Statistics with Confidence (eBook)

Confidence Intervals and Statistical Guidelines

Douglas Altman, David MacHin, Trevor Bryant, Martin Gardner (Herausgeber)

eBook Download: EPUB

2013 | 2. Auflage
John Wiley & Sons (Verlag)
978-1-118-70250-5 (ISBN)

Infos

This highly popular introduction to confidence intervals has been thoroughly updated and expanded. It includes methods for using confidence intervals, with illustrative worked examples and extensive guidelines and checklists to help the novice.

Douglas Altman FMedSci was an English statistician best known for his work on improving the reliability and reporting of medical research and for highly cited papers on statistical methodology. David Machin is Professor of Media and Communication at örebro University, Sweden. He has published numerous books and journal papers mostly drawing on linguistic methods.

Inhalt

Contributors viii

Source of Contents ix

Introduction xi
Douglas G. Altman, David Machin, Trevor N. Bryant

PART I: ESTIMATION AND CONFIDENCE INTERVALS

1 Estimating with Confidence 3
Martin J. Gardner, Douglas G. Altman

2 Confidence Intervals in Practice 6
Douglas G. Altman

3 Confidence Intervals Rather Than P Values 15
Marin J. Gardner, Douglas G. Altman

4 Means and Their Differences 28
Douglas G. Altman, Martin J. Gardner

5 Medians and Their Differences 36
Michael J. Campbell, Martin J. Gardner

6 Proportions and Their Differences 45
Robert G. Newcombe, Douglas G. Altman

7 Epidemiological Studies 57
Julie A Morris, Martin J. Gardner

8 Regression and Correlation 73
Douglas G. Altman, Martin J. Gardner

9 Time to Event Studies 93
David Machin, Martin J. Gardner

10 Diagnostic Tests 105
Douglas G. Altman

11 Clinical Trials and Meta-Analyses 120
Douglas G. Altman

12 Confidence Intervals and Sample Sizes 139
Leslie E. Daly

13 Special Topics 153
Michael J. Campbell, Leslie E. Daly, David Machin

PART II: STATISTICAL GUIDELINES AND CHECKLISTS

14 Statistical Guidelines for Contributors to Medical Journals 171
Douglas G. Altman, Sheila M. Gore, Martin J. Gardner, Stuart J. Pocock

15 Statistical Checklists 191
Martin J. Gardner, David Machin, Michael J. Campbell, Douglas G. Altman

PART III. NOTATION, SOFTWARE, AND TABLES

16 Notation 205
Douglas G. Altman

17 Computer Software for Calculating Confidence Intervals (CIA) 208
Trevor N. Bryant

18 Tables for the Calculation of Confidence Intervals 214
Martin J. Gardner

Index 233

Rezensionen

"The great value of this book is that it presents, in an easily
understood form, the methods which will be needed in most
situations" - Journal of Epidemiology and Community Health

"...this is a superb book, full of useful information.

...The book is logically organized into 18 short, highly
readable chapters.

...as a teaching tool, it is invaluable...this book is a handy
reference to have on one's bookshelf with nearly all confidence
interval formulae organized in one place.

...In summary, Statistics with Confidence and the CIA software
are resources that every biostatistician could benefit from."

TSHS, pp. 4-5

Textauszug

3

Confidence intervals rather than P values

MARTIN J GARDNER, DOUGLAS G ALTMAN

Summary

• Overemphasis on hypothesis testing—and the use of P values to dichotomise results as significant or non-significant—has detracted from more useful approaches to interpreting study results, such as estimation and confidence intervals.
• In medical studies investigators should usually be interested in determining the size of difference of a measured outcome between groups, rather than a simple indication of whether or not it is statistically significant.
• Confidence intervals present a range of values, on the basis of the sample data, in which the population value for such a difference is likely to lie.
• Confidence intervals, if appropriate to the type of study, should be used for major findings in both the main text of a paper and its abstract.

Introduction

Over recent decades the use of statistics in medical journals has increased tremendously. One unfortunate consequence has been a shift in emphasis away from the basic results towards an undue concentration on hypothesis testing. In this approach data are examined in relation to a statistical “null” hypothesis, and the practice has led to the mistaken belief that studies should aim at obtaining “statistical significance”. On the contrary, the purpose of most research investigations in medicine is to determine the magnitude of some factor(s) of interest. For example, a laboratory-based study may investigate the difference in mean concentrations of a blood constituent between patients with and without a certain illness, while a clinical study may assess the difference in prognosis of patients with a particular disease treated by alternative regimens in terms of rates of cure, remission, relapse, survival, etc. The difference obtained in such a study will be only an estimate of what we really need, which is the result that would have been obtained had all the eligible subjects (the “population”) been investigated rather than just a sample of them. What authors and readers should want to know is by how much the illness modified the mean blood concentrations or by how much the new treatment altered the prognosis, rather than only the level of statistical significance.

The excessive use of hypothesis testing at the expense of other ways of assessing results has reached such a degree that levels of significance are often quoted alone in the main text and abstracts of papers, with no mention of actual concentrations, proportions, etc., or their differences. The implication of hypothesis testing—that there can always be a simple “yes” or “no” answer as the fundamental result from a medical study—is clearly false and used in this way hypothesis testing is of limited value (see chapter 14).

We discuss here the rationale behind an alternative statistical approach—the use of confidence intervals; these are more informative than P values, and we recommend them for papers presenting research findings. This should not be taken to mean that confidence intervals should appear in all papers; in some cases, such as where the data are purely descriptive, confidence intervals are inappropriate and in others techniques for obtaining them are complex or unavailable.

