# An Introduction to Medical Statistics

## Overview of An Introduction to Medical Statistics

An Introduction to Medical Statistics, now in its third edition, is a book for medical students, doctors, medical researchers, and all who want an introduction to statistics in a medical or health context. The book has 410 pages with 118 figures.

The approach is firmly embedded in medical research, all the methods described being illustrated with the use of real data, either from my own research or from the medical literature. Equations and formulae are given where appropriate and manual calculation is described, but the use of computers for calculations is emphasised, together with the graphical methods which computers make easy. For those who do not like to take things on trust, mathematical appendices are included which explain the derivation of the various statistical formulae, and graphical simulations are used to illustrate some of the more surprising statistical principles.

The book begins with the design of clinical and epidemiological studies, then describes methods for summarising and presenting the data collected. Next probability is introduced, and the ways in which it can be used to interpret data. The most commonly used statistical methods are described, their assumptions and how these can be checked, their interpretation, and how to choose the appropriate method for the analysis of different types of data in various circumstances. Methods of particular relevance to medical studies are discussed, such as the estimation of reference ranges, the analysis of survival data, and the study of mortality. The book finishes with chapters on multifactorial analyses and the choice of sample size.

Two types of exercises are included: 100 multiple choice questions of the five branch True/False type, and long exercises involving calculations. Full solutions are given.

## Third edition

The third edition was published in August 2000. Due to cunning typesetting, the length of the third edition is similar to that of the second edition, but several new topics have been added and others extended.

New topics in the third edition include:

• Consent in clinical trials
• Ecological studies
• Conditional probability
• Confidence interval for a proportion when numbers are small
• Correct confidence interval for group comparisons
• Random effects in analysis of variance
• Units of analysis and cluster-randomized trials
• Intraclass correlation
• Number needed to treat

Topics which have been considerably revised and/or extended include:

• Experimental units
• Histograms and other frequency graphs
• Variables which follow a Normal distribution
• The Normal plot
• The use of transformations
• The Mann-Whitney U test
• Odds and odds ratios
• Repeatability and measurement error
• Sensitivity and specificity
• Interaction in multiple regression
• Logistic regression

A general change throughout the book is that sections containing material usually found only in postgraduate courses have been starred *, so that undergraduates can omit them at first reading.

The third edition was published together with a book by Martin Bland and Janet Peacock: Statistical Questions in Evidence-based Medicine, published by Oxford University Press in September, 2000.

## Reviews

### Extracts from reviews of the first edition

The first edition was well reviewed, e.g.:
At last I have a book on medical statistics that I can safely recommend to my students. --- Journal of the Royal Statistical Society.
It is a book which I think anyone teaching an introductory course in medical statistics should seriously consider as the main text. --- Statistics in Medicine.
If you want understand some of the statistical ideas important to medicine but fear being overwhelmed by mathematics you will welcome "An Introduction to Medical Statistics" by M. Bland. --- British Medical Journal.

### Reviews of the second edition

European Journal of Orthodontics

Martin Bland's textbook is one of those most commonly recommended by academic medical statisticians in the UK for students and professionals in health-related disciplines. According to the British Medical Journal reviewer of the first edition, `If you want to understand some of the statistical ideas important to medicine but fear being overwhelmed by mathematics you will welcome this book'. And it is certainly sufficiently explicit and prescriptive for those at the research stage of their careers. The second edition is rather longer than the first, in particular sections on multifactorial methods and determination of sample size have been greatly expanded to form additional chapters. Each chapter includes several traditional multiple choice questions, and a longer question: a section at the back of the book gives full solutions to both. As in most other biostatistics texts, the clinical and epidemiological examples used are medical rather than dental, but do not presuppose specialized medical knowledge: the issues in dental specialties are fundamentally similar, and a dental reader should find the medical orientation no obstacle. The second edition is still good value at 14.95 pounds.

R. G. Newcombe. (1996) European Journal of Orthodontics 18(3) , 308.

N.B. The price is now higher, but still good value! -- MB.

Title: An Introduction to Medical Statistics
Author: Martin Bland
Publisher: Oxford Medical Publications
Price: \$27.95.
Comment: This paperback makes aspects of statistics and design of experiments, sampling and observational studies, data presentation, probability and other painful aspects of statistics relatively painless although it does have a lot of math.

