Designed for students training to become biostatisticians as well as practicing biostatisticians, Inference Principles for Biostatisticians presents the theoretical and conceptual foundations of biostatistics. It covers the theoretical underpinnings essential to understanding subsequent core methodologies in the field.
Drawing on his extensive experience teaching graduate-level biostatistics courses and working in the pharmaceutical industry, the author explains the main principles of statistical inference with many examples and exercises. Extended examples illustrate key concepts in depth using a specific biostatistical context. In addition, the author uses simulation to reinforce the repeated sampling interpretation of numerous statistical concepts. Reducing the computational complexities, he provides simple R functions for conducting simulation studies.
This text gives graduate students with diverse backgrounds across the health, medical, social, and mathematical sciences a solid, unified foundation in the principles of statistical inference. This groundwork will lead students to develop a thorough understanding of biostatistical methodology.
Table of Contents
Probability and Random Samples
Statistics and data reduction
Estimators and estimates
Properties of estimators
Large sample properties
Towards hypothesis testing
Sufficient statistics and data reduction
Maximum likelihood estimation
Computation of the MLE
Information and standard errors
Properties of the MLE
Further estimation methods
Hypothesis Testing Concepts
Acceptance versus non-rejection
Power and sample size
Hypothesis Testing Methods
Approaches to hypothesis testing
Likelihood ratio test
Comparison of the three approaches
Hypotheses about all parameters
Hypotheses about one parameter
Hypotheses about some parameters
Test-based confidence intervals
Probability and uncertainty
Prior and posterior distributions
Conjugate prior distributions
Estimation of a normal mean
Non-informative prior distributions
Connection to likelihood inference
Further Inference Topics
Appendix A: Common probability distributions
Appendix B: Simulation tools
Ian C. Marschner is head of the Department of Statistics and a professor of statistics at Macquarie University. He is also a professor of biostatistics in the National Health and Medical Research Council (NHMRC) Clinical Trials Centre at the University of Sydney. He has over 25 years of experience as a biostatistician working on health and medical research, particularly involving clinical trials and epidemiological studies of cardiovascular disease, cancer, and HIV/AIDS. He was previously director of the Asia Biometrics Centre with Pfizer and an associate professor of biostatistics at Harvard University.
"It gently but rigorously introduces most concepts used in statistical inference, with illustrative examples. It forms a useful reference for lecturers and for scientists/biostatisticians who are daily faced with tasks in biomedical data analysis."
—Matthieu Vignes, PhD, Institute of Fundamental Sciences, Massey University in Australian & New Zealand Journal of Statistics
"The first thing to like about it is the size! No weighty tome to fill students with dread. . . the practical issues of dealing with multiparameter models and elimination of nuisance parameters are well described and the calculation shown in detail."
—Cono Ariti, International Society for Clinical Biostatistics
"… covers not only the core theoretical foundations of the subject, but also many real-life applications and examples that the author drew from his extensive teaching and industry experience. … Simulations are designed to reinforce the repeated sampling interpretation and many R functions are made available for readers to have an easy hands-on experience. All these efforts allow the book to empower readers to develop their own thorough understanding of biostatistical methods."
—Journal of Biopharmaceutical Statistics