Understanding Biostatistics -- Contents -- Preface -- 1 Statistics and medical science -- 1.1 Introduction -- 1.2 On the nature of science -- 1.3 How the scientific method uses statistics -- 1.4 Finding an outcome variable to assess your hypothesis -- 1.5 How we draw medical conclusions from statistical results -- 1.6 A few words about probabilities -- 1.7 The need for honesty: the multiplicity issue -- 1.8 Prespecification and p-value history -- 1.9 Adaptive designs: controlling the risks in an experiment -- 1.10 The elusive concept of probability -- 1.11 Comments and further reading -- References -- 2 Observational studies and the need for clinical trials -- 2.1 Introduction -- 2.2 Investigations of medical interventions and risk factors -- 2.3 Observational studies and confounders -- 2.4 The experimental study -- 2.5 Population risks and individual risks -- 2.6 Confounders, Simpson's paradox and stratification -- 2.7 On incidence and prevalence in epidemiology -- 2.8 Comments and further reading -- References -- 3 Study design and the bias issue -- 3.1 Introduction -- 3.2 What bias is all about -- 3.3 The need for a representative sample: on selection bias -- 3.4 Group comparability and randomization -- 3.5 Information bias in a cohort study -- 3.6 The study, or placebo, effect -- 3.7 The curse of missing values -- 3.8 Approaches to data analysis: avoiding self-inflicted bias -- 3.9 On meta-analysis and publication bias -- 3.10 Comments and further reading -- References -- 4 The anatomy of a statistical test -- 4.1 Introduction -- 4.2 Statistical tests, medical diagnosis and Roman law -- 4.3 The risks with medical diagnosis -- 4.3.1 Medical diagnosis based on a single test -- 4.3.2 Bayes' theorem and the use and misuse of screening tests -- 4.4 The law: a non-quantitative analogue -- 4.5 Risks in statistical testing.

4.5.1 Does tonsillectomy increase the risk of Hodgkin's lymphoma? -- 4.5.2 General discussion about statistical tests -- 4.6 Making statements about a binomial parameter -- 4.6.1 The frequentist approach -- 4.6.2 The Bayesian approach -- 4.7 The bell-shaped error distribution -- 4.8 Comments and further reading -- References -- 4.A Appendix: The evolution of the central limit theorem -- 5 Learning about parameters, and some notes on planning -- 5.1 Introduction -- 5.2 Test statistics described by parameters -- 5.3 How we describe our knowledge about a parameter from an experiment -- 5.4 Statistical analysis of two proportions -- 5.4.1 Some ways to compare two proportions -- 5.4.2 Analysis of the group difference -- 5.5 Adjusting for confounders in the analysis -- 5.6 The power curve of an experiment -- 5.7 Some confusing aspects of power calculations -- 5.8 Comments and further reading -- References -- 5.A Appendix: Some technical comments -- 5.A.1 The non-central hypergeometric distribution and 2 × 2 tables -- 5.A.2 The gamma and χ2 distributions -- 6 Empirical distribution functions -- 6.1 Introduction -- 6.2 How to describe the distribution of a sample -- 6.3 Describing the sample: descriptive statistics -- 6.4 Population distribution parameters -- 6.5 Confidence in the CDF and its parameters -- 6.6 Analysis of paired data -- 6.7 Bootstrapping -- 6.8 Meta-analysis and heterogeneity -- 6.9 Comments and further reading -- References -- 6.A Appendix: Some technical comments -- 6.A.1 The extended family of the univariate Gaussian distributions -- 6.A.2 The Wiener process and its bridge -- 6.A.3 Confidence regions for the CDF and the Kolmogorov-Smirnov test -- 7 Correlation and regression in bivariate distributions -- 7.1 Introduction -- 7.2 Bivariate distributions and correlation -- 7.3 On baseline corrections and other covariates.

7.4 Bivariate Gaussian distributions -- 7.5 Regression to the mean -- 7.6 Statistical analysis of bivariate Gaussian data -- 7.7 Simultaneous analysis of two binomial proportions -- 7.8 Comments and further reading -- References -- 7.A Appendix: Some technical comments -- 7.A.1 The regression to the mode equation -- 7.A.2 Analysis of data from the multivariate Gaussian distribution -- 7.A.3 On the geometric approach to univariate confidence limits -- 8 How to compare the outcome in two groups -- 8.1 Introduction -- 8.2 Simple models that compare two distributions -- 8.3 Comparison done the horizontal way -- 8.4 Analysis done the vertical way -- 8.5 Some ways to compute p-values -- 8.6 The discrete Wilcoxon test -- 8.7 The two-period crossover trial -- 8.8 Multivariate analysis and analysis of covariance -- 8.9 Comments and further reading -- References -- 8.A Appendix: About U-statistics -- 9 Least squares, linear models and beyond -- 9.1 Introduction -- 9.2 The purpose of mathematical models -- 9.3 Different ways to do least squares -- 9.4 Logistic regression, with variations -- 9.5 The two-step modeling approach -- 9.6 The effect of missing covariates -- 9.7 The exponential family of distributions -- 9.8 Generalized linear models -- 9.9 Comments and further reading -- References -- 10 Analysis of dose response -- 10.1 Introduction -- 10.2 Dose-response relationship -- 10.3 Relative dose potency and therapeutic ratio -- 10.4 Subject-specific and population averaged dose response -- 10.5 Estimation of the population averaged dose-response relationship -- 10.6 Estimating subject-specific dose responses -- 10.7 Comments and further reading -- References -- 11 Hazards and censored data -- 11.1 Introduction -- 11.2 Censored observations: incomplete knowledge -- 11.3 Hazard models from a population perspective -- 11.4 The impact of competing risks.

11.5 Heterogeneity in survival analysis -- 11.6 Recurrent events and frailty -- 11.7 The principles behind the analysis of censored data -- 11.8 The Kaplan-Meier estimator of the CDF -- 11.9 Comments and further reading -- References -- 11.A Appendix: On the large-sample approximations of counting processes -- 12 From the log-rank test to the Cox proportional hazards model -- 12.1 Introduction -- 12.2 Comparing hazards between two groups -- 12.3 Nonparametric tests for hazards -- 12.4 Parameter estimation in hazard models -- 12.5 The accelerated failure time model -- 12.6 The Cox proportional hazards model -- 12.7 On omitted covariates and stratification in the log-rank test -- 12.8 Comments and further reading -- References -- 12.A Appendix: Comments on interval-censored data -- 13 Remarks on some estimation methods -- 13.1 Introduction -- 13.2 Estimating equations and the robust variance estimate -- 13.3 From maximum likelihood theory to generalized estimating equations -- 13.4 The analysis of recurrent events -- 13.5 Defining and estimating mixed effects models -- 13.6 Comments and further reading -- References -- 13.A Appendix: Formulas for first-order bias -- Index.