Statistical Methods in Medical Research

by Armitage, Peter; Berry, Geoffrey; Matthews, J. N. S.

• ISBN13: 9780632052578
• ISBN10: 0632052570
• Edition: 4th
• Format: Hardcover
• Copyright: 2001-11-28
• Publisher: Wiley-Blackwell

Summary

The explanation and implementation of statistical methods for the medical researcher or statistician remains an integral part of modern medical research. This book explains the use of experimental and analytical biostatistics systems. Its accessible style allows it to be used by the non-mathematician as a fundamental component of successful research.Since the third edition, there have been many developments in statistical techniques. The fourth edition provides the medical statistician with an accessible guide to these techniques and to reflect the extent of their usage in medical research.The new edition takes a much more comprehensive approach to its subject. There has been a radical reorganization of the text to improve the continuity and cohesion of the presentation and to extend the scope by covering many new ideas now being introduced into the analysis of medical research data. The authors have tried to maintain the modest level of mathematical exposition that characterized the earlier editions, essentially confining the mathematics to the statement of algebraic formulae rather than pursuing mathematical proofs.Received the Highly Commended Certificate in the Public Health Category of the 2002 BMA Books Competition.

Author Biography

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.

Table of Contents

Preface to the fourth edition	ix
The scope of statistics	1	(7)
Describing data	8	(39)
Diagrams	8	(3)
Tabulation and data processing	11	(8)
Summarizing numerical data	19	(12)
Means and other measures of location	31	(2)
Taking logs	33	(3)
Measures of variation	36	(8)
Outlaying observations	44	(3)
Probability	47	(36)
The meaning of probability	47	(3)
Probability calculations	50	(4)
Bayes' theorem	54	(5)
Probability distributions	59	(4)
Expectation	63	(2)
The binomial distribution	65	(6)
The Poisson distribution	71	(5)
The normal (or Gaussian) distribution	76	(7)
Analysing means and proportions	83	(64)
Statistical inference: tests and estimation	83	(9)
Inferences from means	92	(10)
Comparison of two means	102	(10)
Inferences from proportions	112	(8)
Comparison of two proportions	120	(17)
Sample-size determination	137	(10)
Analysing variances, counts and other measures	147	(18)
Inferences from variances	147	(6)
Inferences from counts	153	(5)
Ratios and other functions	158	(4)
Maximum likelihood estimation	162	(3)
Bayesian methods	165	(22)
Subjective and objective probability	165	(3)
Bayesian inference for a mean	168	(7)
Bayesian inference for proportions and counts	175	(4)
Further comments on Bayesian methods	179	(4)
Empirical Bayesian methods	183	(4)
Regression and correlation	187	(21)
Association	187	(2)
Linear regression	189	(6)
Correlation	195	(3)
Sampling errors in regression and correlation	198	(6)
Regression to the mean	204	(4)
Comparison of several groups	208	(28)
One-way analysis of variance	208	(7)
The method of weighting	215	(3)
Components of variance	218	(5)
Multiple comparisons	223	(4)
Comparison of several proportions: the 2 x k contingency table	227	(4)
General contingency tables	231	(2)
Comparison of several variances	233	(1)
Comparison of several counts: the Poisson heterogeneity test	234	(2)
Experimental design	236	(36)
General remarks	236	(2)
Two-way analysis of variance: randomized blocks	238	(8)
Factorial designs	246	(11)
Latin squares	257	(4)
Other incomplete designs	261
Split-unit designs	256	(16)
Analysing non-normal data	272	(40)
Distribution-free methods	272	(1)
One-sample tests for location	273	(4)
Comparison of two independent groups	277	(8)
Comparison of several groups	285	(4)
Rank correlation	289	(3)
Permutation and Monte Carlo tests	292	(6)
The bootstrap and the jack knife	298	(8)
Transformations	306	(6)
Modelling continuous data	312	(66)
Analysis of variance applied to regression	312	(5)
Errors in both variables	317	(3)
Straight lines through the origin	320	(2)
Regression in groups	322	(9)
Analysis of covariance	331	(6)
Multiple regression	337	(10)
Multiple regression in groups	347	(7)
Multiple regression in the analysis of non-orthogonal data	354	(2)
Checking the model	356	(19)
More on data transformation	375	(3)
Further regression models for a continuous response	378	(77)
Polynomial regression	378	(9)
Smoothing and non-parametric regression	387	(10)
Reference ranges	397	(11)
Non-linear regression	408	(10)
Multilevel models	418	(12)
Longitudinal data	430	(19)
Time series	449	(6)
Multivariate methods	455	(30)
General	455	(1)
Principal components	456	(8)
Discriminant analysis	464	(17)
Cluster analysis	481	(2)
Concluding remarks	483	(2)
Modelling categorical data	485	(18)
Introduction	485	(3)
Logistic regression	488	(8)
Polytomous regression	496	(3)
Poisson regression	499	(4)
Empirical methods for categorical data	503	(25)
Introduction	503	(1)
Trends in proportions	504	(5)
Trends in larger contingency tables	509	(2)
Trends in counts	511	(1)
Other components of x2	512	(4)
Combination of 2 x 2 tables	516	(5)
Combination of larger tables	521	(3)
Exact tests for contingency tables	524	(4)
Further Bayesian methods	528	(40)
Background	528	(1)
Prior and posterior distributions	529	(9)
The Bayesian linear model	538	(10)
Markov chain Monte Carlo methods	548	(12)
Model assessment and model choice	560	(8)
Survival analysis	568	(23)
Introduction	568	(1)
Life-tables	569	(2)
Follow-up studies	571	(3)
Sampling errors in the life-table	574	(1)
The Kaplan-Meier estimator	575	(1)
The logrank test	576	(6)
Parametric methods	582	(1)
Regression and proportional-hazards models	583	(5)
Diagnostic methods	588	(3)
Clinical trials	591	(57)
Introduction	591	(1)
Phase I and Phase II trials	592	(2)
Planning a Phase III trial	594	(6)
Treatment assignment	600	(4)
Assessment of response	604	(2)
Protocol departures	606	(7)
Data monitoring	613	(10)
Interpretation of trial results	623	(4)
Special designs	627	(14)
Meta-analysis	641	(7)
Statistical methods in epidemiology	648	(69)
Introduction	648	(1)
The planning of surveys	649	(10)
Rates and standardization	659	(8)
Surveys to investigate associations	667	(4)
Relative risk	671	(11)
Attributable risk	682	(3)
Subject-years method	685	(4)
Age-period-cohort analysis	689	(3)
Diagnostic tests	692	(6)
Kappa measure of agreement	698	(6)
Intraclass correlation	704	(3)
Disease screening	707	(4)
Disease clustering	711	(6)
Laboratory assays	717	(26)
Biological assay	717	(2)
Parallel-line assays	719	(5)
Slope-ratio assays	724	(3)
Quantal-response assays	727	(3)
Some special assays	730	(10)
Tumour incidence studies	740	(3)
Appendix tables	743	(17)
A1 Areas in tail of the normal distribution	744	(2)
A2 Percentage points of the X2 distribution	746	(2)
A3 Percentage points of the t distribution	748	(2)
A4 Percentage points of the F distribution	750	(4)
A5 Percentage points of the distribution of Studentized range	754	(2)
A6 Percentage points for the Wilcoxon signed rank sum test	756	(1)
A7 Percentage points for the Wilcoxon two-sample rank sum test	757	(1)
A8 Sample size for comparing two proportions	758	(1)
A9 Sample size for detecting relative risk in case-control study	759	(1)
References	760	(25)
Author index	785	(10)
Subject index	795