Lectures

This page contains the course lecture notes, organized by week. Each row corresponds to a week of the course, with a short description of its contents. The notes open via the icon on the right (Week 0 as a web page, later weeks as PDF files).

Opens the written lecture notes for that week (PDF).

Notes for later weeks are posted here as the course progresses. We recommend reading the notes before class and revisiting them alongside the labs.

Week 0: Math Foundations A self-paced refresher on the mathematical tools the course leans on: notation, functions and logarithms, calculus, and working with expectations. Opens as a web page.
Week 1: Randomized Controlled Trials & Emulation Why trials anchor causal questions: eligibility, time zero, assignment, adherence, and emulating a target trial with observational data.
Week 2: Data Collection From estimands to data requirements: censoring, truncation, competing events, and pairing estimands with estimators.
Week 3: Outcome-Dependent Sampling Case-control and case-cohort designs, control-sampling schemes, and what outcome-dependent sampling buys and costs.
Week 4: Regression as a Toolkit One machine, three uses: descriptive, predictive, and causal questions; least squares and maximum likelihood under the hood; and the three roadmaps.
Week 5: The Anatomy of a Regression Model The slots of a regression model and the choices they encode: left and right hand sides, target versus nuisance functions, links, distributions, offsets, and the parametric to nonparametric spectrum.
Week 6: Generalized Linear Models One loop, two functions: every GLM as iteratively reweighted least squares with a variance function and a link plugged in; the exponential family and canonical links; a menu of families fit to simulated and NHEFS data; and why the family is a choice about the variance, not the coefficient.
Week 7: Variance Estimation Where standard errors come from: sampling variability through the superpopulation lens; the model-based variance built from residuals and the design matrix; sandwich estimators for non-constant variance and clustered data (HC0 to HC3, cluster-robust, and the link to GEE); and normal, percentile, and BCa bootstrap intervals, each computed by hand and checked against the packaged versions.
Week 8: Conditional vs. Marginal Adjustment What the exposure coefficient actually returns: collapsibility and the characteristic collapsibility function, with Jensen's inequality explaining why the odds ratio is noncollapsible while risk differences and ratios are not; conditionally adjusted estimates read from a model versus marginally adjusted estimates obtained by standardizing its predictions (the g formula) or by inverse probability weighting; interactions, the stratified outcome model, and bootstrap intervals for all of it on the NHEFS data.