1 Introduction
1.1 Statistics and medicine
1.2 Statistics and mathematics
1.3 Statistics and computing
1.4 Assumptions and approximations
1.5 The scope of this book
2 The design of experiments
2.1 Comparing treatments
2.2 Random allocation
2.3 Stratification
2.4 Methods of allocation without random numbers
2.5 Volunteer bias
2.6 Intention to treat
2.7 Cross-over designs
2.8 Selection of subjects for clinical trials
2.9 Response bias and placebos
2.10 Assessment bias and double blind studies
2.11 Laboratory experiments
2.12 Experimental units and cluster randomized trials
2.13 Consent in clinical trials
2.14 Minimization
2.15 Multiple choice questions: Clinical trials
2.16 Exercise: The ‘Know Your Midwife’ trial
3 Sampling and observational studies
3.1 Observational studies
3.2 Censuses
3.3 Sampling
3.4 Random sampling
3.5 Sampling in clinical and epidemiological studies
3.6 Cross-sectional studies
3.7 Cohort studies
3.8 Case–control studies
3.9 Questionnaire bias in observational studies
3.10 Ecological studies
3.11 Multiple choice questions: Observational studies
3.12 Exercises: Campylobacter jejuni infection
4 Summarizing data
4.1 Types of data
4.2 Frequency distributions
4.3 Histograms and other frequency graphs
4.4 Shapes of frequency distribution
4.5 Medians and quantiles
4.6 The mean
4.7 Variance, range and interquartile range
4.8 Standard deviation
4.9 Multiple choice questions: Summarizing data
4.10 Exercise: Student measurements and a graph of study numbers
Appendix 4A: The divisor for the variance
Appendix 4B: Formulae for the sum of squares
5 Presenting data
5.1 Rates and proportions
5.2 Significant figures
5.3 Presenting tables
5.4 Pie charts
5.5 Bar charts
5.6 Scatter diagrams
5.7 Line graphs and time series
5.8 Misleading graphs
5.9 Using different colours
5.10 Logarithmic scales
5.11 Multiple choice questions: Data presentation
5.12 Exercise: Creating presentation graphs
Appendix 5A: Logarithms
6 Probability
6.1 Probability
6.2 Properties of probability
6.3 Probability distributions and random variables
6.4 The Binomial distribution
6.5 Mean and variance
6.6 Properties of means and variances
6.7 The Poisson distribution
6.8 Conditional probability
6.9 Multiple choice questions: Probability
6.10 Exercise: Probability in court
Appendix 6A: Permutations and combinations
Appendix 6B: Expected value of a sum of squares
7 The Normal distribution
7.1 Probability for continuous variables
7.2 The Normal distribution
7.3 Properties of the Normal distribution
7.4 Variables which follow a Normal distribution
7.5 The Normal plot
7.6 Multiple choice questions: The Normal distribution
7.7 Exercise: Distribution of some measurements obtained by students
Appendix 7A: Chi-squared, t, and F
8 Estimation
8.1 Sampling distributions
8.2 Standard error of a sample mean
8.3 Confidence intervals
8.4 Standard error and confidence interval for a proportion
8.5 The difference between two means
8.6 Comparison of two proportions
8.7 Number needed to treat
8.8 Standard error of a sample standard deviation
8.9 Confidence interval for a proportion when numbers are small
8.10 Confidence interval for a median and other quantiles
8.11 Bootstrap or resampling methods
8.12 What is the correct confidence interval?
8.13 Multiple choice questions: Confidence intervals
8.14 Exercise: Confidence intervals in two acupuncture studies
Appendix 8A: Standard error of a mean
9 Significance tests
9.1 Testing a hypothesis
9.2 An example: The sign test
9.3 Principles of significance tests
9.4 Significance levels and types of error
9.5 One and two sided tests of significance
9.6 Significant, real and important
9.7 Comparing the means of large samples
9.8 Comparison of two proportions
9.9 The power of a test
9.10 Multiple significance tests
9.11 Repeated significance tests and sequential analysis
9.12 Significance tests and confidence intervals
9.13 Multiple choice questions: Significance tests
9.14 Exercise: Crohn's disease and cornflakes
10 Comparing the means of small samples
10.1 The t distribution
10.2 The one sample t method
10.3 The means of two independent samples
10.4 The use of transformations
10.5 Deviations from the assumptions of t methods
10.6 What is a large sample?
10.7 Serial data
10.8 Comparing two variances by the F test
10.9 Comparing several means using analysis of variance
10.10 Assumptions of the analysis of variance
10.11 Comparison of means after analysis of variance
10.12 Random effects in analysis of variance
10.13 Units of analysis and cluster randomized trials
10.14 Multiple choice questions: Comparisons of means
10.15 Exercise: Some analyses comparing means
Appendix 10A: The ratio mean/standard error
11 Regression and correlation
11.1 Scatter diagrams
11.2 Regression
11.3 The method of least squares
11.4 The regression of X on Y
11.5 The standard error of the regression coefficient
11.6 Using the regression line for prediction
11.7 Analysis of residuals
11.8 Deviations from assumptions in regression
11.9 Correlation
11.10 Significance test and confidence interval for r
11.11 Uses of the correlation coefficient
11.12 Using repeated observations
11.13 Intraclass correlation
11.14 Multiple choice questions: Regression and correlation
