Inference Principles for Biostatisticians: 1st Edition (Hardback) book cover

Inference Principles for Biostatisticians

1st Edition

By Ian C. Marschner

Chapman and Hall/CRC

274 pages | 28 B/W Illus.

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pub: 2014-12-11
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Description

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.

Reviews

"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

Table of Contents

Probability and Random Samples

Statistical inference

Probability

Random variables

Probability distributions

Independence

Random samples

Sampling bias

Sampling variation

Large samples

Extended example

Estimation Concepts

Statistical models

Parametric models

Statistics and data reduction

Estimators and estimates

Properties of estimators

Large sample properties

Interval estimation

Coverage probability

Towards hypothesis testing

Extended example

Likelihood

Statistical likelihood

Likelihood function

Log-likelihood function

Sufficient statistics and data reduction

Multiple parameters

Nuisance parameters

Extended example

Estimation Methods

Maximum likelihood estimation

Computation of the MLE

Information and standard errors

Properties of the MLE

Multiple parameters

Further estimation methods

Extended example

Hypothesis Testing Concepts

Hypotheses

Statistical tests

Acceptance versus non-rejection

Statistical errors

Power and sample size

P-values

Extended example

Hypothesis Testing Methods

Approaches to hypothesis testing

Likelihood ratio test

Score test

Wald test

Comparison of the three approaches

Multiple parameters

Hypotheses about all parameters

Hypotheses about one parameter

Hypotheses about some parameters

Test-based confidence intervals

Extended example

Bayesian Inference

Probability and uncertainty

Bayes’ rule

Prior and posterior distributions

Conjugate prior distributions

Estimation of a normal mean

Credible intervals

Non-informative prior distributions

Multiple parameters

Connection to likelihood inference

Extended example

Further Inference Topics

Exact methods

Non-parametric methods

Semi-parametric methods

Bootstrapping

Permutation methods

Extended example

Appendix A: Common probability distributions

Appendix B: Simulation tools

About the Author

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.

About the Series

Chapman & Hall/CRC Biostatistics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MED090000
MEDICAL / Biostatistics