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Inference Principles for Biostatisticians


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Table of Contents

Probability and Random Samples
Statistical inference
Random variables
Probability distributions
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
Statistical tests
Acceptance versus non-rejection
Statistical errors
Power and sample size
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
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.


"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

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