+\text { time }+\ &+\text { treatment group } \times \text { time }+\text { error. } \end{aligned}
However, the prerequisite for the analysis of variance model is the homogeneity assumption for the subject-specific response profile over time within each treatment group so that the mean response profile within each treatment group is meaningful and thus the treatment effect can be evaluated by the difference in mean response profiles. If the subject by time interaction within each treatment group is not negligible, the mean response profile within each group could be inappropriate measures for treatment effect. To deal with this type of heterogeneity, see Chapter $11 .$

In this chapter, we shall use the notation “triply subscripted array”, which is frequently used in analysis of variance models, which is different from the repeated measures design described in Chapter 1 . For the $i$ th subject $\left(i=1, \ldots, n_k\right)$ nested in each treatment group $k$, let $y_{k i j}$ denote the primary response variable at the $j$ th measurement time $t_j$.

## 统计代写|广义线性模型代写generalized linear model代考|Superiority and non-inferiority

$$H_0: \beta_3 \geq 0, \text { versus } H_1: \beta_3<0 .$$ 如果一个阳性 $\beta_3$ 表示好处，那么它们是 $$H_0: \beta_3 \leq 0, \text { versus } H_1: \beta_3>0 .$$

$\beta_3$ 表示收益，假设是
$$H_0: \beta_3 \leq-\Delta, \text { versus } H_1: \beta_3>-\Delta,$$

$$H_0: \beta_3 \geq \Delta, \text { versus } H_1: \beta_3<\Delta$$

## 统计代写|广义线性模型代写generalized linear model代考|Analysis of variance model

1. 目的: 比较 $G$ 治疗组包括对照组。
2. 试验设计：平行组随机对照试验，假设 $n_k$ 受试者被分配到治疗组 $k(=1,2, \ldots, G), n_1+$ $n_2+\cdots n_G-N$ ，其中第一个治疗组 $(k-1)$ 定义为对照组。
3. 重复测量设计：基本 1:T 重复测量设计在章节中描述 1 .
基本设计的典型统计模型或方差分析模型将是
Response $=$ Grand mean $+$ Treatment group $+$ time $+\quad+$ treatment group $\times$ time $+$ err
然而，方差分析模型的先决条件是每个治疗组内受试者特异性反应曲线随时间的同质性假设，因此每个治疗组内的 平均反应曲线是有意义的，因此可以通过差异评估治疗效果在平均响应配置文件中。如果每个治疗组内的受试者时 间交互作用不可忽略，则每组内的平均反应曲线可能是治疗效果的不适当测量。要处理这种类型的异质性，请参阅 第11.
在本章中，我们将使用方差分析模型中经常使用的符号“三下标数组”，这与第 1 章中描述的重复测量设计不同。为 了 $i$ 主题 $\left(i=1, \ldots, n_k\right)$ 嵌套在每个治疗组中 $k$ ，让 $y_{k i j}$ 表示主要响应变量 $j$ 测量时间 $t_j$.

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## MATLAB代写

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