Essential Statistics for Medical Practice: A case-study approach

222 Pages·1994·4.728 MB·English

by  D. G. Rees (auth.)

Essential Statistics for
Medical Practice
A case-study approach
D.C. Rees
Senior Lecturer in Statistics
Oxford Brookes University
UK
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
First edition 1994
© D. G. Rees 1994
Originally published by Chapman & Hall in 1994
Typeset in 10/12pt Palatino by Best-set Typesetter Ltd., Hong Kong
ISBN 978-0-412-59930-9 ISBN 978-1-4899-4505-1 (eBook)
DOI 10.1007/978-1-4899-4505-1
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To the memory of Florence
Nightingale, her work and her
inspiration
With Miss Nightingale statistics were a passion and not merely
a hobby ... But she loved statistics not for their own sake, but
for their practical uses. It was by the statistical method that she
had driven home the lessons of the Crimean hospitals. It was the
study of statistics that had opened her eyes to the preventable
mortality among the Army at home ... She was in very serious,
and even in bitter, earnest a passionate statistician.
Contents
Preface xi
Acknowledgements xiii
Overview of the use of basic statistical methods in
medical studies xv
Part One Discussion of Case Studies 1
1 Preliminary trial of the effect of general practice
based nutritional advice 3
1.1 Discussion 18
2 Randomized controlled trial of anti-smoking advice
by nurses in general practice 23
2.1 Discussion 33
3 Psychological distress: outcome and consultation
rates in one general practice 37
3.1 Discussion 48
4 Use of regression analysis to explain the variation
in prescribing rates and costs between family
practitioner committees 53
4.1 Discussion 66
5 Hidden psychiatric illness: use of the general health
questionnaire in general practice 71
5.1 Discussion 83
6 A randomized controlled trial of surgery for glue ear 85
6.1 Discussion 106
vi Contents
Part Two Statistical Methods 109
7 Data, tables, graphs, summary statistics and
probability 111
7.1 Data 111
7.2 Tables and graphs 113
7.3 Summary statistics for numerical variables 114
7.4 Summary statistics for non-numerical
variables 119
7.5 Probability 121
8 Hypothesis tests and confidence intervals for means 127
8.1 Introduction 127
8.2 Confidence interval for a population mean
(large samples) 128
8.3 Interpretation of a confidence interval 129
8.4 Confidence interval for a population mean
(small samples) 130
8.5 Hypothesis test for a population mean
(small or large samples) 131
8.6 The confidence interval and hypothesis test
approaches compared 134
8.7 Confidence interval and hypothesis test for
comparing two means (paired t-test) 134
8.8 Confidence interval and hypothesis test for
comparing two means (unpaired t-test) 137
8.9 Practical and statistical significance 140
8.10 What if the assumptions of the methods in
this chapter are not valid? 141
9 More on comparing means, the analysis of variance
and the F-test 143
9.1 Introduction 143
9.2 Why not carry out t-tests to compare the
means in pairs? 144
9.3 A numerical example of one-way ANOVA 144
9.4 A posterior test after ANOVA 147
9.5 The F-test to compare two variances 148
10 Hypothesis tests and confidence intervals for
percentages 151
10.1 In trod uction 151
10.2 Confidence interval for a percentage 152
Contents vii
10.3 Hypothesis test for a percentage 153
10.4 Confidence interval for the difference
between two percentages 154
10.5 Hypothesis test for the difference between
two percentages 155
11 Further tests for percentages 163
11.1 The Fisher exact test 163
11.2 X2 (chi-square) trend test 165
12 Regression and correlation 167
12.1 Introduction 167
12.2 Simple linear regression 168
12.3 Correlation coefficient 170
12.4 ANOVA applied to simple linear regression
analysis 171
12.5 How useful is the regression equation? 174
12.6 Introduction to multiple regression analysis 175
12.7 How good is our predicted value of y in
simple linear regression analysis? 178
12.8 Correlation, further discussion 180
13 Sensitivity and specificity 183
13.1 Definitions 183
13.2 Example from case study 5 184
14 Study design 187
14.1 Introduction 187
14.2 Study size 189
15 Calculators and computers 195
15.1 Introduction 195
15.2 MINIT AB examples 196
Appendix A Further reading 207
Appendix B Statistical tables 209
Index 217
Preface
Books on medical statistics usually start with elementary stat