11.15 Exercise: Serum potassium and ambient temperature
Appendix 11A: The least squares estimates
Appendix 11B: Variance about the regression line
Appendix 11C: The standard error of b
12 Methods based on rank order
12.1 Non-parametric methods
12.2 The Mann-Whitney U test
12.3 The Wilcoxon matched pairs test
12.4 Spearman's rank correlation coefficient, rho
12.5 Kendall's rank correlation coefficient, tau
12.6 Continuity corrections
12.7 Parametric or non-parametric methods?
12.8 Multiple choice questions: Rank-based methods
12.9 Exercise: Some applications of rank-based methods
13 The analysis of cross-tabulations
13.1 The chi-squared test for association
13.2 Tests for 2 by 2 tables
13.3 The chi-squared test for small samples
13.4 Fisher's exact test
13.5 Yates' continuity correction for the 2 by 2 table
13.6 The validity of Fisher's and Yates' methods
13.7 Odds and odds ratios
13.8 The chi-squared test for trend
13.9 Methods for matched samples
13.10 The chi-squared goodness of fit test
13.11 Multiple choice questions: Categorical data
13.12 Exercise: Some analyses of categorical data
Appendix 13A: Why the chi-squared test works
Appendix 13B: The formula for Fisher's exact test
Appendix 13C: Standard error for the log odds ratio
14 Choosing the statistical method
14.1 Method oriented and problem oriented teaching
14.2 Types of data
14.3 Comparing two groups
14.4 One sample and paired samples
14.5 Relationship between two variables
14.6 Multiple choice questions: Choice of statistical method
14.7 Exercise: Choosing a statistical method
15 Multifactorial methods
15.1 Multiple regression
15.2 Significance tests and estimation in multiple regression
15.3 Using multiple regression for adjustment
15.4 Transformations in multiple regression
15.5 Interaction in multiple regression
15.6 Polynomial regression
15.7 Assumptions of multiple regression
15.8 Qualitative predictor variables
15.9 Multi-way analysis of variance
15.10 Logistic regression
15.11 Stepwise regression
15.12 Seasonal effects
15.13 Dealing with counts: Poisson regression and negative binomial regression
15.14 Other regression methods
15.15 Data where observations are not independent
15.16 Multiple choice questions: Multifactorial methods
15.17 Exercise: A multiple regression analysis
16 Time to event data
16.1 Time to event data
16.2 Kaplan-Meier survival curves
16.3 The logrank test
16.4 The hazard ratio
16.5 Cox regression
16.6 Multiple choice questions: Time to event data
16.7 Exercise: Survival after retirement
17 Meta-analysis
17.1 What is a meta-analysis?
17.2 The forest plot
17.3 Getting a pooled estimate
17.4 Heterogeneity
17.5 Measuring heterogeneity
17.6 Investigating sources of heterogeneity
17.7 Random effects models
17.8 Continuous outcome variables
17.9 Dichotomous outcome variables
17.10 Time to event outcome variables
17.11 Individual participant data meta-analysis
17.12 Publication bias
17.13 Network meta-analysis
17.14 Multiple choice questions: Meta-analysis
17.15 Exercise: Dietary sugars and body weight
18 Determination of sample size
18.1 Estimation of a population mean
18.2 Estimation of a population proportion
18.3 Sample size for significance tests
18.4 Comparison of two means
18.5 Comparison of two proportions
18.6 Detecting a correlation
18.7 Accuracy of the estimated sample size
18.8 Trials randomized in clusters
18.9 Multiple choice questions: Sample size
18.10 Exercise: Estimation of sample sizes
19 Missing data
19.1 The problem of missing data
19.2 Types of missing data
19.3 Using the sample mean
19.4 Last observation carried forward
19.5 Simple imputation
19.6 Multiple imputation
19.7 Why we should not ignore missing data
19.8 Multiple choice questions: Missing data
19.9 Exercise: Last observation carried forward
20 Clinical measurement
20.1 Making measurements
20.2 Repeatability and measurement error
20.3 Assessing agreement using Cohen's kappa
20.4 Weighted kappa
20.5 Comparing two methods of measurement
20.6 Sensitivity and specificity
20.7 Normal range or reference interval
20.8 Centile charts
20.9 Combining variables using principal components analysis
20.10 Composite scales and subscales
20.11 Internal consistency of scales and Cronbach's alpha
20.12 Presenting composite scales
20.13 Multiple choice questions: Measurement
20.14 Exercise: Two measurement studies
21 Mortality statistics and population structure
21.1 Mortality rates
21.2 Age standardization using the direct method
21.3 Age standardization by the indirect method
21.4 Demographic life tables
21.5 Vital statistics
21.6 The population pyramid
21.7 Multiple choice questions: Population and mortality
21.8 Exercise: Mortality and type 1 diabetes
22 The Bayesian approach
22.1 Bayesians and Frequentists
22.2 Bayes' theorem
22.3 An example: the Bayesian approach to computer-aided diagnosis
22.4 The Bayesian and frequency views of probability
22.5 An example of Bayesian estimation
22.6 Prior distributions
22.7 Maximum likelihood
22.8 Markov Chain Monte Carlo methods
22.9 Bayesian or Frequentist?
22.10 Multiple choice questions: Bayesian methods
22.11 Exercise: A Bayesian network meta-analysis
Appendix 1: Suggested answers to multiple choice questions and exercises
References
Index
