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Models of physical systems are used to explain and predict experimental results and observations. When students encounter discrepancies between the actual and expected behavior of a system, they revise their models to include the newly…

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…

Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In…

Decomposing an exposure effect on an outcome into separate natural indirect effects through multiple mediators requires strict assumptions, such as correctly postulating the causal structure of the mediators, and no unmeasured confounding…

It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to…

Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…

Practitioners in medicine, business, political science, and other fields are increasingly aware that decisions should be personalized to each patient, customer, or voter. A given treatment (e.g. a drug or advertisement) should be…

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent…

The implicit theory that a simulation represents is precisely not in the individual choices but rather in the 'envelope' of possible trajectories - what is important is the shape of the whole envelope. Typically a huge amount of computation…

Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely…

Relationship between two popular modeling frameworks of causal inference from observational data, namely, causal graphical model and potential outcome causal model is discussed. How some popular causal effect estimators found in…

In this paper, a model for understanding the effects of selection using systems- level computational approaches is introduced. A number of concepts and principles essential for understanding the motivation for constructing the model will be…

All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…

I set up a potential outcomes framework to analyze spillover effects using instrumental variables. I characterize the population compliance types in a setting in which spillovers can occur on both treatment take-up and outcomes, and provide…

Social network interference induces complex dependencies where a unit's outcome is influenced not only by its own exposure and mediator but also by those of connected neighbors. In such settings, a significant challenge lies in…

We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in…

We consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment…

Environmental epidemiologists are increasingly interested in establishing causality between exposures and health outcomes. A popular model for causal inference is the Rubin Causal Model (RCM), which typically seeks to estimate the average…

In survival analysis, cure models have gained much importance due to rapid advancements in medical sciences. More recently, a subset of cure models, called destructive cure models, have been studied extensively under competing risks…

Mediation analysis is concerned with the decomposition of the total effect of an exposure on an outcome into the indirect effect through a given mediator, and the remaining direct effect. This is ideally done using longitudinal measurements…