Statistics in Medicine

Robert H. Riffenburgh

• Publisher: Academic Press
• Year: 2012
• eBook ISBN: 9780123848659
• Edition: 3
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Statistics in Medicine, Third Edition makes medical statistics easy to understand by students, practicing physicians, and researchers. The book begins with databases from clinical medicine and uses such data to give multiple worked-out illustrations of every method. The text opens with how to plan studies from conception to publication and what to do with your data, and follows with step-by-step instructions for biostatistical methods from the simplest levels (averages, bar charts) progressively to the more sophisticated methods now being seen in medical articles (multiple regression, noninferiority testing). Examples are given from almost every medical specialty and from dentistry, nursing, pharmacy, and health care management. A preliminary guide is given to tailor sections of the text to various lengths of biostatistical courses.- User-friendly format includes medical examples, step-by-step methods, and check-yourself exercises appealing to readers with little or no statistical background, across medical and biomedical disciplines- Facilitates stand-alone methods rather than a required sequence of reading and references to prior text- Covers trial randomization, treatment ethics in medical research, imputation of missing data, evidence-based medical decisions, how to interpret medical articles, noninferiority testing, meta-analysis, screening number needed to treat, and epidemiology- Fills the gap left in all other medical statistics books between the reader's knowledge of how to go about research and the book's coverage of how to analyze results of that researchNew in this Edition: - New chapters on planning research, managing data and analysis, Bayesian statistics, measuring association and agreement, and questionnaires and surveys- New sections on what tests and descriptive statistics to choose, false discovery rate, interim analysis, bootstrapping, Bland-Altman plots, Markov chain Monte Carlo (MCMC), and Deming regression- Expanded coverage on probability, statistical methods and tests relatively new to medical research, ROC curves, experimental design, and survival analysis- 35 Databases in Excel format used in the book and can be downloaded and transferred into whatever format is needed along with PowerPoint slides of figures, tables, and graphs from the book included on the companion site, http://www.elsevierdirect.com/companion.jsp?ISBN=9780123848642- Medical subject index offers additional search capabilities

Chapter 1

Planning Studies
From Design to Publication

(A few statistical terms commonly appearing in medical articles appear in this chapter without having been previously defined. In case a reader encounters an unfamiliar one, a glossary at the chapter’s end provides interim definitions pending formal definitions later in this book.)

1.1 Organizing a Study

A study must be organized sooner or later. Planning in advance from an overview down to details increases efficiency, reduces false starts, reduces errors, and shortens the time spent. The lazy and least stressful way to do it, in the sense of least work overall, is thorough planning up front.

1.2 Stages of Scientific Knowledge

Stages

We gather data because we want to know something. These data are useful only if they provide information about what we want to know. A scientist usually seeks to develop knowledge in three stages. The first stage is to describe a class of scientific events. The second stage is to explain these events. The third stage is to predict the occurrence of these events. The ability to predict an event implies some level of understanding of the rule of nature governing the event. The ability to predict outcomes of actions allows the scientist to make better decisions about such actions. At best, a general scientific rule may be inferred from repeated events of this type. Following is a brief explanation of the three stages of gathering knowledge.

The Causative Process is of Interest, Not the Data

A process, or set of forces, generates data related to an event. It is this process, not the data per se, that interests us.

Description: the stage in which we seek to describe the data-generating process in cases for which we have data from that process. Description would answer questions such as: What is the range of prostate volumes for a sample of urology patients? What is the difference in average volume between patients with negative biopsy results and those with positive results?

Explanation: the stage in which we seek to infer characteristics of the (overall) data-generating process when we have only part (usually a small part) of the possible data. Inference would answer questions such as: For a sample of patients with prostate problems, can we expect the average of volumes of patients with positive biopsy results to be less than those of patients with negative biopsy results, for all men with prostate problems? Such inferences usually take the form of tests of hypotheses.

Prediction: the stage in which we seek to make predictions about a characteristic of the data-generating process on the basis of newly taken related observations. Such a prediction would answer questions such as: On the basis of a patient’s negative digital rectal examination, prostate-specific antigen (PSA) of 9, and prostate volume of 30 ml, what is the probability that he has prostate cancer? Such predictions allow us to make decisions on how to treat our patients to change the chances of an event. For example: Should I perform a biopsy on my patient? Predictions usually take the form of a mathematical model of the relationship between the predicted (dependent) variable and the predictor (independent) variables.

Phase I–IV Studies

Stages representing increasing knowledge in medical investigations often are categorized by phases. A Phase I investigation is devoted to discovering if a treatment is safe and in gaining enough understanding of the treatment to design formal studies. For example, a new drug is assessed to learn the level of dosage to study and if this level is safe in its main and side effects. A Phase II investigation is a preliminary investigation of the effectiveness of treatment. Is this drug more effective than existing drugs? Is the evidence of effectiveness strong enough to justify further study? Phase III is a large-scale verification of the early findings, the step from “some evidence” to “proof” (or, more exactly, close enough to proof to be accepted in general medical practice). The drug was shown more effective on several Phase II studies of 20 or 30 patients each over a scatter of subpopulations; now it must be shown to be more effective on, perhaps, 10 000 patients, in a sample comprehensively representing the entire population. In Phase IV, an established treatment is monitored to detect any changes in the treatment of a population of patients that would affect its use. Long-term toxicities must be detected. It must be determined if a microorganism being killed by a drug can evolve to become partially immune to it.