Presentation of study results: limitations of P values

The common simple statements “P < 0·05”, “P > 0·05”, or “P = NS” convey little information about a study’s findings and rely on an arbitrary convention of using the 5% level of statistical significance to define two alternative outcomes—significant or not significant—which is not helpful and encourages lazy thinking. Furthermore, even precise P values convey nothing about the sizes of the differences between study groups. Rothman pointed this out in 1978 and advocated the use of confidence intervals,1 and in 1984 he and his colleagues repeated the proposal.2 This plea has been echoed by many others since (see chapter 2).

Presenting P values alone can lead to their being given more merit than they deserve. In particular, there is a tendency to equate statistical significance with medical importance or biological relevance. But small differences of no real interest can be statistically significant with large sample sizes, whereas clinically important effects may be statistically non-significant only because the number of subjects studied was small.

Presentation of study results: confidence intervals

It is more useful to present sample statistics as estimates of results that would be obtained if the total population were studied. The lack of precision of a sample statistic—for example, the mean—which results from both the degree of variability in the factor being investigated and the limited size of the study, can be shown advantageously by a confidence interval.

A confidence interval produces a move from a single value estimate—such as the sample mean, difference between sample means, etc.—to a range of values that are considered to be plausible for the population. The width of a confidence interval associated with a sample statistic depends partly on its standard error, and hence on both the standard deviation and the sample size (see appendix 1 for a brief description of the important, but often misunderstood, distinction between the standard deviation and standard error). It also depends on the degree of “confidence” that we want to associate with the resulting interval.

Suppose that in a study comparing samples of 100 diabetic and 100 non-diabetic men of a certain age a difference of 6·0 mmHg was found between their mean systolic blood pressures and that the standard error of this difference between sample means was 2·5 mmHg, comparable to the difference between means in the Framingham study.3 The 95% confidence interval for the population difference between means is from 1·1 to 10·9 mmHg and is shown in Figure 3.1 together with the original data. Details of how to calculate the confidence interval are given in chapter 4.

Put simply, this means that there is a 95% chance that the indicated range includes the “population” difference in mean blood pressure levels—that is, the value which would be obtained by including the total populations of diabetics and non-diabetics at which the study is aimed. More exactly, in a statistical sense, the confidence interval means that if a series of identical studies were carried out repeatedly on different samples from the same populations, and a 95% confidence interval for the difference between the sample means calculated in each study, then, in the long run, 95% of these confidence intervals would include the population difference between means.

Figure 3.1 Systolic blood pressures in 100 diabetics and 100 nondiabetics with mean levels of 146·4 and 140·4 mmHg respectively. The difference between the sample means of 6.0 mmHg is shown to the right together with the 95% confidence interval from 1·1 to 10·9 mmHg.

The sample size affects the size of the standard error and this in turn affects the width of the confidence interval. This is shown in Figure 3.2, which shows the 95% confidence interval from samples with the same means and standard deviations as before but only half as large—that is, 50 diabetics and 50 non-diabetics. Reducing the sample size leads to less precision and an increase in the width of the confidence interval, in this case by some 40%.

The investigator can select the degree of confidence associated with a confidence interval, though 95% is the most common choice—just as a 5% level of statistical significance is widely used. If greater or less confidence is required different intervals can be constructed: 99%, 95%, and 90% confidence intervals for the data in Figure 3.1 are shown in Figure 3.3. As would be expected, greater confidence that the population difference is within a confidence interval is obtained with wider intervals. In practice, intervals other than 99%, 95%, or 90% are rarely quoted. Appendix 2 explains the general method for calculating a confidence interval appropriate for most of the methods described in this book. In brief, a confidence interval is obtained by subtracting from, and adding to, the estimated statistic of interest (such as a mean difference) a multiple of its standard error (SE). A few methods described in this book, however, do not follow this pattern.

Figure 3.2 As Figure 3.1 but showing results from two samples of half the size—that is, 50 subjects each. The means and standard deviations are as in fig 3.1, but the 95% confidence interval is wider, from –1·0 to 13·0 mmHg, owing to the smaller sample sizes.

Confidence intervals convey only the effects of sampling variation on the precision of the estimated statistics and cannot control for non-sampling errors such as biases in design, conduct, or analysis.

Figure 3.3 Confidence intervals associated with differing degrees of “confidence” using the same data as in Figure 3.1.

Sample sizes and confidence intervals

In general, increasing the sample size will reduce the width of the confidence interval. If we assume the same means and standard deviations as in the example, Figure 3.4 shows the resulting 99%, 95%, and 90% confidence intervals for the difference in mean blood pressures for sample sizes of up to 500 in...

Produkt-Details

• Erscheint lt. Verlag: 3.6.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Medizin / Pharmazie ► Allgemeines / Lexika
• Themenwelt: Studium ► Querschnittsbereiche ► Epidemiologie / Med. Biometrie
• Schlagworte: acclaimed classic • accompanying • Analyses • Chapters • CIA • confidence • Contributions • Diagnostic • Disk • enables confidence intervals • Intervals • Introduction • Medical • Medical Science • Medical Statistics & Epidemiology • Medizin • Medizinische Statistik u. Epidemiologie • Meta • Methods • New • statisticians • Statistics • Studies • widely
• ISBN-10: 1-118-70250-6 / 1118702506
• ISBN-13: 978-1-118-70250-5 / 9781118702505