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What is Biostatistics?

CONTENTS

• 1.1 Overview
• 1.2 Some Statistical Terminology
  • 1.2.1 Population and Sample
  • 1.2.2 Homogeneity and Variation
  • 1.2.3 Parameter and Statistic
  • 1.2.4 Types of Data
  • 1.2.5 Error
• 1.3 Workflow of Applied Statistics
• 1.4 Statistics and Its Related Disciplines
• 1.5 Statistical Thinking
• 1.6 Summary
• 1.7 Exercises

1.1 Overview

Data are present everywhere in our lives, and almost all types of scientific research have to deal with the collection, description, or analysis of data. This makes statistics one of the most powerful methodologies across all disciplines for exploring the unknown world. Statistics is a discipline on its own and has a wide spectrum of theories, methods, and applications. A prerequisite for discussing the theory and application of statistics is the definition and statement of its objectives. According to Merriam-Webster's Collegiate Dictionary, statistics is "a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data." According to the Random House College Dictionary, it is "the science that deals with the collection, classification, analysis, and interpretation of information or data." According to The New Oxford English-Chinese Dictionary, it is "the practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample." Although there are some differences among these definitions, each definition implies that statistics is a science of data and uses the theory of mathematical statistics to make inferences.

The application of statistical theories and methods to medical research fields is termed "medical statistics," or more broadly, biostatistics when applied to life sciences.

There are two branches of biostatistics based on its functions: (i) statistical description is concerned with the organization, summarization, and description of data; and (ii) statistical inference is concerned with the use of sample data to make inferences about the characteristics of a larger set of data. This division of descriptive and inferential statistics helps us to establish a progressive learning framework for statistics. However, this division is not always necessary in scientific activities where the two branches complement each other in deepening our knowledge of the real world.

We briefly review the development of biostatistics. In London in 1603, the Bills of Mortality began to be published weekly, which is generally considered to mark the beginning of biostatistics. Since then, related theories have continued to emerge, and the early twentieth century ushered in the peak of development of biostatistics. Several pioneers played a crucial role in the development of the theoretical framework and applications of biostatistics. G.J. Mendel (1822-1884), the father of modern genetics, used probability rules to discover the basic laws of biogenetics in the 1860s. He is considered to be one of the first to apply mathematical methods to biology. K. Pearson (1857-1936), the founding father of modern statistics, established the world's first department of statistics at University College London in 1911, and developed several key statistical theories (e.g., measure of correlation and ?2 distribution). W.S. Gosset (1876-1937) proposed the t distribution and t-test in 1908, which laid the foundation for the sampling distribution of the sample mean, and signified the establishment of small sample theory and methodology. R.A. Fisher (1890-1962) developed statistical significance tests, and various sampling distributions, and established the experimental design method and related statistical analysis technique. These were collected in Design of Experiments, which was first published in 1935. With the efforts of these pioneers and other statisticians, after hundreds of years, a complete theoretical system of biostatistics had formed.

At the present time, the development of biostatistics is being driven by the unprecedented and still growing range of life science applications using advances in computing power and computer technology, and new formats of data that continue to emerge. Despite this, the ideas of basic statistics have not changed: to make an inference about a population based on information contained in a sample from that population and to provide an associated measure of goodness for the inference.

1.2 Some Statistical Terminology

In this text, we aim to explain basic statistical methods commonly applied in biomedical research. Before this, we provide an overview of several statistical terms, which are the premise for further learning.

1.2.1 Population and Sample

A population (statistical population or target population) is a certain or some characteristics of study subjects that are our target of interest. Population is usually denoted by X (also called random variable), and can be viewed as a dataset. The basic unit that constitutes the population is called the individual .

The dataset that defines a population is typically large or conceptual. The former suggests a finite population because it has a finite number of individuals regardless of how large it is. For example, the dataset of the heights of all the college freshman boys in Beijing in 2020 is a finite population (though very large). When the dataset only exists conceptually, we call it an infinite population, for example, the weights of infants and the antihypertensive treatment effects of a certain drug. The sampling theory and statistical inference principle introduced in this text are based on an infinite population.

A sample, denoted by X1, X2,., Xn (n is the sample size), is a subset of data selected from a population. The purpose of obtaining a sample is to infer about the characteristics of its underlying unknown population.

The process of drawing a sample from a population is termed sampling. In practice, depending on the research objectives and feasibility, samples can be obtained using random or non-random sampling. A random sample is obtained through probability sampling. In this text, we generally assume the use of a simple random sample in which each individual in the population has an equal chance of being sampled. Non-random sampling relies on the subjective judgment of the researcher and is beyond the scope of this text.

Note the following: (i) The concept of population is different in biomedical research and statistical terminology. In biomedical research, the term "study population" (or study subject) typically refers to a group of humans or other species of organism, whereas the characteristics of the study subjects are the population we are interested in statistics. For example, in a study of blood glucose concentrations among 3-year-old children, all children of that age are regarded as the study population. However, from a statistical point of view, all blood glucose concentrations in children of that age constitute the population of interest. (ii) Although the dataset of a population is typically large, the essential difference between the population and the sample is not the amount of data we have, but the objective of the research. If the objective is to provide a description only, then the data we have can be regarded as a population, regardless of how small it is, whereas if the objective is to draw an inference, then we need to clarify what population we are interested in, and consider how to obtain a representative sample, or how good the sample at hand is. The representativeness of the sample of the population is a very important basis for a reasonable inference.

1.2.2 Homogeneity and Variation

In statistics, homogeneity means the similarity among individuals within a population. In fact, without homogeneity, we can rarely define a population. The individual differences in a homogenous population are termed variation.

Example 1.1 Survey of the height of college freshman boys in Beijing in 2020. Homogeneity: College freshman boys in Beijing in 2020. Variation: Individual differences in height.

Example 1.2 Study of the antihypertensive treatment effects of a drug. Homogeneity: Hypertensive patients taking this drug. Variation: Individual differences in the treatment effects.

From Examples 1.1 and 1.2, we can see that homogeneity refers to similarities in the nature, condition, or background of individuals in a population. The mission of statistics can be interpreted as describing the features of a homogenous population and identifying the heterogeneity of different populations. Variation is an inherent attribute of life sciences, and biomedical researchers should learn to use statistical methods to reveal the laws of biological phenomena in the context of variation.

1.2.3 Parameter and Statistic

A descriptive measure of the characteristics calculated on a population is called a population parameter, or simply, a parameter, generally denoted by the Greek letter ?. For example, in the survey of the height of freshman boys, the population mean...