Statistics with Confidence: Confidence Intervals and Statistical Guidelines

Contents

Contributors

Source of contents

Introduction

Part I Estimation and Confidence Intervals

1 Estimating with confidence

2 Confidence intervals in practice

Surveys of the use of confidence intervals in medical journals

Misuse of confidence intervals

Dissenting voices

3 Confidence intervals rather than P values

Presentation of study results: limitations of P values

Presentation of study results: confidence intervals

Sample sizes and confidence intervals

Confidence intervals and statistical significance

Suggested mode of presentation

Appendix 1: Standard deviation and standard error

Appendix 2: Constructing confidence intervals

4 Means and their differences

Two samples: unpaired case

Two samples: paired case

Non-Normal data

5 Medians and their differences

Medians and other quantiles

Differences between medians

6 Proportions and their differences

Two samples: unpaired case

Two samples: paired case

When no events are observed

7 Epidemiological studies

Relative risks, attributable risks and odds ratios

Incidence rates, standardised ratios and rates

8 Regression and correlation

Linear regression analysis

Binary outcome variable—logistic regression

Outcome is time to an event—Cox regression

Several explanatory variables—multiple regression

Correlation analysis

Technical details: formulae for regression and correlation analyses

9 Time to event studies

Survival proportions

Median survival time Single sample

The hazard ratio

10 Diagnostic tests

Classification into two groups

Classification into more than two groups

Diagnostic tests based on measurements

Comparison of assessors—the kappa statistic

11 Clinical trials and meta-analyses

Randomised controlled trials

12 Confidence intervals and sample sizes

Confidence intervals and P values

Sample size and hypothesis tests

Sample size and confidence intervals

Confidence intervals and null values

Confidence intervals, power and worthwhile differences

Explanation of the anomaly

Proposed solutions

Confidence intervals and standard sample size tables

Sample size for comparison of two independent means

Sample size for comparison of two independent proportions

13 Special topics

The substitution method

Exact and mid-P confidence intervals

Bootstrap confidence intervals

Multiple comparisons

Part II Statistical Guidelines and Checklists

14 Statistical guidelines for contributors to medical journals

Methods section

Results section: statistical analysis

Results section: presentation of results

Discussion section: interpretation

Concluding remarks

15 Statistical checklists

Uses of the checklists

Outline of the BMJ checklists

Reporting randomised controlled trials: the CONSORT statement

Checklists for other types of study

Part III Notation, Software, and Tables

16 Notation

17 Computer software for calculating confidence intervals (CIA)

Outline of the CIA program

Software updates and bug fixes

18 Tables for the calculation of confidence intervals