A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that leverages information in multiple outcomes to deal with unmeasured confounding. The key assumption in our approach is conditional independence among multiple outcomes. In contrast to existing proposals in the literature, the roles of multiple outcomes in our key identification assumption are symmetric, hence the name parallel outcomes. We show nonparametric identifiability with at least three parallel outcomes and provide parametric estimation tools under a set of linear structural equation models. Our proposal is evaluated through a set of synthetic and real data analyses.
Under what circumstances is it a threat to the parallel trends assumption required for Difference in Differences (DiD) studies if treatment decisions are based on past values of the outcome? We explore via simulation studies whether parallel trends holds across a grid of data generating processes generally conducive to parallel trends (random walk, Hidden Markov Model, and constant direct additive confounding), study designs (never treated, not yet treated, or later treated control groups), and outcome responsiveness of treatment (yes or no). We interpret the upshot of our simulation results t…
This paper assesses when the validity of difference-in-differences depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger ``parallel trends''-type condition holds for the cumulative distribution function of untreated potential outcomes. This condition for parallel trends to be insensitive to functional form is satisfied if and essentially only if the population can be partitioned into a subgroup for which treatment is effectively randomly assigned and a remaining…
This paper illustrates the use of entropy balancing in difference-in-differences analyses when pre-intervention outcome trends suggest a possible violation of the parallel trends assumption. We describe a set of assumptions under which weighting to balance intervention and comparison groups on pre-intervention outcome trends leads to consistent difference-in-differences estimates even when pre-intervention outcome trends are not parallel. Simulated results verify that entropy balancing of pre-intervention outcomes trends can remove bias when the parallel trends assumption is not directly satis…
A parametric expression for causal natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator. The proposed effect decomposition does not require the outcome to be rare and generalizes the existing ones, allowing for interactions between both the exposure and the mediator and confounding covariates. Further, it outlines the relationship between the causal effects and the correspondent pathway-specific logistic regression parameters, in parallel with results derived under the rare outcome assumption. Formulae for standard errors, obtained via the d…
Multivariate outcomes are common in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials (SW-CRTs) with multivariate outcomes that differentiate the within-period and between-period intracluster correlation coefficients (ICCs). Under a multivariate linear mixed model, we derive the joint distribution of the intervention test stati…
The difference-in-differences (DID) design is widely used in observational studies to estimate the causal effect of a treatment when repeated observations over time are available. Yet, almost all existing methods assume linearity in the potential outcome (parallel trends assumption) and target the additive effect. In social science research, however, many outcomes of interest are measured on an ordinal scale. This makes the linearity assumption inappropriate because the difference between two ordinal potential outcomes is not well defined. In this paper, I propose a method to draw causal infer…
National University of Singapore（新加坡国立大学）；AWS AI Labs（AWS人工智能实验室）；Harvard University（哈佛大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Many modern applications collect data that comes in federated spirit, with data kept locally and undisclosed. Till date, most insight into the causal inference requires data to be stored in a central repository. We present a novel framework for causal inference with federated data sources. We assess and integrate local causal effects from different private data sources without centralizing them. Then, the treatment effects on subjects from observational data using a non-parametric reformulation of the classical potential outcomes framework is estimated. We model the potential outcomes as a ran…
Multi-task learning is increasingly used to investigate the association structure between multiple responses and a single set of predictor variables in many applications. In the era of big data, the coexistence of incomplete outcomes, large number of responses, and high dimensionality in predictors poses unprecedented challenges in estimation, prediction, and computation. In this paper, we propose a scalable and computationally efficient procedure, called PEER, for large-scale multi-response regression with incomplete outcomes, where both the numbers of responses and predictors can be high-dim…
Considering parallel tempering and comparing post-treatment procedures in Bayesian Profile Regression Models for a survival outcome and correlated exposures
We propose a distributed quadratic inference function framework to jointly estimate regression parameters from multiple potentially heterogeneous data sources with correlated vector outcomes. The primary goal of this joint integrative analysis is to estimate covariate effects on all outcomes through a marginal regression model in a statistically and computationally efficient way. We develop a data integration procedure for statistical estimation and inference of regression parameters that is implemented in a fully distributed and parallelized computational scheme. To overcome computational and…
