What is the relationship between the cause of an effect and the effect of a cause?
Essay 2
Before the second essay, some notes from the response to Essay 1: The first essay got an interesting question on LinkedIn from the super amazing economist and health systems researcher: Dr. Nachiket Mor.
Nachiket asked:
Does this issue become a challenge because most epidemiologists start with data and then search for causation? My understanding of science is that it always begins with conjecture (theory) and hypotheses about causation, which we then attempt to falsify through data. I have encountered this opposite approach in public health and social sciences, which may be the root of the problem. What do you think?
I hurriedly responded to him:
One of the major concerns in epidemiology has been that there is no overarching theory. Multi-causality was proposed a while back and there was socio-ecological theory. However, my reading is that these took a back seat when the specific hypotheses emanating from the theories became somewhat intractable to test. Since then epidemiology has been pushing to be an interventional science where the goal is to estimate the causal effects of well-defined interventions. This is similar to the the rise of RCTs in developmental economics. However, as I have argued in the essay, this approach is further atheoretic. Not having theory is certainly a problem. However, I think that's a problem in several sciences and many sciences do a good job of hiding that :) I think what's happening in epidemiology is that there's a greater awareness to question what the theory would look like.
A couple notes on this response:
My reading on socio-ecological theory is quite new and hence incomplete. There could be other technical or political reasons (i.e., having to do not with the science of the discipline but with how the people in the discipline are feeling, where their allegiance lies, what agenda they set, etc.) that did not let socio-ecological theory pick up. I happy to get suggestions for more reading on this.
My central argument was that I with agree with Nachiket that lack of overarching theory is an issue for epidemiology - and thereby for public health.
However, I am not sure if it this issue is due to the influences of social sciences on epidemiology. I am not a sociologist and have almost no training in humanities. However, reading some of Emile Durkheim’s work last year, made me realize that sociologists love theory. Additionally, interactions with social epidemiologists at Columbia and beyond have further made it clear that the atheoretic approach epidemiology likes to take under the garb of ‘evidence-based’ is displeases social epidemiologists. Having trained primarily as a biologist (and in a more niche way as a neuroscientist), I would argue that it is the influence of biomedicine that makes epidemiology atheoretic.
At the risk of receiving retaliation, I am going to make a big two-part claim that I cannot completely argue in this small note (however, I promise to write about this in detail sometime in the future) — Except maybe for evolution, biology has no theory. Further, when if consider evolution to be the guiding theory of biology, not all biologists are consciously mindful of it. Nor can they connect their findings to the larger grounding theory. I am aware that I am not the first one to make this claim. However, I do think that the issue that the practitioners of biology and thereby biomedicine cannot easily access an underlying theory is not talked about enough. This has implications for epidemiology and public health too. Note that I am not suggesting that the theory of biology (if there is one) would be the default theory of epidemiology. However, it would surely be a contesting theory for epidemiologists to consider.
Anyway, I decided to include this note as a prologue to the second essay because its connected to the topic of this essay: that there are more than one ways to define ‘what is a cause’. Now, on to the essay!
In this essay, I will demonstrate that despite the philosophical differences, there are points of compatibility between the approaches investigating ‘a cause of an effect’ and ‘an effect of a cause’, such that they can be combined in studies assessing causation. The first section focuses on deconstructing and comparing the definitions of ‘a cause of an effect’ by Mackie 1965 and Chapter 2 ‘Causation and Causal Inference’ in the 3rd Edition of Modern Epidemiology aka Rothman et al. 2008 (referred to as Rothman going ahead). In the second section, I will rely on the causal effect definition from my previous essay to enlist points of contention and compatibility between the approaches to study a cause of an effect and a cause of an effect. In the last section, I propose the conditions under which the approaches can be combined.
Section I: What is a ‘cause of an effect’?
