An Introduction to Medical Statistics

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Cover Preface to the Fourth Edition Contents Detailed Contents Chapter 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 Chapter 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 Chapter 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 Exercise: Campylobacter jejuni infection Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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, ρ 12.5 Kendall's rank correlation coefficient, τ 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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