1.3 Science Underlying Clinical Decision Making

The Scientific Method

Science is a collection of fact and theory resting on information obtained by using a particular method that is therefore called the scientific method. This method is a way of obtaining information constrained by a set of criteria. The method is required to be objective; the characteristics should be made explicit and mean the same to every user of the information. The method should be unbiased, free of personal or corporate agendas; the purpose is to investigate the truth and correctness of states and relationships, not to “prove” them. The true scientific approach allows no preference for outcome. The method should involve the control of variables; ideally it should eliminate as far as practicable all sources of influence but one, so that the existence of and extent of influence of that one source is undeniable. The method should be repeatable; other investigators should be able to repeat the experiment and obtain the same results. The method should allow the accumulation of results; only by accumulation does the information evolve from postulate to theory to fact. The scientific method is the goal of good study design.

Jargon in Science

Jargon may be defined as technical terminology or as pretentious language. The public generally thinks of it as the latter. To the public, carcinoma is jargon for cancer, but to the professional, technical connotation is required for scientific accuracy. We need to differentiate between jargon for pomposity and jargon for accuracy, using it only for the latter and not unnecessarily. The same process occurs in statistics. Some statistical terms are used loosely and often erroneously by the public, who miss the technical implications. Examples are randomness, probability, and significance. Users of statistics should be aware of the technical accuracy of statistical terms and use them correctly.

Evidence

The accumulating information resulting from medical studies is evidence. Some types of study yield more credible evidence than others. Anecdotal evidence, often dismissed by users seeking scientific information, is the least credible, yet is still evidence. The anecdotal information that patients with a particular disease often improve more quickly than usual when taking a certain herb may give the rate of improvement but not the rate of failure of the treatment. It may serve as a candle in a dark room. However, such evidence may suggest that a credible study be done. The quality of the study improves as we pass through registries, case-control studies, and cohort studies, to the current gold standard of credibility, the randomized controlled prospective clinical trial (RCT). (See Sections 1.5 and 1.6 for more information on types of studies.) It is incumbent on the user of evidence to evaluate the credibility of the cumulative evidence: number of accumulated studies, types of studies, quality of control over influencing factors, sample sizes, and peer reviews. Evidence may be thought of as the blocks that are combined to build the scientific edifice of theory and fact. The more solid blocks should form the cornerstones and some blocks might well be rejected.

Evidence versus Proof

The results of a single study are seldom conclusive. We seldom see true proof in science. As evidence accrues from similar investigations, confidence increases in the correctness of the answer. The news media like to say, “The jury is still out”. In a more accurate rendition of that analogy, the jurors come in and lodge their judgment one at a time – with no set number of jurors.

Evidence-Based Medicine

Evidence-based medicine (EBM) melds the art and science of medicine. Evidence-based medicine is just the ideal paradigm of health care practice, with the added requirement that updated credible evidence associated with treatment be sought, found, assessed, and incorporated into practice. It is much the way we all think we practice, but it ensures consideration of the evidence components. It could be looked at somewhat like an airliner cockpit check; even though we usually mentally tick off all the items, formal guides verify that we have not overlooked something.

One rendition of the EBM sequence might be the following: (1) we acquire the evidence: the patient’s medical history, the clinical picture, test results, and relevant published studies. (2) We update, assess, and evaluate the evidence, eliminating evidence that is not credible, weighting that remaining evidence according to its credibility, and prioritizing that remaining according to its relevance to the case at hand. (3) We integrate the evidence of different types and from difference sources. (4) We add non-medical aspects, for example, cost considerations, the likelihood of patient cooperation, and the likelihood of patient follow-up. (5) Finally, we embed the integrated totality of evidence into a decision model.

1.4 Why Do We Need Statistics?

Primary Objective

A primary objective of statistics is to make an inference about a population based on a sample from that population.

Population versus Sample

The term population refers to all members of a defined group and the term sample to a subset of the population. As an example, patients in a hospital would constitute the entire population for a study of infection control in that hospital. However, for a study of infected patients in the nation’s hospitals, the same group of patients would be but a tiny sample. The same group can be a sample for one question about its characteristics and a population for another question.

Objective Restated

The symbol α is assigned to the chance of being wrong if we decide a treatment difference exists. We may restate this common objective of statistics as follows: based on a sample, we conclude that a treatment difference exists in the population if the risk of being wrong (a false positive difference) is less than an agreed u...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication1
• Dedication2
• Foreword to the Third Edition
• Foreword to the Second Edition
• Foreword to the First Edition
• Acknowledgments
• Databases
• How to Use This Book
• Chapter 1. Planning Studies
• Chapter 2. Planning Analysis
• Chapter 3. Probability and Relative Frequency
• Chapter 4. Distributions
• Chapter 5. Descriptive Statistics
• Chapter 6. Finding Probabilities
• Chapter 7. Confidence Intervals
• Chapter 8. Hypothesis Testing
• Chapter 9. Tests on Categorical Data
• Chapter 10. Risks, Odds, and ROC Curves
• Chapter 11. Tests on Ranked Data
• Chapter 12. Tests on Means of Continuous Data
• Chapter 13. Multi-Factor ANOVA and ANCOVA
• Chapter 14. Tests on Variability and Distributions
• Chapter 15. Managing Results of Analysis
• Chapter 16. Equivalence Testing
• Chapter 17. Bayesian Statistics
• Chapter 18. Sample Size Estimation and Meta-Analysis
• Chapter 19. Modeling Concepts and Methods
• Chapter 20. Clinical Decisions Based on Models
• Chapter 21. Regression and Correlation
• Chapter 22. Multiple and Curvilinear Regression
• Chapter 23. Survival, Logistic Regression, and Cox Regression
• Chapter 24. Sequential Analysis and Time Series
• Chapter 25. Epidemiology
• Chapter 26. Measuring Association and Agreement
• Chapter 27. Questionnaires and Surveys
• Chapter 28. Methods You Might Meet, But Not Every Day
• Answers to Chapter Exercises
• Tables of Probability Distributions
• Refernces and Data Sources
• Symbol Index
• Statistical Subject Index
• Medical Subject Index