arXiv subjects

Elizabeth L. Ogburn

Publications and source records attributed to Elizabeth L. Ogburn.

28 records · Page 2Linked to original sources

arXiv2020

Causal inference, social networks, and chain graphs

Traditionally, statistical and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as social networks, where individuals may interact with one another such that treatments may spill over from the treated individual to their social contacts and outcomes may be contagious. Existing models proposed for causal inference using observational data from networks of interacting individuals have two major shortcomings. First, they often require a level of granularity in the data that is practically infeasible to collect in most settings, and second, the models are high-dimensional and often too big to fit to the available data. In this paper we illustrate and justify a parsimonious parameterization for network data with interference and contagion. Our parameterization corresponds to a particular family of graphical models known as chain graphs. We argue that, in some settings, chain graph models approximate the marginal distribution of a snapshot of a longitudinal data generating process on interacting units. We illustrate the use of chain graphs for causal inference about collective decision making in social networks using data from U.S. Supreme Court decisions between 1994 and 2004 and in simulations.

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arXiv2020

Network Dependence Can Lead to Spurious Associations and Invalid Inference

Researchers across the health and social sciences generally assume that observations are independent, even while relying on convenience samples that draw subjects from one or a small number of communities, schools, hospitals, etc. A paradigmatic example of this is the Framingham Heart Study (FHS). Many of the limitations of such samples are well-known, but the issue of statistical dependence due to social network ties has not previously been addressed. We show that, along with anticonservative variance estimation, this can result in spurious associations due to network dependence. Using a statistical test that we adapted from one developed for spatial autocorrelation, we test for network dependence in several of the thousands of influential papers that have been published using FHS data. Results suggest that some of the many decades of research on coronary heart disease, other health outcomes, and peer influence using FHS data may suffer from spurious associations, error-prone point estimates, and anticonservative inference due to unacknowledged network dependence. These issues are not unique to the FHS; as researchers in psychology, medicine, and beyond grapple with replication failures, this unacknowledged source of invalid statistical inference should be part of the conversation.

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arXiv2020

Testing for Network and Spatial Autocorrelation

Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in continuous variables. In this paper we propose two contributions to the literature on tests for autocorrelation. First, we propose a new test for autocorrelation in categorical variables. While some methods currently exist for assessing spatial autocorrelation in categorical variables, the most popular method is unwieldy, somewhat ad hoc, and fails to provide grounds for a single omnibus test. Second, we discuss the importance of testing for autocorrelation in data sampled from the nodes of a network, motivated by social network applications. We demonstrate that our proposed statistic for categorical variables can both be used in the spatial and network setting.

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arXiv2019

Comment on "Blessings of Multiple Causes"

(This comment has been updated to respond to Wang and Blei's rejoinder [arXiv:1910.07320].) The premise of the deconfounder method proposed in "Blessings of Multiple Causes" by Wang and Blei [arXiv:1805.06826], namely that a variable that renders multiple causes conditionally independent also controls for unmeasured multi-cause confounding, is incorrect. This can be seen by noting that no fact about the observed data alone can be informative about ignorability, since ignorability is compatible with any observed data distribution. Methods to control for unmeasured confounding may be valid with additional assumptions in specific settings, but they cannot, in general, provide a checkable approach to causal inference, and they do not, in general, require weaker assumptions than the assumptions that are commonly used for causal inference. While this is outside the scope of this comment, we note that much recent work on applying ideas from latent variable modeling to causal inference problems suffers from similar issues.

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arXiv2019

The magnitude and direction of collider bias for binary variables

Suppose we are interested in the effect of variable $X$ on variable $Y$. If $X$ and $Y$ both influence, or are associated with variables that influence, a common outcome, called a collider, then conditioning on the collider (or on a variable influenced by the collider -- its "child") induces a spurious association between $X$ and $Y$, which is known as collider bias. Characterizing the magnitude and direction of collider bias is crucial for understanding the implications of selection bias and for adjudicating decisions about whether to control for variables that are known to be associated with both exposure and outcome but could be either confounders or colliders. Considering a class of situations where all variables are binary, and where $X$ and $Y$ either are, or are respectively influenced by, two marginally independent causes of a collider, we derive collider bias that results from (i) conditioning on specific levels of, or (ii) linear regression adjustment for, the collider (or its child). We also derive simple conditions that determine the sign of such bias.

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arXiv2017

Challenges to estimating contagion effects from observational data

A growing body of literature attempts to learn about contagion using observational (i.e. non-experimental) data collected from a single social network. While the conclusions of these studies may be correct, the methods rely on assumptions that are likely--and sometimes guaranteed to be--false, and therefore the evidence for the conclusions is often weaker than it seems. Developing methods that do not need to rely on implausible assumptions is an incredibly challenging and important open problem in statistics. Appropriate methods don't (yet!) exist, so researchers hoping to learn about contagion from observational social network data are sometimes faced with a dilemma: they can abandon their research program, or they can use inappropriate methods. This chapter will focus on the challenges and the open problems and will not weigh in on that dilemma, except to mention here that the most responsible way to use any statistical method, especially when it is well-known that the assumptions on which it rests do not hold, is with a healthy dose of skepticism, with honest acknowledgment and deep understanding of the limitations, and with copious caveats about how to interpret the results.