### Reviews of the third edition

The third edition was reviewed by Les Huson (The Statistician, 50, 548). The review ends:
The coverage may not be very different from that of other introductory texts, but in my view the style and content are, and they alone make this text one of the best of its kind. The approach is very data driven, and the use of real data makes this even more appealing. The concern throughout is with statistical practice -- i.e. with extracting meaningful information from real data -- and not statistical theory, although the necessary theoretical ideas are explained in a non-mathematical way. The writing style -- first person throughout -- is also attractive and makes the text easy to read and digest, although it should also be said that this book contains a large amount of material and to work through it thoroughly takes time! Using the companion volume also [Statistical Questions in Evidence-based Medicine], and working through the exercises, would mean a very thorough course of study indeed.

All in all, this is an excellent book -- it has been on my bookshelf since the first edition, and in my view it should be the first choice for any student wanting a serious introduction to the practice of medical statistics.

## Availability

An Introduction to Medical Statistics (ISBN 0 19 262428 8) is published world-wide by Oxford University Press in two versions: the standard soft cover edition (UK price 18.95 pounds) and the subsidised English Language Book Service for developing countries. In the USA it is published by Oxford University Press Inc., New York. The ISBN is 0 19 263269 8.

There is an Arabic edition, published by the Arab Center for Arabization, Translation, Authorship and Publication (ACATAP), Damascus.

## Sales

First edition: 16,000 copies (1987 to 1995).
Second edition: 13,495 copies (May 1995 to March 2001).
Second edition (ELBS): 1,551 copies (February 1997 to March 2001).
Third edition: 15,275 copies (August 2000 to March 2005).
Total sales to September 2004: 46,000 copies.

## Corrections

### Corrections to the second edition

Despite the combined proof-reading efforts of Doug Altman, Janet Peacock, and myself, a few errors remain. An up to date list of corrections to the second edition is maintained on this site.

### Corrections to the third edition

An up to date list of corrections to the third edition is maintained on this site.

