Statistical Methods in Medical Research (eBook)

Peter Armitage has a Cambridge M.A. in mathematics and a London Ph.D, in Statistics. He was a Statistician for the Medical Research Council from 1947-61, and Professor of Medical Statistics at the London School of Hygiene and Tropical Medicine from 1961-76. He then moved to Oxford, first as Professor of Biomathematics, later as Professor of Applied Statistics and head of the new Department of Statistics, retiring in 1990. His research has centred around the development of methods for medical statistics, especially clinical trials. He is a Past President of the International Biometric Society, International Society for Clinical Biostatistics, and Royal Statistical Society, and edited Biometrics 1980-84. He was appointed C.B.E. in 1984. Geoffrey Berry is an Emeritus Professor of Epidemiology and Biostatistics at the School of Public Health, University of Sydney School of Medicine.

Contents 7
Preface to the fourth edition 11
1 The scope of statistics 15
2 Describing data 22
2.1 Diagrams 22
2.2 Tabulation and data processing 25
2.3 Summarizing numerical data 33
2.4 Means and other measures of location 45
2.5 Taking logs 47
2.6 Measures of variation 50
2.7 Outlying observations 58
3 Probability 61
3.1 The meaning of probability 61
3.2 Probability calculations 64
3.3 Bayes' theorem 68
3.4 Probability distributions 73
3.5 Expectation 77
3.6 The binomial distribution 79
3.7 The Poisson distribution 85
3.8 The normal (or Gaussian) distribution 90
4 Analysing means and proportions 97
4.1 Statistical inference: tests and estimation 97
4.2 Inferences from means 106
4.3 Comparison of two means 116
4.4 Inferences from proportions 126
4.5 Comparison of two proportions 135
4.6 Sample-size determination 151
5 Analysing variances, counts and other measures 161
5.1 Inferences from variances 161
5.2 Inferences from counts 167
5.3 Ratios and other functions 172
5.4 Maximum likelihood estimation 176
6 Bayesian methods 179
6.1 Subjective and objective probability 179
6.2 Bayesian inference for a mean 182
6.3 Bayesian inference for proportions and counts 189
6.4 Further comments on Bayesian methods 193
6.5 Empirical Bayesian methods 197
7 Regression and correlation 201
7.1 Association 201
7.2 Linear regression 203
7.3 Correlation 209
7.4 Sampling errors in regression and correlation 212
7.5 Regression to the mean 218
8 Comparison of several groups 222
8.1 One-way analysis of variance 222
8.2 The method of weighting 229
8.3 Components of variance 232
8.4 Multiple comparisons 237
8.5 Comparison of several proportions: the 2 x k contingency table 241
8.6 General contingency tables 245
8.7 Comparison of several variances 247
8.8 Comparison of several counts: the Poisson heterogeneity test 248
9 Experimental design 250
9.1 General remarks 250
9.2 Two-way analysis of variance: randomized blocks 252
9.3 Factorial designs 260
9.4 Latin squares 271
9.5 Other incomplete designs 275
9.6 Split-unit designs 279
10 Analysing non-normal data 326
10.1 Distribution-free methods 286
10.2 One-sample tests for location 287
10.3 Comparison of two independent groups 291
10.4 Comparison of several groups 299
10.5 Rank correlation 303
10.6 Permutation and Monte Carlo tests 306
10.7 The bootstrap and the jackknife 312
10.8 Transformations 320
11 Modelling continuous data 7
11.1 Analysis of variance applied to regression 326
11.2 Errors in both variables 331
11.3 Straight lines through the origin 334
11.4 Regression in groups 336
11.5 Analysis of covariance 345
11.6 Multiple regression 351
11.7 Multiple regression in groups 361
11.8 Multiple regression in the analysis of non-orthogonal data 368
11.9 Checking the model 370
11.10 More on data transformation 389
12 Further regression models for a continuous response 392
12.1 Polynomial regression 392
12.2 Smoothing and non-parametric regression 401
12.3 Reference ranges 411
12.4 Non-linear regression 422
