When a treatment influences both the primary response and the covariate, a standard analysis of covariance may misrepresent the real treatment effect by adjusting out that part of the effect which is manifest in the covariate. What parametric function should we examine if the treatments influence the covariate? An informative analysis would let the complete effects of the levels emerge, yet per...

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanie...

In many learning settings, the source data available to train a regression model differs from the target data it encounters when making predictions due to input distribution shift. Appropriately dealing with this situation remains an important challenge. Existing methods attempt to “reweight” the source data samples to better represent the target domain, but this introduces strong inductive bia...

The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in the analysis of observational data. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers...

This chapter addresses strategies for selecting variables for adjustment in nonexperimental comparative effectiveness research (CER), and uses causal graphs to illustrate the causal network relating treatment to outcome. While selection approaches should be based on an understanding of the causal network representing the common cause pathways between treatment and outcome, the true causal netwo...

Consider a linear model y = Xβ + z, z ∼ N(0, σIn). The Gram matrix Θ = 1 n X ′X is non-sparse, but it is approximately the sum of two components, a low-rank matrix and a sparse matrix, where neither component is known to us. We are interested in the Rare/Weak signal setting where all but a small fraction of the entries of β are nonzero, and the nonzero entries are relatively small individually....

The effects of improving covariate measurement are investigated when the covariate is endogenous even in the absence of measurement error. Reducing measurement error can exacerbate the finite sample bias of Two-Stage Least Squares. An application reveals this is of practical importance. JEL: C36, C81

When reporting results from survival analysis, investigators often present crude Kaplan-Meier survival curves and adjusted relative hazards from the Cox proportional hazards model. Occasionally, the investigators will also provide a graphical representation of adjusted survival curves based on regression estimates and the average covariate values in the study groups. In this paper, the authors ...

The accelerated life model assumes that the failure time associated with a multi-dimensional covariate process is contracted or expanded relative to that of the zero-valued covariate process. In the present paper, the rate of contraction/expansion is formulated by a parametric function of the covariate process while the baseline failure time distribution is unspecified. Estimating functions for...