According to Mackie, a cause (X) of an effect (Y) can be defined in relation to a causal field F such that X is at least an INUS (Insufficient but Non-redundant part of an Unnecessary but Sufficient) condition (of Y in F) — there is a condition, given the extant features characterizing F, that is necessary and sufficient for Y, and which is of one of the forms: (AX or B), (X, B), AX, X. I will focus on two relevant elements of this definition of a cause: at least an INUS condition and causal field. X as ‘at least an INUS condition’ comes with the following conditions:
a) that there exist some minimally sufficient conditions of Y.
b) X might be a conjunct (a part of) all the possible minimally sufficient conditions but it doesn’t need to be.
c) A by itself is not sufficient for Y. This ensures that X (in (AX or B) and AX) is non-redundant. Per these, X does not have to be either a necessary or a sufficient condition of Y for it to be an INUS condition. It just should be a non-redundant part of a minimally sufficient condition of Y. The above three clauses (a, b, and c) define X as an INUS condition.
d) For the extended definition of at least an INUS condition, we should include: If there is only one minimally sufficient condition containing X (i.e., AX).
e) If X is itself a minimally sufficient condition (X or B) or X is the only necessary and minimally sufficient condition for Y.
Mackie’s analysis argues that when we use ‘X causes Y’ in a lay sense, the underlying formalism of cause X is that it is at least an INUS condition (Mackie 1965 pg 249). Mackie defines the second element, causal field F, as the wider region in which the effect Y sometimes occurs and sometimes does not. Mackie’s example of influenza (pg 249), makes it seem that the causal field refers to study populations. However, in the example of ‘what causes skin cancer’, Mackie invokes contrasts (before vs. after, case vs. control). Applying the causal field to the house that caught fire, Mackie notes that what we mean by causal field and what we include in it, would change based on the nature and purpose of our inquiry. Hence, I am unsure if the causal field has (or even needs) a precise definition. Causal field is tied to the question: what we interested in.
I will now briefly summarize Rothman’s sufficient-cause model (SCM). Here, a cause is defined as an antecedent event, condition, or characteristic that was necessary for that outcome occurring at that moment, given that the other conditions are fixed. While there is not much to deconstruct in this definition since it is conventionally used in epidemiology, it is important to lay out some definitions and concepts integral to the causal model.
A sufficient cause is defined as a complete causal mechanism, a minimal set of conditions and events that ensure that an outcome will occur. This is equivalent to the minimally sufficient condition defined by Mackie. An outcome Y can have multiple sufficient causes, each of which can be represented by a diagram (See Figure 2.1 for example. However, it is not until pg 9 that Rothman refers to such figures as pie diagrams). This is similar to clause ‘a’ in Mackie’s definition that elaborates on INUS condition as a part of a minimally sufficient condition.
A component cause is one of the non-superfluous causes in the constellation of causes that form a sufficient cause, which is required and must be present or have occurred at the instance of the occurrence of the outcome. Rothman’s component cause is the same as Mackie’s INUS condition. Requiring any component causes (X and others) to be non-superfluous is the same as non-redundancy noted in Mackie's clause ‘c’. Rothman clarifies that ‘necessary’, as used in the definition at the beginning of the paragraph, pertains to the necessity of the component cause (X) to be present in one of the sufficient causes of Y. Hence, X could be but it isn't necessarily a necessary cause of Y. For a component cause X to be a necessary cause of Y, it must be present in all the sufficient causes of Y. This is equivalent to clause ‘d’ in Mackie’s definition.
For X to be a sufficient cause of Y, there must be a causal pie diagram with X as the only component without any other causal components. This is equivalent to clause ‘e’ of Mackie. Component causes can occur in more than one sufficient cause, which is similar to clause ‘b’ in Mackie's analysis.
Rothman specifies the need for a clearly defined alternative or reference condition for the indexed component cause (Rothman pg 3). However, beyond this and a mention of “given that the other conditions are fixed” while defining a cause – which itself isn't defined further – Rothman does not seem to indulge in a description equivalent to the causal field.
