Biostatistics for Epidemiologists

Anders Ahlbom

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9780873719124
• eBook ISBN: 9781351463669
• Edition: 1
• Topic: Medicine
• Subtopic: Probability & Statistics

Biostatistics for Epidemiologists is a unique book that provides a collection of methods that can be used to analyze data in most epidemiological studies. It examines the theoretical background of the methods described and discusses general principles that apply to the analysis of epidemiological data. Specific topics addressed include statistical interference in epidemiological research, important methods used for analyzing epidemiological data, multivariate models, dose-response analysis, analysis of the interaction between causes of disease, meta-analysis, and computer programs. Biostatistics for Epidemiologists will be a useful guide for all epidemiologists and public health professionals who rely on biostatistical data in their work.

Chapter 1

INTRODUCTION

“Vital statistics and their analysis are essential features of public health work, to define its problems, to determine, as far as possible, cause and effect, and to measure the success or failure of the steps taken to deal with such problems. They are fundamental to the study of epidemiology.”

Hill AB: Principles of Medical Statistics. The Lancet Limited, 1967 (First edition 1937).

Epidemiology is the study of the occurrence of disease. The occurrence of disease is studied in relation to factors relating to the individual, his environment and his lifestyle with the aim of establishing the causes of disease. The interpretation of an epidemiological study must always take the validity and the precision of the study into consideration. How one assesses the validity of an epidemiological study is discussed in books on the methodology of epidemiology (see the reference section at the end of this book), while the issue of precision is addressed in books on biostatistics. Biostatistics also includes methods which enable one to take systematic errors, such as the influence of other factors, into account when one is analyzing data, as well as methods for studying the effects of the interaction of risk factors.

The field of biostatistics covers the statistical methods used in biological and medical research. This is a very wide field and strictly speaking does not exclude any area of statistical methodology. In this book we limit ourselves to methods used in epidemiology. Thus the methods are discussed in an epidemiological context and the examples used are from the field of epidemiology. This is not to say that these methods do not have applications in other fields, such as in survival analysis, evaluation of clinical trials or studies of health care use.

The aims of this book are threefold. The first is to provide a collection of methods which can be used to analyze data in most epidemiologic studies. In other words, one should be able to use the book as a statistics handbook or maybe “cookbook” for epidemiology. The second aim is to give an understanding of the theoretical background to the methods described here. With this we hope to demonstrate what the methods can actually achieve and the assumptions upon which they are based. For this reason, the book contains a number of derivations of formulae or, where this would carry too far, some principles as to how derivations could be carried out. The third aim of the book is to discuss some general principles which apply to the analysis of epidemiological data and how the precision of an epidemiologic study can best be described. One example of this is the discussion of the role of significance testing.

The book consists of three parts. The first is preparatory and features a summary of those aspects of the theory of probability which are of importance for the statistical theory which is then taken up. This part of the book also contains a discussion about statistical inference in general and a discussion about statistical inference in epidemiological research in particular. The second part of the book describes the most important methods used for analyzing epidemiological data. It begins with an analysis of descriptive data and goes on to discuss the analysis of effect measures, i.e. measures used to compare exposed and unexposed. This is done firstly without taking any background factors into consideration, then when doing so—in other words crude and stratified analysis. The final part of this section takes up more specific areas. Multivariate models, dose-response analysis, analysis of the interaction between causes of disease, meta-analysis and computer programs are all discussed here.

NOTE: In the examples featured in the text and in the exercises in Appendix 2, the results are generally given with 3-digit accuracy. When relevant, intermediate results are given with four digits accuracy but the calculations have been carried out on the computer which always used maximum accuracy.

Chapter 2

PROBABILITY THEORY

“When they saw a random relationship between what goes into a system and what comes out, they assumed that they would have to build randomness into any realistic theory. The modern study of chaos began with the creeping realization in the 1960s that quite simple mathematical equations could model systems every bit as violent as a waterfall…In weather, for example, this translates into what is only half-jokingly known as the Butterfly Effect — the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York.”

Gleick J: Chaos. Making a New Science. Viking Penguin, Inc., 1987.

One of the main objectives of the statistical analysis of a collected material is to determine the importance of the study’s random errors. What can we conclude about the “true” value from an obtained study result? Our conclusions are based on what is known about the probability of different results given different assumptions about the “true” values. Probability theory forms the basis for these calculations.

In this chapter we will go through some of the basic concepts used in probability theory which are of particular importance for the applications discussed in this book. For a more comprehensive presentation of these concepts, we recommend a textbook on this subject, such as one of those referred to in the reading list at the end of the book.

2.1 SOME BASIC PRINCIPLES

The probability of an event, E, for example that a randomly chosen person has diabetes, is written P(E) and is a number between 0 and 1, where P(E) = 0 when E is impossible and 1 when E is sure to occur. If E₁ and E₂ are two events which cannot happen at the same time, then the probability of at least one of them occurring is P(E₁) + P(E₂).

The complementary event to E is denoted as E* and is the alternative to E. In other words, it is what happens when E does not happen. If E is defined as ...

Table of contents

• Cover
• Title Page
• Copyright Page
• Foreword
• The Author
• Table of Contents
• Foreword
• Chapter 1: Introduction
• Chapter 2: Probability Theory
• Chapter 3: Statistical Inference
• Chapter 4: The P-Value, the P-Value Function and the Confidence Interval
• Chapter 5: Descriptive Epidemiologic Measures
• Chapter 6: Measures of Effect for Crude Analysis
• Chapter 7: Measures of Effect in Stratified Analysis
• Chapter 8: Multivariate Models
• Chapter 9: Analysis of Effect Modification and Synergism
• Chapter 10: Several Exposure Levels
• Chapter 11: Meta Analysis
• Chapter 12: Computer Programs
• Appendix 1
• Appendix 2
• References
• Index