Practical statistics for medical research

[Title page]......Page 3
[Contents]......Page 6
Preface......Page 9
1.1 Statistics at large......Page 13
1.2 Statistics in medicine......Page 15
1.3 Statistics in medical research......Page 16
1.4 What does statistics cover?......Page 17
1.5 The scope of this book......Page 20
2.2 Categorical data......Page 22
2.3 Numerical data......Page 23
2.4 Other types of data......Page 25
2.5 Censored data......Page 28
2.8 Dealing with numbers......Page 29
3.1 Introduction......Page 31
3.2 Averages......Page 33
3.3 Describing variability......Page 34
3.4 Quantifying variability......Page 43
3.5 Two variables......Page 50
3.6 The effect of transforming the data......Page 53
3.7 Data presentation......Page 54
Exercises......Page 57
4.1 Introduction......Page 60
4.2 Probability......Page 61
4.4 Probability distributions......Page 62
4.5 The Normal distribution......Page 63
4.6 The Lognormal distributions......Page 72
4.7 The Binomial distribution......Page 75
4.8 The Poisson distribution......Page 78
4.9 Mathematical calculations......Page 80
Exercises......Page 83
5.1 Introduction......Page 86
5.2 Categories of research design......Page 87
5.3 Sources of variation......Page 90
5.4 An experiment: is the blood pressure the same in both arms?......Page 91
5.5 The design of experiments......Page 92
5.6 The structure of an experiment......Page 95
5.7 Random allocation......Page 97
5.9 Observational studies......Page 103
5.10 The case-control study......Page 105
5.11 The cohort study......Page 108
5.12 The cross-sectional study......Page 111
5.13 Studies of change over time......Page 113
5.14 Choosing a study design......Page 114
Exercises......Page 115
6.2 Advantages of using a computer......Page 119
6.3 Disadvantages of using a computer......Page 120
6.4 Types of statistical program......Page 122
6.5 Evaluating a statistical package......Page 123
6.6 Strategy for computer-aided analysis......Page 124
6.7 Forms for data collection......Page 126
6.8 Plotting......Page 131
6.10 Misuses of the computer......Page 132
6.11 Concluding remarks......Page 133
7.2 Data checking......Page 134
7.3 Outliers......Page 138
7.4 Missing data......Page 142
7.5 Data screening......Page 144
7.6 Why transform data?......Page 155
7.7 Other features of the data......Page 158
Exercises......Page 161
8.1 Introduction......Page 164
8.2 Sampling distributions......Page 165
8.3 A demonstration of the distribution of sample means......Page 167
8.4 Estimation......Page 172
8.5 Hypothesis testing......Page 177
8.6 Non-parametric methods......Page 183
8.7 Statistical modelling......Page 185
8.8 Estimation or hypothesis testing?......Page 186
8.9 Strategy for analysing data......Page 187
8.10 Presentation of results......Page 188
Exercises......Page 189
9.2 Choosing an appropriate method of analysis......Page 191
9.3 The t distribution......Page 193
9.4 One group of observations......Page 195
9.5 Two groups of paired observations......Page 201
9.6 Two independent groups of observations......Page 203
9.7 Analysis of skewed data......Page 211
9.8 Three or more independent groups of observations......Page 217
9.9 One way analysis of variance – mathematics and worked example......Page 230
9.10 Presentation of results......Page 232
9.11 Summary......Page 234
Exercises......Page 235
10.1 Introduction......Page 241
10.2 One proportion......Page 242
10.3 Proportions in two independent groups......Page 244
10.4 Two paired proportions......Page 247
10.6 The analysis of frequency tables......Page 253
10.7 2 × 2 frequency tables – comparison of two proportions......Page 262
10.8 2 × k tables – comparison of several proportions......Page 271
10.9 Large tables with ordered categories......Page 277
10.11 Comparing risks......Page 278
10.13 Summary......Page 283
Exercises......Page 284
11.1 Association, prediction and agreement......Page 289
11.2 Correlation......Page 290
11.3 Use and misuse of correlation......Page 294
11.4 Rank correlation......Page 297
11.5 Adjusting a correlation for another variable......Page 300
11.6 Use of the correlation coefficient in assessing non-Normality......Page 303
11.7 Correlation – mathematics and worked examples......Page 305
11.8 Interpretation of correlation......Page 308
11.10 Regression......Page 311
11.11 Use of regression......Page 318
11.12 Extensions......Page 321
11.13 Regression – mathematics and worked example......Page 322
11.14 Interpretation of regression......Page 328
11.15 Relation to other analyses......Page 330
11.16 Presentation of regression......Page 331
11.17 Regression or correlation?......Page 332
Exercises......Page 333
12.2 Analysis of variance and multiple regression......Page 337
12.3 Two way analysis of variance......Page 338
12.4 Multiple regression......Page 348
12.5 Logistic regression......Page 363
12.6 Discriminant analysis......Page 370
12.7 Other methods......Page 372
Exercises......Page 373
13.1 Introduction......Page 377
13.2 Survival probabilities......Page 379
13.3 Comparing survival curves in two groups......Page 383
13.4 Mathematical calculations and worked examples......Page 389
13.5 Incorrect analyses......Page 397
13.6 Modelling survival – the Cox regression model......Page 399
13.8 Presentation of results ......Page 405
Exercises ......Page 406
14.2 Method comparison studies ......Page 408
14.3 Inter-rater agreement ......Page 415
14.4 Diagnostic tests ......Page 421
14.5 Reference intervals ......Page 431
14.6 Serial measurements ......Page 438
14.7 Cyclic variation ......Page 445
Exercises ......Page 447
15.1 Introduction ......Page 452
15.2 Design of clinical trials ......Page 453
15.3 Sample size ......Page 467
15.4 Analysis ......Page 473
15.5 Interpretation of results ......Page 483
15.6 Writing up and assessing clinical trials ......Page 485
Exercises ......Page 486
16.1 Introduction ......Page 489
16.2 The growth of statistics in medical research ......Page 490
16.3 Statistics in published papers ......Page 493
16.4 Reading a scientific paper ......Page 505
16.5 Writing a scientific paper ......Page 510
Exercises ......Page 511
A1.2 Basic ideas ......Page 517
A1.3 Mathematical symbols ......Page 521
A1.5 Glossary of notation ......Page 522
B1 The Normal distribution – areas in one tail (z → P)......Page 526
B2 The Normal distribution – two-tailed areas (z → P)......Page 530
B3 The Normal distribution – standard Normal deviates corresponding to specific two-sided tail areas (P → z)......Page 532
B4 The t distribution......Page 533
B5 The Chi squared (χ²) distribution......Page 535
B6 The F distribution......Page 536
B7 Pearson’s correlation coefficient (r)......Page 540
B8 Spearman’s rank correlation coefficient (r_s)......Page 542
B9 The Wilcoxon one sample (or matched pairs) test......Page 543
B10 The Mann-Whitney test (Wilcoxon two sample test)......Page 544
B11 Ranks for obtaining a confidence interval for the median......Page 547
B12 The Shapiro-Francia W' test of non-Normality......Page 550
B13 Random digits......Page 552
Answers to exercises ......Page 558
References ......Page 587
Index ......Page 601