Reorganizing Graduate Statistical Inference for Modern Biostatistical Practice

Abstract

First-year graduate courses in statistical inference within PhD programs in biostatistics often follow a classical mathematical statistics progression through probability models, data reduction, point estimation, testing and interval estimation, and asymptotic evaluation. This organization has clear pedagogical strengths, but may provide less guidance when the probability model is not the natural starting point. We propose a complementary target-first organization for a graduate statistical inference course in biostatistics. The course begins with the scientific question and target parameter, then introduces statistical model classes, estimation, first-order sampling behavior, inference, and efficiency within a common framework. Classical methods such as maximum likelihood, method of moments, estimating equations, confidence intervals, hypothesis tests, bootstrap and jackknife methods, and the Cramér--Rao bound are organized within a common inferential workflow. A central advantage of this organization is that the same workflow provides a natural bridge from classical inference to modern statistical problems, including flexible estimation using machine learning and artificial intelligence, policy learning, anytime-valid inference, and modern Bayesian methods.