Inference Principles for Biostatisticians

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.

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

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.