istical techniques of data presentation and analysis, building
up to more advanced techniques. Relevant examples from the
literature, for example medical journals, are quoted as each
technique is introduced.
This book is different! I start from where the medical profes
sional starts when reading the literature, namely with a medical
investigation which nearly always contains some use of sta
tistical methods. So in Part One I have taken six real case
studies from recent medical journals and discussed each in
turn, using a common format, with particular emphasis on the
statistics. Forward references are made from the case studies to
examples in Part Two, which draws together similar examples
and discusses the background assumptions, limitations and
applicability of the statistical methods described.
I have limited this book to only the most basic, but neverthe
less useful, methods, because my aim is to provide a readable
and relatively short primer, rather than a long text which might
deter the busy health professional.
Acknowledgements
Miss Nightingale's mastery of the art of marshalling facts to
logical conclusions was recognised by her election in 1858 as a
member of the Statistical Society.
I would like to thank the editor of the British Journal of General
Practice (formerly the Journal of the Royal College of General Prac
titioners) for permission to reproduce five articles (case studies
1-5), and the production director of the British Medical Journal
for permission to reproduce one article (case study 6).
I would further like to thank the following authors and
publishers for their kind permission to adapt from the follow
ing tables: Pearson, E.S. and Hartley, H.O. (1966), Biometrika
Tables for Statisticians, vol I, 3rd edition, Cambridge University
Press, Cambridge (Tables B.1-B.4); and Mead, R. and Curnow,
R.N. (1983), Statistical Methods in Agriculture and Experimental
Biology, Chapman & Hall, London (Table B.5).
The quotations before or after various sections and chapters
are taken from a biography written by Sir Edward Cook (1913),
The Life of Florence Nightingale, Vol I 1820-1861 and Vol II
1862-1910, Macmillan, London, with permission from the
publishers. The quotations are the biographer's words unless
otherwise stated.
Thanks also to David Mant, Department of Community
Medicine and General Practice, University of Oxford, and to
Peter Anderson, formerly Director of HEA Primary Health
Care Unit, Churchill Hospital, Oxford, for initial discussions
and assistance with the choice of relevant case studies.
Most of all, I am grateful to my wife, Merilyn, for her help in
the production of the various drafts and for her support and
encouragement throughout.
Overview of the use of
basic statistical methods in
medical studies
Data are collected from patients in order to diagnose and treat
their medical conditions, and to make them well again. In
medical studies we usually need to collect data from one or
more groups of patients who have something in common, such
as suffering from the same disease. We may then wish to
compare sub-groups of patients, for example those treated by
one method and those treated by another method. The simplest
way to compare the sub-groups will probably be in terms of
means or percentages, depending on the type of variable of
interest. For example, if the treatments given to sub-groups 1
and 2 are one of two drugs designed to reduce blood pressure,
we would wish to compare the mean reduction in blood pres
sure for each of the sub-groups. Whereas, if the two treatments
given result in either 'success' (disease cured) or 'failure'
(disease not cured) for each patient, we would wish to compare
the percentages achieving success for the treatments. Means
and percentages are examples of summary (or 'descriptive')
statistics, and these and others are discussed in the first chapter
of Part Two (Chapter 7).
The other aspect of the medical data we collect is that they
represent only some of the possible data that we could have
collected. We, of course, restrict ourselves to collecting only
data for variables which are relevant to the objectives of our
study. Even so, if our objective is, for example, to 'compare the
reduction in blood pressure resulting from the applications of
drugs A and B' we will have to restrict ourselves to collecting