In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a m...

In this chapter we show how algebraic geometry can be used to define and then analyse the properties of certain important classes of discrete probability models described through probability trees. Our aim is to show how much wider classes of discrete statistical models than have been considered previously have a useful algebraic formulation and unlike its competitors this class is closed under...

Understanding the causal relationship between intervention and outcome is at the heart of most research in the health sciences, and a variety of statistical methods have been developed to address causality. However, noncompliance with treatment assignment is a key source of complication for causal inference. Estimation of causal effects is likely to be compounded by the presence of noncomplianc...

We study the structural identification of causal effects with conditioning instruments within the settable system framework. In particular, we provide causal and predictive conditions sufficient for conditional exogeneity to hold. We provide two procedures based on “exclusive of A” (~A)-causality matrices and the direct causality matrix for inferring conditional causal isolation among vectors o...

Neighborhood built environment characteristics may encourage physical activity, but previous literature on the topic has been critiqued for its reliance on cross-sectional data. In this issue of the Journal, Knuiman et al. (Am J Epidemiol. 2014;180(5):453–461) present longitudinal analyses of built environment characteristics as predictors of neighborhood transportation walking. We take this op...

This article examines the causal link between family background characteristics—parental education and family size—and returns to schooling. I implement a model of schooling and earnings with heterogeneous returns to education using data from the Occupational Change in a Generation Survey. I find that men raised in larger families have substantially lower returns to education, whereas the combi...

Randomized controlled trials of interventions to improve adherence to antiretroviral medications are not always feasible. Marginal structural models (MSM) are a statistical methodology that aims to replicate the findings of randomized controlled trials using observational data. Under the assumption of no unmeasured confounders, 3 MSM estimators are available to estimate the causal effect of an ...