Interactions and Complexity: Goals and Limitations

We thank Morabia for his insightful commentary on the historical development of interaction analysis within epidemiology and on the ambiguous role interactions played in the development of epidemiology itself. Our tutorial was, of course, intended to be precisely that, a tutorial, rather than an historical account, and Morabia’s commentary thus provides an important and engaging supplement to what we wrote.

Morabia argues that interaction presents, to epidemiology, a certain tension between population thinking, on the one hand, and the complexities of multifactorial disease causation, on the other hand – a tension that perhaps kept some scientists of the past from group comparisons, and thus, from epidemiologic analysis. Morabia poses the question, “At which point does the analysis of interaction become incompatible with epidemiology?” At what point does the analysis of interaction elude the traditional epidemiologic approach of group comparison? Morabia notes that all of the examples in our tutorial involved only “two-way” interaction, and that, in extreme scenarios, with many exposures and all higher order interactions present, population thinking and group comparisons break down.

One emphasis of our tutorial was that it is important for an investigator to clarify why interaction is being studied. The purposes and goals of interaction analysis are diverse, and concepts and methods must be chosen accordingly. Goals range from targeting subpopulations aimed at maximizing intervention effectiveness to uncovering mechanisms for disease causation. The tension that Morabia comments upon arguably relates to different goals in different ways.

A plethora of interactions across many exposures does indeed render population thinking and group comparisons essentially useless if the goal is to uncover these interactions in multifactorial models of disease causation; such complexity is intractable with traditional epidemiologic tools. ^[1] In contrast, the goal of determining which of two subpopulations to treat if resources are limited is a question that can be addressed by traditional epidemiologic analysis, and that can be addressed even if the underlying causal mechanisms are multifactorial and intractably complex. The potential underlying complexity of interactions does not threaten this specific goal.

And it is arguably this goal of determining which of two or more subpopulations would benefit most from intervention which has been, and continues to be, of greatest public health importance. Moreover, there have arguably been more successes in determining for which of two subpopulations a treatment is more effective, than there have been in using interaction analysis to truly uncover biological interactive mechanisms.

As pointed out by Morabia (2014), and in our tutorial (VanderWeele and Knol, 2014), and as was established in the epidemiologic over 30 years (Rothman et al., 1980), departure from additivity constitutes the metric by which we are to assess which subpopulation would benefit more from treatment. As discussed and illustrated in our tutorial, the additive, not the multiplicative scale, gives insight into this. It is therefore striking how few epidemiologic studies evaluate interaction on the additive scale (Knol et al., 2009).

Of course even detecting such additive interaction can be difficult with traditional epidemiologic tools, and the comparison of comparisons required for it can necessitate very large sample sizes indeed. However, the power and sample size tools that are available for additive interaction (VanderWeele, 2012) do, in some sense, allow us to take a step at quantifying that tension between interaction and population group thinking. We can have some insight into when our interaction analyses are still within the purview of what is possible by group comparisons. With sufficiently large studies, using interaction analysis to target subpopulations for treatment can be done, and it can be done even in the face of underlying complexity.

Moreover, with the goal of targeting subpopulations, we are not restricted to just “one other factor” in the same way we might be when trying to understand mechanisms and disease causation. As discussed in our tutorial, methods have been, and are being, developed to make treatment decisions that incorporate potential interaction between the treatment and many other variables (Cai et al., 2011; Zhang et al., 2013; Abadie et al., 2014). There are statistical challenges and more methodological development remains to be done, but initial indications suggest that these methods too can be used in moderately large samples, even in the face of intractable complexity at the level of individual disease causation, if the goal is simply identifying subpopulations for increased treatment effectiveness. ^[2] In the “omics” era, with ever-increasing information available on the genetic context and background of individuals, such methods, and what will likely be their subsequent extensions, may prove to be very important. There is likely a good deal more to be said about leveraging interaction for the purposes of personalized treatment decisions.

And with that with ever-increasing information on, not only on an individual’s own genetic background but even on molecular characteristics of the disease itself (e.g. tumors, Ogino et al., 2012), perhaps we have begun to come full circle and to return to what, in Morabia’s words, were “the concepts of health and disease of the past … that allowed for innumerable levels of interaction between the human body and all the elements of the universe [so that] every individual was different and every case of disease had its specific determinant.” What was, again in Morabia’s words, “‘antique holistic’ ideas…”, is, today, celebrated, in the conjoining of epidemiology and molecular pathology, as the “Unique Disease Principle” (Ogino et al., 2013) and as the way forward for research. The tensions between interaction and population thinking re-emerge, in forms perhaps even stronger than in the past.

Interactions thus may indeed be epidemiology’s brinkmanship, but effective brinkmanship requires the drawing of distinctions. Whereas we may be severely limited in our capacity to use population thinking and group comparisons in uncovering interactions for mechanisms or disease causation between more than two factors, we are arguably not so constrained with optimizing treatment decisions. We can make some progress at optimizing treatment decisions for nuanced subpopulations or even toward making personalized treatment decisions, even if the underlying reality and interactions are complex. More research, both theoretical and empirical, will be needed, but “interaction analysis” along the lines of optimizing individual treatment decisions based on a large number of markers may prove to be one of the most important expansions of the epidemiologic methods toolkit in the decades ahead.

We cannot hope, however, to address these future challenges of interaction analysis without having first thoroughly understood the basics; and yet, it is surprising how often the basics of interaction are themselves poorly understood, which was, of course, the motivation for the writing of our tutorial.