### 统计代写|生物统计学作业代写Biostatistics代考|Mantel–Haenszel Method

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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|生物统计学作业代写Biostatistics代考|Mantel–Haenszel Method

In most investigations we are concerned with one primary outcome, such as a disease, and are focusing on one primary (risk) factor, such as an exposure with a possible harmful effect. There are situations, however, where an investigator may want to adjust for a confounder that could influence the outcome of a statistical analysis. A confounder, or confounding variable, is a variable that may be associated with either the disease or exposure or both. For example, in Example 1.2, a case-control study was undertaken to investigate the relationship between lung cancer and employment in shipyards during World War II among male residents of coastal Georgia. In this case, smoking is a possible counfounder; it has been found to be associated with lung cancer and it may be associated with employment because construction workers are likely to be smokers. Specifically, we want to know:

(a) Among smokers, whether or not shipbuilding and lung cancer are related
(b) Among nonsmokers, whether or not shipbuilding and lung cancer are related

In fact, the original data were tabulated separately for three smoking levels (nonsmoking, moderate smoking, and heavy smoking); in Example 1.2, the last two tables were combined and presented together for simplicity. Assuming that the confounder, smoking, is not an effect modifier (i.e., smoking does not alter the relationship between lung cancer and shipbuilding), however, we do not want to reach separate conclusions, one at each level of smoking. In those cases, we want to pool data for a combined decision. When both the disease and the exposure are binary, a popular method used to achieve this task is the Mantel-Haenszel method. This method provides one single estimate for the common odds ratio and can be summarized as follows:

1. We form $2 \times 2$ tables, one at each level of the confounder.
2. At a level of the confounder, we have the data listed in Table 1.17.
Since we assume that the confounder is not an effect modifier, the odds ratio is constant across its levels. The odds ratio at each level is estimated by $a d / b c$; the Mantel-Haenszel procedure pools data across levels of the confounder to obtain a combined estimate (some kind of weighted average of level-specific odds ratios):
$$\mathrm{OR}_{\mathrm{MH}}=\frac{\sum a d / n}{\sum b c / n}$$

## 统计代写|生物统计学作业代写Biostatistics代考|Standardized Mortality Ratio

In a cohort study, the follow-up death rates are calculated and used to describe the mortality experience of the cohort under investigation. However, the observed mortality of the cohort is often compared with that expected from the death rates of the national population (used as standard or baseline). The basis of this method is the comparison of the observed number of deaths, $d$, from the cohort with the mortality that would have been expected if the group had experienced death rates similar to those of the national population of which the cohort is a part. Let $e$ denote the expected number of deaths; then the comparison is based on the following ratio, called the standardized mortality ratio:
$$\mathrm{SMR}=\frac{d}{e}$$
The expected number of deaths is calculated using published national life tables, and the calculation can be approximated as follows:
$$e \simeq \lambda T$$
where $T$ is the total follow-up time (person-years) from the cohort and $\lambda$ the annual death rate (per person) from the referenced population. Of course, the annual death rate of the referenced population changes with age. Therefore, what we actually do in research is more complicated, although based on the same idea. First, we subdivide the cohort into many age groups, then calculate the product $\lambda T$ for each age group using the correct age-specific rate for that group, and add up the results.

Example 1.20 Some 7000 British workers exposed to vinyl chloride monomer were followed for several years to determine whether their mortality experience differed from those of the general population. The data in Table $1.22$ are for deaths from cancers and are tabulated separately for four groups based on years since entering the industry. This data display shows some interesting features:

1. For the group with $1-4$ years since entering the industry, we have a death rate that is substantially less than that of the general population

$(\mathrm{SMR}=0.445$ or $44.5 \%)$. This phenomenon, known as the healthy worker effect, is probably a consequence of a selection factor whereby workers are necessarily in better health (than people in the general population) at the time of their entry into the workforce.