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arXiv2016

High-dimensional Multivariate Mediation: with Application to Neuroimaging Data

Mediation analysis has become an important tool in the behavioral sciences for investigating the role of intermediate variables that lie in the path between a randomized treatment and an outcome variable. The influence of the intermediate variable on the outcome is often explored using structural equation models (SEMs), with model coefficients interpreted as possible effects. While there has been significant research on the topic in recent years, little work has been done on mediation analysis when the intermediate variable (mediator) is a high-dimensional vector. In this work we present a new method for exploratory mediation analysis in this setting called the directions of mediation (DMs). The first DM is defined as the linear combination of the elements of a high-dimensional vector of potential mediators that maximizes the likelihood of the SEM. The subsequent DMs are defined as linear combinations of the elements of the high-dimensional vector that are orthonormal to the previous DMs and maximize the likelihood of the SEM. We provide an estimation algorithm and establish the asymptotic properties of the obtained estimators. This method is well suited for cases when many potential mediators are measured. Examples of high-dimensional potential mediators are brain images composed of hundreds of thousands of voxels, genetic variation measured at millions of SNPs, or vectors of thousands of variables in large-scale epidemiological studies. We demonstrate the method using a functional magnetic resonance imaging (fMRI) study of thermal pain where we are interested in determining which brain locations mediate the relationship between the application of a thermal stimulus and self-reported pain.

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arXiv2015

Incorporating Contact Network Structure in Cluster Randomized Trials

Whenever possible, the efficacy of a new treatment, such as a drug or behavioral intervention, is investigated by randomly assigning some individuals to a treatment condition and others to a control condition, and comparing the outcomes between the two groups. Often, when the treatment aims to slow an infectious disease, groups or clusters of individuals are assigned en masse to each treatment arm. The structure of interactions within and between clusters can reduce the power of the trial, i.e. the probability of correctly detecting a real treatment effect. We investigate the relationships among power, within-cluster structure, between-cluster mixing, and infectivity by simulating an infectious process on a collection of clusters. We demonstrate that current power calculations may be conservative for low levels of between-cluster mixing, but failing to account for moderate or high amounts can result in severely underpowered studies. Power also depends on within-cluster network structure for certain kinds of infectious spreading. Infections that spread opportunistically through very highly connected individuals have unpredictable infectious breakouts, which makes it harder to distinguish between random variation and real treatment effects. Our approach can be used before conducting a trial to assess power using network information if it is available, and we demonstrate how empirical data can inform the extent of between-cluster mixing.

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arXiv2015

Causal Diagrams for Interference

The term "interference" has been used to describe any setting in which one subject's exposure may affect another subject's outcome. We use causal diagrams to distinguish among three causal mechanisms that give rise to interference. The first causal mechanism by which interference can operate is a direct causal effect of one individual's treatment on another individual's outcome; we call this direct interference. Interference by contagion is present when one individual's outcome may affect the outcomes of other individuals with whom he comes into contact. Then giving treatment to the first individual could have an indirect effect on others through the treated individual's outcome. The third pathway by which interference may operate is allocational interference. Treatment in this case allocates individuals to groups; through interactions within a group, individuals may affect one another's outcomes in any number of ways. In many settings, more than one type of interference will be present simultaneously. The causal effects of interest differ according to which types of interference are present, as do the conditions under which causal effects are identifiable. Using causal diagrams for interference, we describe these differences, give criteria for the identification of important causal effects, and discuss applications to infectious diseases.

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arXiv2014

Vaccines, Contagion, and Social Networks

Consider the causal effect that one individual's treatment may have on another individual's outcome when the outcome is contagious, with specific application to the effect of vaccination on an infectious disease outcome. The effect of one individual's vaccination on another's outcome can be decomposed into two different causal effects, called the "infectiousness" and "contagion" effects. We present identifying assumptions and estimation or testing procedures for infectiousness and contagion effects in two different settings: (1) using data sampled from independent groups of observations, and (2) using data collected from a single interdependent social network. The methods that we propose for social network data require fitting generalized linear models (GLMs). GLMs and other statistical models that require independence across subjects have been used widely to estimate causal effects in social network data, but, because the subjects in networks are presumably not independent, the use of such models is generally invalid, resulting in inference that is expected to be anticonservative. We introduce a way to ensure that GLM residuals are uncorrelated across subjects despite the fact that outcomes are non-independent. This simultaneously demonstrates the possibility of using GLMs and related statistical models for network data and highlights their limitations.

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