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Biostatistical Methods: The Assessment of Relative Risks, 2nd Edition

Biostatistical Methods: The Assessment of Relative Risks, 2nd Edition

John M. Lachin

ISBN: 978-1-118-62584-2

Aug 2014

672 pages



Praise for the First Edition

". . . an excellent textbook . . . an indispensable reference for biostatisticians and epidemiologists."
International Statistical Institute

A new edition of the definitive guide to classical and modern methods of biostatistics

Biostatistics consists of various quantitative techniques that are essential to the description and evaluation of relationships among biologic and medical phenomena. Biostatistical Methods: The Assessment of Relative Risks, Second Edition develops basic concepts and derives an expanded array of biostatistical methods through the application of both classical statistical tools and more modern likelihood-based theories. With its fluid and balanced presentation, the book guides readers through the important statistical methods for the assessment of absolute and relative risks in epidemiologic studies and clinical trials with categorical, count, and event-time data.

Presenting a broad scope of coverage and the latest research on the topic, the author begins with categorical data analysis methods for cross-sectional, prospective, and retrospective studies of binary, polychotomous, and ordinal data. Subsequent chapters present modern model-based approaches that include unconditional and conditional logistic regression; Poisson and negative binomial models for count data; and the analysis of event-time data including the Cox proportional hazards model and its generalizations. The book now includes an introduction to mixed models with fixed and random effects as well as expanded methods for evaluation of sample size and power. Additional new topics featured in this Second Edition include:

  • Establishing equivalence and non-inferiority
  • Methods for the analysis of polychotomous and ordinal data, including matched data and the Kappa agreement index
  • Multinomial logistic for polychotomous data and proportional odds models for ordinal data
  • Negative binomial models for count data as an alternative to the Poisson model
  • GEE models for the analysis of longitudinal repeated measures and multivariate observations

Throughout the book, SAS is utilized to illustrate applications to numerous real-world examples and case studies. A related website features all the data used in examples and problem sets along with the author's SAS routines.

Biostatistical Methods, Second Edition is an excellent book for biostatistics courses at the graduate level. It is also an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.


Preface to First Edition. 

1 Biostatistics and Biomedical Science.

1.1 Statistics and the Scientific Method.

1.2 Biostatistics.

1.3 Natural History of Disease Progression.

1.4 Types of Biomedical Studies.

1.5 Studies of Diabetic Nephropathy.

2 Relative Risk Estimates and Tests for Independent Groups.

2.1 Probability As a Measure of Risk.

2.2 Measures of Relative Risk.

2.3 Large Sample Distribution.

2.4 Sampling Models Likelihoods.

2.5 Exact Inference.

2.6 Large Sample Inferences.


2.8 Other Measures of Differential Risk.

2.9 Polychotomous and Ordinal Data.

2.10 Two Independent Groups With Polychotomous Response.

2.11 Multiple Independent Groups.

2.12 Problems.

3 Sample Size, Power, and Efficiency.

3.1 Estimation Precision.

3.2 Power of Z-Tests.

3.3 Test for Two Proportions.

3.4 Power of Chi-Square Tests.


3.6 Efficiency.

3.7 Problems.

4 Stratified-Adjusted Analysis for Independent Groups.

4.1 Introduction.

4.2 Mantel-Haenszel Test and Cochran’s Test.

4.3 Stratified-Adjusted Estimators.

4.4 Nature of Covariate Adjustment.

4.5 Multivariate Tests of Hypotheses.

4.6 Tests of Homogeneity.

4.7 Efficient Tests of No Partial Association.

4.8 Asymptotic Relative Efficiency of Competing Tests.

4.9 Maximin-Efficient Robust Tests.

4.10 Random Effects Model.

4.11 Power and Sample Size for Tests of Association.

4.12 Polychotomous and Ordinal Data.

4.13 Problems.

5 Case-Control and Matched Studies.

5.1 Unmatched Case-Control (Retrospective) Sampling.

5.2 Matching.

5.3 Tests of Association for Matched Pairs.

5.4 Measures of Association for Matched Pairs.

5.5 Pair-Matched Retrospective Study.

5.6 Power Function of McNemar’s Test.

5.7 Stratified Analysis of Pair-Matched Tables.

5.8 Multiple Matching-Mantel-Haenszel Analysis.

5.9 Matched Polychotomous Data.

5.10 Kappa Index of Agreement. 

5.11 Problems.

6 Applications of Maximum Likelihood and Efficient Scores.

6.1 Binomial.

6.2 2x2 Table: Product Binomial (Unconditionally).

6.3 2x2 Table, Conditionally.

6.4 Score-Based Estimate.

6.5 Stratified Score Analysis of Independent 2x2 Tables.

6.6 Matched Pairs.

6.7 Iterative Maximum Likelihood.

6.8 Problems.

7 Logistic Regression Models.

7.1 Unconditional Logistic Regression Model.

7.2 Interpretation of the Logistic Regression Model.

7.3 Tests of Significance.

7.4 Interactions.

7.5 Measures of the Strength of Association.

7.6 Conditional Logistic Regression Model for Matched Sets.

7.7 Models for Polychotomous or Ordinal Data.

7.8 Random Effects and Mixed Models.

7.9 Models for Multivariate or Repeated Measures.

7.10 Problems.

8 Analysis of Count Data.

8.1 Event Rates and the Homogeneous Poisson Model.

8.2 Over Dispersed Poisson Model.

8.3 Poisson Regression Model.

8.4 Over Dispersed and Robust Poisson Regression.

8.5 Conditional Poisson Regression for Matched Sets.

8.6 Negative Binomial Models.

8.7 Power and Sample Size.

8.8 Multiple Outcomes.

8.9 Problems.

9 Analysis of Event-Time Data.

9.1 Introduction to Survival Analysis.

9.2 Lifetable Construction.

9.3 Family of Weighted Mantel-Haenszel Tests.

9.4 Proportional Hazards Models.

9.5 Evaluation of Sample Size and Power.

9.6 Additional Models.

9.7 Analysis of Recurrent Events.

9.8 Problems.

Appendix Statistical Theory.

A.1 Introduction.

A.2 Central Limit Theorem and the Law of Large Numbers.

A.3 Delta Method.

A.4 Slutsky’s Convergence Theorem.

A.5 Least Squares Estimation.

A.6 Maximum Likelihood Estimation and Efficient Scores.

A.7 Tests of Significance.

A.8 Explained Variation.

A.9 Robust Inference.

A.10 Generalized Linear Models and Quasi-Likelihood.

A.11 Generalized Estimating Equations (GEE).


Author Index.

Subject Index. 

"Biostatistical methods, second edition is an excellent book for biostatistics courses at the graduate level. It is also an invaluable reference for biostatisticians, applied statisticians, and epidemiologists." (Mathematical Reviews, 2011)

"The author of this book has made a tremendous effort in covering a gamut of tests, methods, and ideas for biostatistical problem solving . . . In conclusion, the book is recommended to all in biostatistics as a technical reference." (Journal of Biopharmaceutical Statistics, 1 September 2012)

"...Biostatistics is set apart from other statistics specialties by its focus on the assessment of risks and relative risks through clinical research," states Lachin (George Washington U.) in the preface to the first edition (2001). He developed this graduate text to support a course he launched as a joint initiative of the university's department of statistics, its Biostatistics Center, and the School of Public Health and Health Services. Coverage includes discussion of biostatistics and biomedical science, relative risk estimates and tests for independent groups, sample size, stratified adjusted analysis, case-control and matched studies, applications of maximum likelihood and efficient scores, among other topics." (Book News Inc., February 2011)