PRACTICAL STATISTICS FOR MEDICAL RESEARCH

Transcription

1 PRACTICAL STATISTICS FOR MEDICAL RESEARCH Douglas G. Altman Head of Medical Statistical Laboratory Imperial Cancer Research Fund London CHAPMAN & HALL/CRC Boca Raton London New York Washington, D.C.

2 Contents Preface xi Statistics in medical research Statistics at large Statistics in medicine Statistics in medical research What does statistics cover? The scope of this book Types of data Categorical data Numerical data Other types of data Censored data Variability Importance of the type of data Dealing with numbers Describing data Averages Describing variability Quantifying variability Two variables The effect of transforming the data Data presentation Theoretical distributions Probability Samples and populations Probability distributions The Normal distribution

3 The Lognormal distributions The Binomial distribution The Poisson distribution Mathematical calculations The Uniform distribution Concluding remarks Contents vii Designing research Categories of research design 75 Sources of variation 78 An experiment: is the blood pressure the same in both arms? 79 The design of experiments 80 The structure of an experiment 83 Random allocation 85 Minimization 91 Observational studies 91 The case-control study 93 The cohort study 96 The cross-sectional study 99 Studies of change over time 1 Choosing a study design Using a computer Advantages of using a computer Disadvantages of using a computer Types of statistical program Evaluating a statistical package Strategy for computer-aided analysis Forms for data collection Plotting Other uses of computers Misuses of the computer Concluding remarks Preparing to analyse data Data checking Outliers Missing data Data screening

4 vni Contents Why transform data? Other features of the data Concluding remarks Principles of statistical analysis Sampling distributions A demonstration of the distribution of sample means Estimation Hypothesis testing Non-parametric methods Statistical modelling Estimation or hypothesis testing? Strategy for analysing data Presentation of results Summary Comparing groups - continuous data Choosing an appropriate method of analysis The t distribution One group of observations Two groups of paired observations Two independent groups of observations Analysis of skewed data Three or more independent groups of observations One way analysis of variance - mathematics and worked example Presentation of results Summary Comparing groups - categorical data One proportion Proportions in two independent groups Two paired proportions Comparing several proportions The analysis of frequency tables 2 x 2 frequency tables - comparison of two proportions 2 x k tables - comparison of several proportions Large tables with ordered categories

5 k x k tables - analysis of matched variables Comparing risks Presentation of results Summary Contents ix Relation between two continuous variables 277 Association, prediction and agreement 277 Correlation 278 Use and misuse of correlation 282 Rank correlation 285 Adjusting a correlation for another variable 288 Use of the correlation coefficient in assessing non-normality 291 Correlation - mathematics and worked examples Interpretation of correlation Presentation of correlation Regression Use of regression Extensions Regression - mathematics and worked example Interpretation of regression Relation to other analyses Presentation of regression Regression or correlation? Relation between several variables Analysis of variance and multiple regression Two way analysis of variance Multiple regression Logistic regression Discriminant analysis Other methods Analysis of survival times Survival probabilities Comparing survival curves in two groups Mathematical calculations and worked examples Incorrect analyses Modelling survival - the Cox regression model Desien of survival studies

6 x Contents 13.8 Presentation of results Some common problems in medical research Method comparison studies Inter-rater agreement Diagnostic tests Reference intervals Serial measurements Cyclic variation Clinical trials Design of clinical trials Sample size Analysis Interpretation of results Writing up and assessing clinical trials The medical literature The growth of statistics in medical research Statistics in published papers Reading a scientific paper Writing a scientific paper Appendix A Mathematical notation 505 Al.l 505 A1.2 Basic ideas 505 A1.3 Mathematical symbols 509 A1.4 Functions 5 A1.5 Glossary of notation 5 Appendix B Statistical tables 514 Answers to exercises 546 References 575 Index 589