Section II: Points of contention and compatibility between the two approaches
Previously, I used the literature synthesis from multiple thinkers of the potential outcomes framework (POF) to define causal effect as the effect of a cause compared to other cause(s), where a cause is a variable with well-defined potential outcomes that is manipulable or potentially exposable over all units of the study population.
I will first investigate the differences between SCM and POF. First, SCM assumes multifactorial causation of (disease) outcomes (Rothman pg 9). However, the causal effects defined in the POF do not deal with the multi-causality. Instead, the starting point is a treatment defined as a causal contrast.
Second, SCM portrays different qualitative causal mechanisms occurring in the study population members (Rothman pg 11). Hence, the unit of analysis is the causal mechanism. The investigation focuses on finding causes of outcome Y, hypothesizing their interactions, and estimating the strength of effects, among others. On the contrary, the unit of analysis in the POF is the individual study unit such as a person, a plot of land, a school, etc. that is given or has received a certain treatment.
Third, definitions (especially Rubin’s but also those of others) of causal effects in POF explicitly focused on the time point of outcome measurement of Y and the time point of treatment initiation. On the contrary, Rothman's causal models, especially the pie chart representations, are ill-suited for any time specification. They cannot provide information about specific windows in which the different component causes act on the outcome, or if the induction periods are similar or different.
Fourth, estimating the strength of effect under SCM is based on differences or ratios of risk measures such as incidence proportions for a dichotomous outcome with a deterministic link to its causes. Assuming the frequentist conception of risk, the strength of the effect of a component cause depends on the prevalence of its causal complement (i.e., set of all other component causes in all sufficient causes in which a causal factor participates) in the population when captured as a difference, regardless of its etiologic significance in the sufficient cause. When measured as a ratio, it additionally depends on how rare or common components are of sufficient causes in which the specified causal factor is absent. The model assumes that the component is an equal partner in each mechanism in which it appears. Hence, there is no corollary of individual-level causal effect - that is fundamental to POF - in SCM.
Fifth, Rothman includes event, condition, or characteristic (or attribute) in their definition of cause. They use atherosclerosis - something that you can or cannot have - as a cause in an example (see Rothman Pg 7). As long as component causes are identified for the given population and the causes follow SCM’s definition, they do not seem to put any further restrictions on what can or cannot be studied as a cause. This opposes the view held by Holland and Robins & Herman. They believe that an attribute is inherent to the individual study unit and not potentially exposable to all study units. Hence, one cannot even hypothetically imagine a potential outcome, thereby nullifying any possibility of theoretically defining an individual causal effect.
Regardless of the differences, there are some noteworthy points of convergence.
First, both approaches agree on the importance of well-defined reference conditions. Rothman's model considers it for component causes while the POF requires it for the treatment protocol.
Second, the SCM allows the analysis of risks based on possible combinations of the specified component causes. Conventionally, these combinations are dubbed as response types. Such theoretical analysis is similar to that conducted for the potential outcomes of the different treatment assignments if the treatments are to be assigned.
Third, the difference and ratio measures (e.g., incidence proportion differences and ratios used by Rothman, Pgs 6-7) are mathematically of the same form as those used for causal effect estimation in the POF.
The focus and the starting point of inquiry are different between the ‘cause of effect’ & ‘effect of cause’ approaches. Whereas, once a component cause of interest is locked, there are the above-mentioned similarities in consideration for referent, response types given combinations, and estimation of population-level effect strength.
Section III: The combined approach
Understanding the differences and similarities between the two approaches can be used to build a combined approach.1 Consider an outcome Y. SCM is useful for exploring sufficient causes (AXU, BZ, etc.), enlisting component causes (X, A, U, etc.), and understanding how they interact with each other, finally to identify a component cause of interest (X). For compatibility with POF, it is critical to only consider component causes that are not attributes. X with a defined contrast can now be specified further for causal effect estimation under POF. The knowledge about causal partners and complements from SCM can inform the specification of the potential outcomes for Y.
These are some unformed ideas that need more work. Happy to get feedback.