1. We see an attenuation of the healthy worker effect (i.e., a decreasing trend) with the passage of time, so that the cancer death rates show a slight excess after 15 years. (Vinyl chloride exposures are known to induce a rare form of liver cancer and to increase rates of brain cancer.)
Taking the ratio of two standardized mortality ratios is another way of expressing relative risk. For example, the relative risk of the $15+$ years group is $1.58$ times the risk of the risk of the $5-9$ years group, since the ratio of the two corresponding mortality ratios is
$$\frac{111.8}{70.6}=1.58$$
Similarly, the risk of the $15+$ years group is $2.51$ times the risk of the $1-4$ years group because the ratio of the two corresponding mortality ratios is
$$\frac{111.8}{44.5}=2.51$$

## 统计代写|生物统计学作业代写Biostatistics代考|NOTES ON COMPUTATIONS

Much of this book is concerned with arithmetic procedures for data analysis, some with rather complicated formulas. In many biomedical investigations, particularly those involving large quantities of data, the analysis (e.g., regression analysis of Chapter 8) gives rise to difficulties in computational implementation. In these investigations it will be necessary to use statistical software specially designed to do these jobs. Most of the calculations described in this book can be carried out readily using statistical packages, and any student or practitioner of data analysis will find the use of such packages essential.

Methods of survival analysis (first half of Chapter 11), for example, and nonparametric methods (Sections $2.4$ and 7.4), and of multiple regression analysis (Section 8.2) may best be handled by a specialized package such as SAS; in these sections are included in our examples where they were used. However, students and investigators contemplating use of one of these commercial programs should read the specifications for each program before choosing the options necessary or suitable for any particular procedure. But these sections are exceptions, many calculations described in this book can be carried out readily using Microsoft’s Excel, popular software available in every personal computer. Notes on the use of Excel are included in separate sections at the end of each chapter.

A worksheet or spreadsheet is a (blank) sheet where you do your work. An Excel file holds a stack of worksheets in a workbook. You can name a sheet, put data on it and save; later, open and use it. You can move or size your windows by dragging the borders. You can also scroll up and down, or left and right, through an Excel worksheet using the scroll bars on the right side and at the bottom.

An Excel worksheet consists of grid lines forming columns and rows; columns are lettered and rows are numbered. The intersection of each column and row is a box called a cell. Every cell has an address, also called a cell reference; to refer to a cell, enter the column letter followed by the row number. For example, the intersection of column $C$ and row 3 is cell C3. Cells hold numbers, text, or formulas. To refer to a range of cells, enter the cell in the upper left corner of the range followed by a colon (:) and then the lower right corner of the range. For example, $\mathrm{A} 1: \mathrm{B} 20$ refers to the first 20 rows in both columns $\mathrm{A}$ and $B$.

## 统计代写|生物统计学作业代写Biostatistics代考|Mantel–Haenszel Method

(a) 在吸烟者中，造船业与肺癌是否相关
(b) 在不吸烟者中，造船业与肺癌是否相关

1. 我们形成2×2表，在混杂因素的每个级别都有一个。
2. 在混杂因素的层面，我们有表 1.17 中列出的数据。
由于我们假设混杂因素不是效应修饰符，因此优势比在其水平上是恒定的。每个级别的优势比估计为一种d/bC; Mantel-Haenszel 程序汇集了混杂因素水平的数据以获得组合估计（某种特定水平优势比的加权平均值）：
这R米H=∑一种d/n∑bC/n

## 统计代写|生物统计学作业代写Biostatistics代考|Standardized Mortality Ratio

1. 对于组1−4进入这个行业多年以来，我们的死亡率远低于普通人群

(小号米R=0.445或者44.5%). 这种被称为健康工人效应的现象可能是一个选择因素的结果，即工人在进入劳动力市场时（比一般人群中的人）的健康状况必然更好。

1. 随着时间的推移，我们看到了健康工人效应的衰减（即下降趋势），因此癌症死亡率在 15 年后略有增加。（已知氯乙烯暴露会诱发一种罕见的肝癌并增加脑癌的发病率。）
取两个标准化死亡率的比率是表示相对风险的另一种方式。例如，相对风险15+年组是1.58乘以风险的风险5−9年组，因为两个相应的死亡率之比为
111.870.6=1.58
同样，风险15+年组是2.51倍的风险1−4年组，因为两个相应的死亡率之比为
111.844.5=2.51

## 统计代写|生物统计学作业代写Biostatistics代考|NOTES ON COMPUTATIONS

Excel 工作表由形成列和行的网格线组成；列有字母，行有编号。每列和每行的交集是一个称为单元格的框。每个单元格都有一个地址，也称为单元格引用；要引用单元格，请输入列字母，后跟行号。例如，列的交集C第 3 行是单元格 C3。单元格包含数字、文本或公式。要引用单元格区域，请在区域左上角输入单元格，后跟冒号 (:)，然后在区域右下角输入。例如，一种1:乙20指两列中的前 20 行一种和乙.

## 广义线性模型代考

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## MATLAB代写

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