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Understanding biostatistics / by Anders Kallen. — Oxford : Wiley-Blackwell, 2011. – (58.1057/K14) |
Contents
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
4.4 The law: a non-quantitative analogue
4.5 Risks in statistical testing
4.6 Making statements about a binomial parameter
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
5.5 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
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
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
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