12.5 Multilevel models 432
12.6 Longitudinal data 444
12.7 Time series 463
13 Multivariate methods 469
13.1 General 469
13.2 Principal components 470
13.3 Discriminant analysis 478
13.4 Cluster analysis 495
13.5 Concluding remarks 497
14 Modelling categorical data 499
14.1 Introduction 499
14.2 Logistic regression 502
14.3 Polytomous regression 510
14.4 Poisson regression 513
15 Empirical methods for categorical data 517
15.1 Introduction 517
15.2 Trends in proportions 518
15.3 Trends in larger contingency tables 523
15.4 Trends in counts 525
15.5 Other components of X2 526
15.6 Combination of 2 x 2 tables 530
15.7 Combination of larger tables 535
15.8 Exact tests for contingency tables 538
16 Further Bayesian methods 542
16.1 Background 542
16.2 Prior and posterior distributions 543
16.3 The Bayesian linear model 552
16.4 Markov chain Monte Carlo methods 563
16.5 Model assessment and model choice 574
17 Survival analysis 582
17.1 Introduction 582
17.2 Life-tables 583
17.3 Follow-up studies 585
17.4 Sampling errors in the life-table 588
17.5 The Kaplan-Meier estimator 589
17.6 The logrank test 590
17.7 Parametric methods 596
17.8 Regression and proportional-hazards models 597
17.9 Diagnostic methods 602
18 Clinical trials 605
18.1 Introduction 605
18.2 Phase I and Phase II trials 606
18.3 Planning a Phase III trial 608
18.4 Treatment assignment 614
18.5 Assessment of response 618
18.6 Protocol departures 620
18.7 Data monitoring 627
18.8 Interpretation of trial results 637
18.9 Special designs 641
18.10 Meta-analysis 655
19 Statistical methods in epidemiology 662
19.1 Introduction 662
19.2 The planning of surveys 663
19.3 Rates and standardization 673
19.4 Surveys to investigate associations 681
19.5 Relative risk 685
19.6 Attributable risk 696
19.7 Subject-years method 699
19.8 Age-period-cohort analysis 703
19.9 Diagnostic tests 706
19.10 Kappa measure of agreement 712
19.11 Intraclass correlation 718
19.12 Disease screening 721
19.13 Disease clustering 725
20 Laboratory assays 731
20.1 Biological assay 731
20.2 Parallel-line assays 733
20.3 Slope-ratio assays 738
20.4 Quantal-response assays 741
20.5 Some special assays 744
20.6 Tumour incidence studies 754
Appendix tables 757
A1 Areas in tail of the normal distribution 758
A2 Percentage points of the X2 distribution 760
A3 Percentage points of the t distribution 762
A4 Percentage points of the F distribution 764
A5 Percentage points of the distribution of Studentized range 768
A6 Percentage points for the Wilcoxon signed rank sum test 770
A7 Percentage points for the Wilcoxon two-sample rank sum test 771
A8 Sample size for comparing two proportions 772
A9 Sample size for detecting relative risk in case-control study 773
References 774
Author index 799
Subject index 809

On the fourth edition:

'...this breakthrough revision of a classic...is truly
excellent: comprehensive, informative, able to be read at a variety
of levels by a variety of readers, modern and insightful.'

Statistics in Medicine, Volume 22, 2003

'...this is a volume which could usefully, and perhaps should,
be read from cover to cover by anyone embarking on the study of
medical statistics. For those already working in the area, it
should at least be on their bookshelves.'

Short Book Reviews, Volume 22, Number 2, August 2002

'...each edition has improved and expanded considerably on the
last, keeping pace with the ever-changing field of medical
statistics...'

eMJA Bookroom, 2002

On previous editions:

'...this is an excellent book...I strongly recommend this
book...'

International Society for Clinical Biostatistics, December
1997

'...this classical beauty has aged well.'

International Statistical Institute, April 1996

'...readers who...use statistical analysis...must buy this third
edition'

Australian-New Zealand Journal of Surgery, Spring 1995

'...the standard text for professional medical
statisticians.'

Aslib Book Guide, November 1994