## Contents of An Introduction to Medical Statistics

High-lighted sections can be read on the Web. Section in bold are new in the third edition. Sections marked * contain material usually found only in postgraduate courses.
1. Introduction
• Statistics and medicine
• Statistics and mathematics
• Statistics and computing
• The scope of this book
2. The design of experiments
• Comparing treatments
• Random allocation
• * Methods of allocation without random numbers
• Volunteer bias
• Intention to treat
• Cross-over designs
• Selection of subjects for clinical trials
• Response bias and placebos
• Assessment bias and double blind studies
• * Laboratory experiments
• * Experimental units
• * Consent in clinical trials
• Multiple Choice Questions 1 to 6
• Exercise: The `Know Your Midwife' trial
3. Sampling and observational studies
• Observational Studies
• Censuses
• Sampling
• Random sampling
• Sampling in clinical and epidemiological studies
• Cross-sectional studies
• Cohort studies
• Case-control studies
• * Questionnaire bias in observational studies
• * Ecological studies
• Multiple Choice Questions 7 to 13
• Exercise: Campylobacter jejuni infection
4. Summarizing data
• Types of data
• Frequency distributions
• Histograms and other frequency graphs
• Shapes of frequency distribution
• Medians and quantiles
• The mean
• Variance, range and interquartile range
• Standard deviation
• Appendix: The divisor for the variance
• Appendix: Formulae for the sum of squares
• Multiple Choice Questions 14 to 19
• Exercise: Mean and standard deviation
5. Presenting data
• Rates and proportions
• Significant figures
• Presenting tables
• Pie charts
• Bar charts
• Scatter diagrams
• Line graphs and time series
• Logarithmic scales
• Appendix: Logarithms
• Multiple choice questions 20 to 24
• Exercise: Creating graphs
6. Probability
• Probability
• Properties of probability
• Probability distributions and random variables
• The Binomial Distribution
• Mean and variance
• Properties of means and variances
• * The Poisson Distribution
• * Conditional probability
• Appendix: Permutations and combinations
• Appendix: Expected value of a sum of squares
• Multiple choice questions 25 to 31
• Exercise: Probability and the life table
7. The Normal distribution
• Probability distributions for continuous variables
• The Normal distribution
• Properties of the Normal distribution
• Variables which follow a Normal distribution
• The Normal plot
• Appendix: The Chi-squared, t, and F distributions
• Multiple choice questions 32 to 37
• Exercise: A Normal plot
8. Estimation
• Sampling distributions
• Standard error of a sample mean
• Confidence intervals
• Standard error of and confidence interval for a proportion
• The difference between two means
• Comparison of two proportions
• * Standard error of a sample standard deviation
• * Confidence interval for a proportion when numbers are small
• * Confidence interval for a median and other quantiles
• What is the correct confidence interval?
• Multiple choice questions 38 to 43
• Exercise: Means of large samples
9. Significance tests
• Testing a hypothesis
• An example: the sign test
• Principles of significance tests
• Significance levels and types of error
• One and two sided tests of significance
• Significant, real and important
• Comparing the means of large samples
• Comparison of two proportions
• * The power of a test
• * Multiple significance tests
• * Repeated significance tests and sequential analysis
• Multiple Choice Questions 44 to 49
• Exercise: Crohn's disease and cornflakes
10. Comparing the means of small samples
• The t distribution
• The one sample t method
• The means of two independent samples
• The use of transformations
• Deviations from the assumptions of t methods
• What is a large sample?
• * Serial data
• * Comparing two variances by the F test
• * Comparing several means using analysis of variance
• * Assumptions of the analysis of variance
• * Comparison of means after analysis of variance
• * Random effects in analysis of variance
• * Units of analysis and cluster-randomized trials
• Appendix: The ratio mean/standard error
• Multiple choice questions 50 to 56
• Exercise: The paired t method
11. Regression and correlation
• Scatter diagrams
• Regression
• The method of least squares
• * The regression of X on Y
• The standard error of the regression coefficient
• * Using the regression line for prediction
• * Analysis of residuals
• * Deviations from assumptions in regression
• Correlation
• Significance test and confidence interval for r
• Uses of the correlation coefficient
• * Using repeated observations
• * Intraclass correlation
• Appendix: The least squares estimates
• Appendix: The variance about the regression line
• Appendix: The standard error of b
• Multiple choice questions 57 to 61
• Exercise: Comparing two regression lines
12. Methods based on rank order
• * Non-parametric methods
• * The Mann Whitney U Test
• * The Wilcoxon matched pairs test
• * Spearman's rank correlation coefficient, rho
• * Kendall's rank correlation coefficient, tau
• * Continuity corrections
• * Parametric or non-parametric methods?
• Multiple choice questions 62 to 66
• Exercise: Application of rank methods
13. The analysis of cross-tabulations
• The chi-squared test for association
• Tests for 2 by 2 tables
• The chi-squared test for small samples
• Fisher's exact test
• Yates' continuity correction for the 2 by 2 table
• * The validity of Fisher's and Yates' methods
• Odds and odds ratios
• * The chi-squared test for trend
• * Methods for matched samples
• * The chi-squared goodness of fit test
• Appendix: Why the chi-squared test works
• Appendix: The formula for Fisher's exact test
• Appendix: Standard error for the odds ratio
• Multiple choice questions 67 to 73
• Exercise: Admissions to hospital in a heatwave
14. Choosing the statistical method
• * Method oriented and problem oriented teaching
• * Types of data
• * Comparing two groups
• * One sample and paired samples
• * Relationship between two variables
• Multiple choice questions 74 to 80
• * Exercise: Choosing a statistical method
15. Clinical measurement
• Making measurements
• * Repeatability and measurement error
• * Comparing two methods of measurement
• Sensitivity and specificity
• Normal range or reference interval
• * Survival data
• * Computer aided diagnosis
• * Number needed to treat
• Multiple choice questions 81 to 86
• Exercise: A reference interval
16. Mortality statistics and population structure
• Mortality rates
• Age standardization using the direct method
• Age standardization by the indirect method
• Demographic life tables
• Vital statistics
• The population pyramid
• Multiple choice questions 87 to 92
• Exercise: Deaths from volatile substance abuse
17. Multifactorial methods
• * Multiple Regression
• * Significance tests and estimation in multiple regression
• * Interaction in multiple regression
• * Polynomial regression
• * Assumptions of multiple regression
• * Qualitative predictor variables
• * Multi-way analysis of variance
• * Logistic regression
• * Survival data using Cox regression
• * Stepwise regression
• * Meta-analysis: data from several studies
• * Other multifactorial methods
• * Multiple choice questions 93 to 97
• * Exercise: A multiple regression analysis
18. Determination of sample size
• * Estimation of a population mean
• * Estimation of a population proportion
• * Sample size for significance tests
• * Comparison of two means
• * Comparison of two proportions
• * Detecting a correlation
• * Accuracy of the estimated sample size
• * Trials randomized in clusters
• * Multiple choice questions 98 to 100
• * Exercise: Estimation of sample sizes
19. Solutions to exercises
20. References
21. Index

## Search inside the book

You can search for any words inside the book so that you can find out whether An Introduction to Medical Statistics has anything on a topic. This is provided by Amazon as part of their "Search Inside the Book" system.

You can try this link, which should take you straight there: search Intro.

If this does not work, go the Amazon. web site, search for the book, get the details, and click the "Search inside" icon above the cover. You can then search the whole book for any topic. This might help you decide whether this is the book you need.