Elsevier

Annals of Epidemiology

Volume 26, Issue 10, October 2016, Pages 674-680
Annals of Epidemiology

Commentaries on causal identification
Does water kill? A call for less casual causal inferences

https://doi.org/10.1016/j.annepidem.2016.08.016Get rights and content

Abstract

“Can this number be interpreted as a causal effect?” is a key question for scientists and decision makers. The potential outcomes approach, a quantitative counterfactual theory, describes conditions under which the question can be answered affirmatively. This article reviews one of those conditions, known as consistency, and its implications for real world decisions.

Introduction

Long gone are the times when causality was the exclusive realm of philosophers and theologians. Today's scientists embrace causal inference explicitly as a legitimate endeavor. To make causal inferences, scientists do what they do the best: they generate numbers. To understand the conditions under which those numbers can be interpreted as causal effects, scientists use a quantitative counterfactual theory which is often referred to as the potential outcomes approach. (This article will treat “quantitative counterfactual theory” and “potential outcomes approach” as equivalent terms; finer distinctions between them may be proposed but are of little relevance for our discussion.) This theory was formalized by Neyman [1] for randomized experiments, extended to nonexperimental—or observational—studies with time-fixed treatments by Rubin [2], [3] and generalized to randomized and observational settings with time-varying treatments by Robins [4], [5].

The potential outcomes approach provides conceptual definitions and supports analytic methods for researchers interested in producing and interpreting numerical estimates of causal effects. However, the potential outcomes approach is not universally accepted. In this issue of the journal, Schwartz et al. [6] criticize some restrictions imposed on causal inference by quantitative counterfactual theory. A recent article warns that the potential outcomes approach is damaging and “hardline”, is based on “a restrictive set of convictions”, makes “imperious claims”, and “cannot explain how [other approaches work]” [7]. Others have said that the potential outcomes approach is “socially conservative”, because “it neglects, discourages, and dismisses […] radical change.” [8] The critics of quantitative counterfactual theory make it look narrow-minded, arrogant, and even reactionary.

This article is an attempt to address those criticisms and to clarify three common misunderstandings. Several colleagues have recently written lucid commentaries that, with different emphases, address these issues too [9], [10], [11], [12].

As we will see, a first misunderstanding occurs because the potential outcomes approach explicitly highlights the inherent vagueness of all causal questions. In a perfect example of a shoot-the-messenger attitude, some critics have used this transparency of the approach as ammunition against it.

A second misunderstanding arises when critics ask too much from quantitative counterfactual theory. The potential outcomes approach is concerned with questions of the sort “what is the average causal effect of A on Y?” in a particular setting. The answer to these questions is a number (or several numbers) plus a statistical measure of uncertainty. In contrast, philosophical discussions about causality often revolve about questions of the sort “is A a cause of Y?” The answer to these questions is “yes” or “no”, not a number. The potential outcomes approach does not privilege a particular definition of “cause” and therefore may not necessarily provide definite yes/no answers to questions about causes [11].

A third misunderstanding is the idea that the potential outcomes framework restricts causal inference to the effects of humanly feasible, or practicable, interventions [13]. This is not necessarily the case. Much of the trepidation about the potential outcomes approach dissolves after clarifying that the framework is not restricted to feasible interventions.

To help clarify these misunderstandings, we first review the definition of causal contrast and its reliance on a fundamental condition for causal inference from observational data: consistency. Then, we dissect the components of the consistency condition and their implications for estimating causal effects. After briefly discussing the role of two other commonly used conditions (exchangeability and positivity) for causal inference from observational data, we propose a taxonomy of causal questions and their political implications. The goal is to clarify the role of a quantitative counterfactual theory for causal inference in both scientific and policy settings.

Section snippets

Causal contrasts

Questions about the causal effect of a treatment A on an outcome Y in a particular population can be expressed in terms of counterfactual contrasts. For example, we say that the average causal effect of the binary treatment A on the outcome Y is E[Ya = 1] − E[Ya = 0], where Ya = 1 is the (counterfactual or potential) outcome that would have been observed if an individual had received treatment level a = 1, Ya = 0 is the outcome that would have been observed if an individual had received

Component #1 of consistency: Sufficiently well-defined interventions

Let us start by discussing the causal effect of water on death. We will then extend our discussion to more pressing questions about the causal effect of factors like obesity and high blood pressure.

Component #2 of consistency: Linkage between interventions and the data

Suppose the interventions of interest are sufficiently well defined. We can now proceed to conduct the target trial that implements those interventions or, if that is not feasible, to emulate the target trial using observational data. To do so, we need to have data with versions of treatment that correspond to the interventions of interest. As an extreme example, if we had prospective data from a human population exposed to water in varying degrees during a tsunami, we could not reasonably use

Exchangeability and positivity

There is an additional reason why it is important to define and identify the versions of treatment when estimating average causal effects by emulating a target trial from an observational data set: the versions of treatment are not randomly assigned and each of them may be partly determined by different factors. For example, caloric intake is affected by physical activity level, which has a direct effect on mortality and is therefore a confounder for the effect of caloric intake on mortality.

A taxonomy of well-defined interventions and their political implications

Suppose our goal is to estimate the average causal effect of a treatment A on an outcome Y using observational data. Because the interpretation of numerical estimates of the average causal effect requires sufficiently well-defined interventions, we carefully specify the interventions a that define the potential outcome Ya. We can now classify these interventions as either (a) absent in the data or (b) present in the data.

If the interventions of interest are absent in the data, then our effect

Conclusions

The goal of the potential outcomes framework is not to identify causes—or to “prove causality”, as it sometimes said. That causality cannot be proven was already forcibly argued by Hume in the 18th century [39]. Rather, quantitative counterfactual inference helps us predict what would happen under different interventions, which requires our commitment to define the interventions of interest. As Rubin said in 1978: “Without treatment definitions that specify actions to be performed on

Acknowledgments

I am indebted to Dana Flanders, Sander Greenland, Jay Kaufman, James Robins, Sharon Schwartz, Ian Shrier, Sonja Swanson, and Tyler Vanderweele for helpful discussions and comments to earlier versions of this commentary.

The funding for the article is provided by NIH (R01 AI102634).

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  • Cited by (0)

    This commentary is based on a talk delivered at the John Snow Lecture Theater, London School of Hygiene and Tropical Medicine, during the UK Causal Inference Meeting, April 14, 2016.

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