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Marginal structural models are a popular tool for investigating the effects of time-varying treatments, but they require an assumption of no unobserved confounders between the treatment and outcome. With observational data, this assumption…
We propose a powerful adaptive contrast test with ordinal constraint contrast coefficients determined by observed responses. The adaptive contrast test can perform using easily calculated contrast coefficients and existing statistical…
We present a probabilistic ranking model to identify the optimal treatment in multiple-response experiments. In contemporary practice, treatments are applied over individuals with the goal of achieving multiple ideal properties on them…
This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…
Counterfactual inference aims to estimate the counterfactual outcome at the individual level given knowledge of an observed treatment and the factual outcome, with broad applications in fields such as epidemiology, econometrics, and…
Contrastive dimension reduction methods have been developed for case-control study data to identify variation that is enriched in the foreground (case) data X relative to the background (control) data Y. Here, we develop contrastive…
We propose a nonlinear difference-in-differences method to estimate multivariate counterfactual distributions in classical treatment and control study designs with observational data. Our approach sheds a new light on existing approaches…
In the context of individual-level causal inference, we study the problem of predicting whether someone will respond or not to a treatment based on their features and past examples of features, treatment indicator (e.g., drug/no drug), and…
Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews…
Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modeling such heterogeneity. We…
Regression analyses based on transformations of cumulative incidence functions are often adopted when modeling and testing for treatment effects in clinical trial settings involving competing and semi-competing risks. Common frameworks…
Individualizing treatment assignment can improve outcomes for diseases with patient-to-patient variability in comparative treatment effects. When a clinical trial demonstrates that some patients improve on treatment while others do not, it…
Intercurrent events, common in clinical trials and observational studies, affect the existence or interpretation of final outcomes. Principal stratification addresses this challenge by defining local average treatment effect estimands…
Consider an experiment consisting of a set of independent trials for comparing a set of treatments. In each trial, one treatment is chosen and the mean response of the trial is equal to the effect of the chosen treatment. We examine the…
In many practical situations, randomly assigning treatments to subjects is uncommon due to feasibility constraints. For example, economic aid programs and merit-based scholarships are often restricted to those meeting specific income or…
The conditional average treatment effect (CATE) is frequently estimated to refute the homogeneous treatment effect assumption. Under this assumption, all units making up the population under study experience identical benefit from a given…
Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…
Estimating causal effects is vital for decision making. In standard causal effect estimation, treatments are usually binary- or continuous-valued. However, in many important real-world settings, treatments can be structured,…
The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can…