Invited Commentary: The Continuing Need for the Sufficient Cause Model Today

Abstract

In this commentary, I review the insights that have been gained using Rothman's sufficient cause model (Am J Epidemiol. 1976;104(6):587–592). Discussion pertains to the relations of the model to similar conceptualizations in other fields of study, the advances and extensions that have been made to the model since the paper's publication, and its relation to questions of actual causation, along with questions concerning the use of the model in the future of epidemiology.

Kenneth Rothman's paper “Causes” (1) has shaped and continues to shape our understanding of causation in epidemiology. Rothman's insights are numerous. First and foremost, he provides a conceptualization of causation as a state, event, or characteristic that is a necessary element for the sufficiency of a sufficient set (1–4). This understanding of causation is one that is shared by and has arisen in numerous disciplines, including philosophy, psychology, and law (1–6). In some of these disciplines, the conceptualization was introduced before the work of Rothman (2); in others, it followed Rothman's paper (3, 5). Nevertheless, that people in so many disciplines have seemingly independently come to this shared conceptualization of causation suggests that it is fundamental to our thinking about causality.

Moreover, its implications for epidemiology are numerous. The sufficient cause model manifestly makes clear that causation is a multifactorial phenomenon. It is the combination of numerous conditions that give rise to the health outcomes that we seek to study. In most population health settings, it consequently does not make sense to try to identify “the” cause; rather we study “causes,” as in the paper's title (1). Furthermore, when many conditions are required for a particular causal mechanism to be operative, it will sometimes suffice to eliminate just one of them to prevent disease occurrence. If multiple conditions are required for a sufficient cause, then they effectively interact in this sufficient cause sense; each needs the other to set a particular mechanism into motion (1). We can thus sometimes study and identify the numerous causes that, if eliminated, may be sufficient to substantially reduce disease. When many causes are present in the same sufficient cause, the elimination of any of them may suffice to render that sufficient cause inoperative. This is valuable, however, insofar as we can then consider upon which of these various causes it is most practical, ethical, or cost-effective to intervene. However, for this very same reason (and as noted in Rothman's paper), when one calculates attributable fractions for exposures to assess what proportion of disease could be eliminated by eliminating an exposure, the sum can exceed 100%. Thus, simply knowing that the attributable fraction for a particular exposure is very large—even close to 100%—does not in general give us the full picture concerning causal processes, and we must be wary of such reasoning. Perhaps less appreciated is the fact that if a single cause or condition is present in numerous sufficient causes, it can be very difficult to eliminate its effects entirely by simply eliminating other co-causes.

All of these insights follow directly from Rothman's sufficient cause model. Numerous refinements of the model have been made in the now more than 40 years since the paper's publication. Distinctions concerning etiologic and excess attributable fractions related to sufficient causes have been made (7, 8). The framework has been extended to allow for stochastic sufficient causes (9). Theory and methods to assess interactions, in not only in a statistical sense but also a sufficient cause sense, have been developed and have relaxed some of the restrictive assumptions of earlier work (6, 10–12). The theory for empirically testing for such sufficient cause interactions has been extended to n-way interactions (13, 14), ordinal and continuous exposures (15–18), and instances of genetic epistasis (19), as well as to settings of antagonism (20), which were also discussed in Rothman's paper. Moreover, an entire suite of methods has been developed to carry out such testing (6, 21–24). The model has been extended to and used to shed light upon the phenomenon of mediation (25–28), an extension that was in fact mentioned in passing in Rothman's paper. Attempts have been made to better incorporate time into the sufficient cause framework (29–31), an issue that was discussed and was present in Rothman's original paper but that has been absent from much of the work that followed and built upon it. Considerable work in this regard is still needed. All of these have been important and valuable advances.

Nevertheless, despite these advances and the insights that followed from the conceptualization, the model itself continues to be used today principally for teaching and illustrative purposes, rather than in design or analysis. The counterfactual or potential outcomes framework, which more directly makes reference to a comparator condition, has come to dominate more of teaching, methods development, and methods application today (6, 32). Some of this likely has to do with its closer ties to quantification, its focus on a quantitative causal effect estimands, and the lack of alternatives to formalizing such quantification in other approaches (33). Some of this also has to do with the different types of questions that potential outcomes, versus the sufficient cause framework, addresses. The potential outcomes framework is focused upon the effects that follow from individual causes or interventions. The sufficient cause framework begins with the outcome or effect to be explained and considers all of its possible causes. Said succinctly, the potential outcomes framework considers the effects of causes, whereas the sufficient outcomes framework considers the causes of effects. This latter task is more difficult. It is also more closely related to the notion of actual causation, that is, the identification of what it was that led to the outcome or effect in a particular individual case. Such questions are common in legal settings but are much more difficult to answer than are questions about the average effect of a particular intervention.

This question of the identification of actual causes is also one for which it has been notoriously difficult to articulate a necessary and sufficient characterization in the philosophical literature (33–37). These difficulties also end up implying that quantities that may be of interest from a sufficient cause perspective (e.g., How often is this sufficient causes operative? How often do 2 causes ever share the same sufficient cause?) are only partially identified (8). By getting close to the heart of these issues of actual causation, the sufficient cause framework is both richer (there is a many-to-one mapping from sufficient cause models to potential outcomes models (13, 38)) but also less analytically tractable. Indeed, Rothman's paper indicates that the framework is intended to bridge “the gap between metaphysical notions of cause and basic epidemiologic parameters” (1, p. 587). It does this; however, it is not always straightforward (or even possible) to cross that bridge when empirical data are involved.

The future of the use of the sufficient cause model in epidemiology is not entirely clear. The model will surely continue to be included in many introductory epidemiologic methods textbooks. Tests for sufficient cause interaction, while now well-developed and easy to implement (39), continue to be used infrequently. Interest in the model at epidemiologic conferences is dwarfed by that in methods based on the counterfactual model. The number of papers published on the sufficient cause model is a tiny fraction of that published on the potential outcomes model. Yet abandoning the model, at least in our intuitive thinking and understanding of causes, would be a tremendous loss. The model's conceptualization of causation in a multifactorial manner, as well as all that follows from it, leads to important insights in epidemiology and population health, that, if neglected, would impoverish thinking, research, and public health practice. Rothman's paper “Causes” should still be required reading for every student of epidemiology today.