Assessing Causes for Individuals

Having engaged in several litigation cases focusing on the causal effects of pharmaceuticals and medical devices, I appreciate the opportunity to comment on the thought-provoking article by Dawid, Faigman, and Fienberg (2014). There is much to discuss but I will restrict my remarks to the material covered in Sections III and IV.

The authors have introduced a causal parameter that they christen the probability of causation (PC), a ratio of outcome risks in the simple case of only two counterfactual exposure conditions. In addition to highlighting the different perspectives of causes of effects as distinct from effects of causes, an important consequence is to move attention away from the population attributable risk (PAR) among the exposed, and the related requirement that the relative risk (RR) >2 for some courts to recognize individual proof of causation. This view is somewhat misguided to the extent that PAR, like RR, is a population parameter, and not specific to an individual. Of course, PC is also a population parameter, albeit one that focuses directly on individual counterfactual patterns. It remains to be seen whether courts and juries can readily understand the nuanced differences between these causal measures.

Given the marginal nature of PC, it is only immediately relevant to a randomly selected individual from the entire population. Since a plaintiff is not such, I wonder whether the more relevant parameter is Pr(R ₀ = 1| R ₁ = 1 and A = 1) where A denotes the observed exposure condition. This parameter differs from PC, for example, when the probability of exposure (A = 1) differs for individuals with R ₀ = 1 and R ₁ = 1, as compared to other counterfactual patterns. Indeed, it is this parameter that is coined as the probability of necessity (PN) by Pearl (2009a), and further reviewed in Pearl (2009b), where the same aspirin and headache relationship is used illustratively. Pearl notes that Robins and Greenland (1989a) also called Pr(R ₀ = 1| R ₁ = 1 and A = 1) the probability of causation, similarly proposed in a legal context, their discussion in the more complex setting that allows consideration of the time when the adverse outcome occurred.

As noted by the authors, a primary disadvantage of their PC is unidentifiability in almost all circumstances of interest (other than perhaps when the outcome is “temporary” and crossover designs are an experimental possibility). In addition, like PAR, the absence of an additive “calculus” is a challenge to interpretation, that is, the PCs associated with two distinct causal factors may both be greater than 50%. These same issues pertain to Pearl’s PN (and Robin and Greenland’s PC) although these authors also identify upper and lower bounds, where extensive work has been done (Robins and Greenland 1989b; Tian and Pearl 2000). These articles also discuss the relationship between PN and PAR, the latter often referred to as the excess risk ratio. Pearl points out that estimates of the lower bound can often be substantially stronger than merely using PAR. Further, PN may be identifiable under the strong assumptions of monotonicity (loosely speaking, exposure cannot improve any individual’s outcome), and an absence of confounding; in such cases, statistical properties of estimates of PN are relevant (Cai and Kuroki 2006).

Individual causation is undoubtedly important; one often hears the argument that since a plaintiff suffered from many other risk factors, how can one attribute their adverse outcome to the single factor being considered in litigation? In this regard, I usually make the point that the RR (and thus PAR) is likely to be even greater in subpopulations that are at high risk, due to possible effect modification. That is, if one’s risk of an adverse outcome is already high at “baseline,” exposure to an additional risk factor is likely to raise the probability of the outcome more than for individuals at low risk.

In principle, this train of thought suggests that a “possible” approach—to both issues of identifiability and varying effects across individuals—is to focus on the population subgroup that most closely matches the individual of interest on other characteristics that influence risk. There are two fundamental obstacles to this approach, the first that the number of such influential factors may be large so that reasonable estimation of comparative effects in subgroups is impractical without invoking heroic assumptions and/or complex statistical models. The second challenge is that, in litigation, identification of causal effects often requires the synthesis of information across multiple studies, particularly in adverse event situations where single studies are usually designed to measure efficacy at best. In multifactorial settings, it is unlikely that all relevant studies will have measured each influential risk factor let alone reported the information in sufficient detail to allow subsequent investigators to estimate subgroup safety comparisons.

The comments in the last two paragraphs introduce the important role of other cofactors that may also “cause” the adverse outcome, and the absence of methods to separate the PC due solely to exposure and that due to the combination of the exposure and additional cofactors. In another direction, Pearl (1999) discusses the probability of sufficiency, or the probability that a healthy unexposed individual would have experienced the adverse outcome had they been exposed. This is less relevant in a legal context but often an important consideration in policy deliberations.

In terms of discrimination and studies of pay equity, it is less clear that attention should solely be directed to causes of effects rather than effects of causes. Understanding the (direct) effect of sex on observed salaries seems an important evaluation in any employment setting, apart from an individual assessment of whether a woman’s low salary is caused by her sex. For a more technical discussion of pay equity comparisons in terms of modern causal inference ideas, see Hubbard, Jewell, and van der Laan (2011).

In closing, I return to adverse events related to drug exposures. In the drug approval process, we accept measures of average population efficacy while recognizing that the treatment in question may not be efficacious at all for some individuals (and could, in principle, be less effective than a standard comparator). Perhaps the courts need to come to terms with the same understanding in assessing the risks of certain adverse outcomes.