Chapter 1

Biostatistics 101

IN THIS CHAPTER

Getting up to speed on the prerequisites for biostatistics

Understanding the human research environment

Surveying the specific procedures used to analyze biological data

Estimating how many participants you need

Working with distributions

Biostatistics deals with the design and execution of scientific studies involving biology, the acquisition and analysis of data from those studies, and the interpretation and presentation of the results of those analyses. This book is meant to be a useful and easy-to-understand companion to the more formal textbooks used in graduate-level biostatistics courses. Because most of these courses teach how to analyze data from epidemiologic studies and clinical trials, this book focuses on that as well. In this first chapter, we introduce you to the fundamentals of biostatistics.

Brushing Up on Math and Stats Basics

Chapters 2 and 3 are designed to bring you up to speed on the basic math and statistical background that’s needed to understand biostatistics and give you supplementary information or context that you may find useful while reading the rest of this book.

• Many people feel unsure of themselves when it comes to understanding mathematical formulas and equations. Although this book contains fewer formulas than many statistics books, we include them when they help illustrate a concept or describe a calculation that’s simple enough to do by hand. But if you’re a real mathophobe, you probably dread looking at any chapter that has a math expression anywhere in it. That’s why we include Chapter 2, “Overcoming Mathophobia” to show you how to read and understand the basic mathematical notation we use in this book. We cover everything from basic mathematical operations to functions and beyond.
• If you’re in a graduate-level biostatistics course, you’ve probably already taken one or two introductory statistics courses. But that may have been a while ago, and you may feel unsure of your knowledge of the basic statistical concepts. Or you may have little or no formal statistical training but now find yourself in a work situation where you interact with clinical researchers, participate in the design of research projects, or work with the results from biological research. If so, read Chapter 3, which provides an overview of the fundamental concepts and terminology of statistics. There, you get the scoop on topics such as probability, randomness, populations, samples, statistical inference, accuracy, precision, hypothesis testing, nonparametric statistics, and simulation techniques.

Doing Calculations with the Greatest of Ease

For instructional purposes, some chapters in this book include step-by-step instructions for performing statistical tests and analyses by hand. We include such instruction only to illustrate the concepts that are involved in the procedure or to demonstrate calculations that are simple to do manually.

However, we demonstrate many of the statistical functions we talk about in this book using R, which is a free, open-source software package. If you are in a class and assigned a particular software package to use, you will have to use that software for the course, which may be commercial software associated with a fee. However, if you are learning on your own, you may choose to use open-source software, which is free. Chapter 4 provides guidance on both commercial and free software.

Concentrating on Epidemiologic Research

This book covers topics that are applicable to all areas of biostatistics, concentrating on methods that are especially relevant to epidemiologic research — studies involving people. This includes clinical trials, which are experiments done to develop therapeutic interventions such as drugs. Because policy in healthcare is often based on the results from clinical trials, if you make mistake analyzing clinical trial data, it can have disastrous and wide-ranging human and financial consequences. Even if you don’t expect to ever work in a domain that relies heavily on clinical trials (such as drug development research), ensuring that you have a working knowledge of how to manage the statistical issues seen in clinical trials is critical.

Three chapters discuss clinical trials:

• Chapter 5 describes the statistical aspects of clinical trials as three phases. First, it covers the design phase, where a study protocol is written. Next, it describes the execution phase, where data are collected, and efforts are made to prevent invalid or missing data. In the final phase, data from the study are analyzed and interpreted to answer the hypotheses.
• Chapter 7 presents epidemiologic study designs and explains the importance of the clinical trial as a study design.
• Chapter 20 explains the role well-designed clinical trials play in accruing evidence of causal inference in biostatistics.

Much of the work in biostatistics is using data from samples to make inferences about the background population from which the sample was drawn. Now that we have large databases, it is possible to easily take samples of data. Chapter 6 provides guidance on different ways to take samples of larger populations so you can make valid population-based estimates from these samples. Sampling is especially important when doing observational studies. While clinical trials covered are experiments, where participants are assigned interventions, in observational studies, participants are merely observed, with data collected and statistics performed to make inferences. Chapter 7 describes these observational study designs, and the statistical issues that need to be considered when analyzing data arising from such studies.

Data used in biostatistics are often collected in online databases, but some data are still collected on paper. Regardless of the source of the data, they must be put into electronic format and arranged in a certain way to be able to be analyzed using statistical software. Chapter 8 is devoted to describing how to get your data into the computer and arrange it properly so it can be analyzed correctly. It also describes how to collect and validate your data. Then in Chapter 9, we show you how to summarize each type of data and display it graphically. We explain how to make bar charts, box-and-whiskers charts, and more.

Drawing Conclusions from Your Data

Most statistical analysis involves inferring, or drawing conclusions about the population at large based on your observations of a sample drawn from that population. The theory of statistical inference is often divided into two broad sub-theories: estimation theory and decision theory.

Statistical estimation theory

Chapter 10 deals with statistical estimation theory, which addresses the question of how accurately and precisely you can estimate a population parameter from the values you observe in your sample. For example, you may want to estimate the mean blood hemoglobin concentration in adults with Type II diabetes, or the true correlation coefficient between body weight and height in certain pediatric populations. Chapter 10 describes how to estimate these parameters by constructing a confidence interval around your estimate. The confidence interval is the range that is likely to include the true population parameter, which provides an idea of the precision of your estimate.

Statistical decision theory

Much of the rest of this book deals with statistical decision theory, which is how to decide whether some effect you’ve observed in your data reflects a real difference or association in the background population or is merely the result of random fluctuations in your data or sampling. If you measure the mean blood hemoglobin concentration in two different samples of adults with Type II diabetes, you will likely get a different number. But does this difference reflect a real difference between the groups in terms of blood hemoglobin concentration? Or is this difference a result of random fluctuations? Statistical decision theory helps you decide.

In Part 4, we cover statistical decision theory in terms of comparing means and proportions between groups, as well as understanding the relationship between two or more variables.

Comparing groups

In Part 4, we show you different ways to compare groups statistically.

• In Chapter 11, you see how to compare average values between two or more groups by using t tests and ANOVAs. We also describe their nonparametric counterparts that can be used with skewed or other non-normally distributed data.
• Chapter 12 shows how to compare proportions between two or more groups, such as the proportions of patients responding to two different drugs, using the chi-square and Fisher Exact tests on cross-tabulated (cross-tab) data.
• Chapter 13 focuses on one specific kind of cross-tab called the fourfold table, which has exactly two rows and two columns. Because the fourfold table provides the opportunity for some particularly insightful calculations, it’s worth a chapter of its own.
• In Chapter 14, you discover how the terminology used in epidemiologic studies is applied to...