Biostatistical Methods The Assessment of Relative Risks

About this book

This book focuses on the comparison, contrast, and assessment of risks on the basis of clinical investigations. It develops basic concepts as well as deriving biostatistical methods through both the application of classical mathematical statistical tools and more modern likelihood-based theories. The first half of the book presents methods for the analysis of single and multiple 2x2 tables for cross-sectional, prospective, and retrospective (case-control) sampling, with and without matching using fixed and two-stage random effects models.

The text then moves on to present a more modern likelihood- or model-based approach, which includes unconditional and conditional logistic regression; the analysis of count data and the Poisson regression model; the analysis of event time data, including the proportional hazards and multiplicative intensity models; and elements of categorical data analysis (expanded in this edition). SAS subroutines are both showcased in the text and embellished online by way of a dedicated author website. The book contains a technical, but accessible appendix that presents the core mathematical statistical theory used for the development of classical and modern statistical methods.

Contents

Preface. 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. 2.7 SAS PROC FREQ. 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. 3.5 SAS PROC POWER. 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. 5.11 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 535. 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). References.

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Biography

John M. Lachin, ScD, is Co-Director of The Biostatistics Center at The George Washington University, where he also serves as Professor of Biostatistics and Epidemiology, and of Statistics. He has published extensively in his areas of research interest, which include sample size evaluation, group sequential methods, analysis of repeated measures, and survival analysis. A Fellow of the American Statistical Association and the Society for Clinical Trials, Dr. Lachin is the coauthor of Randomization in Clinical Trials: Theory and Practice, also published by Wiley.