Preface
1 Statistics in medical research
1.1 Statistics at large
1.2 Statistics in medicine
1.3 Statistics in medical research
1.4 What does statistics cover?
1.5 The scope of this book
2 Types of data
2.1 Introduction
2.2 Categorical data
2.3 Numerical data
2.4 Other types of data
2.5 Censored data
2.6 Variability
2.7 Importance of the type of dat
a
2.8 Dealing with numbers
3 Describing data
3.1 Introduction
3.2 Averages
3.3 Describing variability
3.4 Quantifying variability
3.5 Two variables
3.6 The effect of transforming the data
3.7 Data presentation
Exercises
4 Theoretical distribution
4.1 Introduction
4.2 Probability
4.3 Samples and populations
4.4 Probability distributions
4.5 The Normal distribution
4.6 The Lognormal distributions
4.7 The Binomial distribution
4.8 The Poisson distribution
4.9 Mathematical calculations
4.10 The Uniform distribution
4.11 Concluding remarks
Exercises
5 Designing research
5.1 Introduction
5.2 Categories of research design
5.3 Sources of variation
5.4 An experiment: is the blood pressure the same in both arms?
5.5 The design of experiments
5.6 The structure of an experiment
5.7 Random allocation
5.8 Minimization
5.9 Observational studie
s
5.10 The case-control study
5.11 The cohort study
5.12 The cross-sectional study
5.13 Studies of change over time
5.14 Choosing a study design
Exercises
6 Using a computer
6.1 Introduction
6.2 Advantages of using a computer
6.3 Disadvantages of using a computer
6.4 Types of statistical program
6.5 Evaluating a statistical package
6.6 Strategy for computer-aided analysis
6.7 Forms for data collection
6.8 Plotting
6.9 Other uses of computers
6.10 Misuses of the computer
6.11 Concluding remarks
7 Preparing to analyse data
7.1 Introduction
7.2 Data checking
7.3 Outliers
7.4 Missing data
7.5 Data screening
7.6 Why transform data?
7.7 Other features of the data
7.8 Concluding remarks
Exercises
8 Principles of statistical analysis
8.1 Introduction
8.2 Sampling distribution
8.3 A demonstration of the distribution of sample means
8.4 Estimation
8.5 Hypothesis testing
8.6 Non-parametric methods
8.7 Statistical modelling
8.8 Estimation or hypothesis testing?
8.9 Strategy for analysing data
8.10 Presentation of results
8.11 Summary
Exercises
9 Comparing groups - continuous data
9.1 Introduction
9.2 Choosing an appropriate method of analysis
9.3 The t distribution
9.4 One group of observations
9.5 Two groups of paired observations
9.6 Two independent groups of observations
9.7 Analysis of skewed data
9.8 Three or more independent groups of observations
9.9 One way analysis of variance — mathematics and worked example
9.10 Presentation of results
9.11 Summary
Exercises
10 Comparing groups - categorical data
10.1 Introduction
10.2 One proportion
10.3 Proportions in two independent groups
10.4 Two paired proportions
10.5 Comparing several proportions
10.6 The analysis of frequency tables
10.7 2x2 frequency tables - comparison of two proportions
10.8 2x2 k tables - comparison of several proportions
10.9 Large tables with ordered categories
10.10 kxk tables - analysis of matched variables
10.11 Comparing risks
10.12 Presentation of results
10.13 Summary
Exercises
11 Relation between two continuous variables
11.1 Association, prediction and agreement
11.2 Correlation
11.3 Use and misuse of correlation
11.4 Rank correlation
11.5 Adjusting a correlation for another variable
11.6 Use of the correlation coefficient in assessing non-Normality
11.7 Correlation — mathematics and worked examples
11.8 Interpretation of correlation
11.9 Presentation of correlation
11.10 Regression
11.11 Use of regression
11.12 Extensions
11.13 Regression — mathematics and worked example
11.14 Interpretation of regression
11.15 Relation to other analyses
11.16 Presentation of regression
11.17 Regression or correlation?
Exercises
12 Relation between several variables
12.1 Introduction
12.2 Analysis of variance and multiple regression
12.3 Two way analysis of variance
12.4 Multiple regression
12.5 Logistic regression
12.6 Discriminant analysis
12.7 Other methods
Exercises
13 Analysis of survival times
13.1 Introduction
13.2 Survival probabilities
13.3 Comparing survival curves in two groups
13.4 Mathematical calculations and worked examples
13.5 Incorrect analyses
13.6 Modelling survival — the Cox regression model
13.7 Design of survival studies
13.8 Presentation of results
Exercises
14 Some common problems in medical research
14.1 Introduction
14.2 Method comparison studies
14.3 Inter-rater agreement
14.4 Diagnostic tests
14.5 Reference intervals
14.6 Serial measurements
14.7 Cyclic variation
Exercises
15 Clinical trials
15.1 Introduction
15.2 Design of clinical trials
15.3 Sample size
15.4 Analysis
15.5 Interpretation of results
15.6 Writing up and assessing clinical trials
Exercises
16 The medical literature
16.1 Introduction
16.2 The growth of statistics in medical research
16.3 Statistics ini published papers
16.4 Reading a scientific paper
16.5 Writing a scientific paper
Exercises
Appendix A Mathematical notation
A1.1 Introduction
A1.2 Basic ideas
A1.3 Mathematical symbols
A1.4 Functions
A1.5 Glossary of notation
Appendix B Statistical tables
Answers to exercises
References
Index
