Conceptual interpretations of predictive versus causal modeling

Question

I'm a relatively non-technical clinician. And I recently came across an excellent paper paper (Schooling & Jones, 2018).The authors essentially implore biomedical researchers to use non-ambiguous language in describing their research questions (and to choose correspondingly appropriate methods to answer those questions). The ambiguity in question relates to the differences between predictive and causal modeling.

There is an excellent table, which summarizes much of the content. Under the “attribute” column you can find “interpretation” which includes several rows highlighting key distinctions.

My question is whether it would be appropriate to modify “predictors of risk” to “predictors of individual risk” for the predictive column, and modify “Effects on risk” to “Effects on population risk”? This was the only ambiguous aspect for me. Given how important it is as a consumer of scientific literature, and potentially as a future researcher, I want to make sure I get this right.

Answer 1

I like that table, too.

To me, your modifications are unnecessarily restrictive. One can ask questions about population risk or subpopulation risk using predictive models. For example, one might want to answer, for a population with certain qualities, what is the average expected risk? You may ask whether population-level or aggregate individual-level factors affect the risk in a population. Your model may not even be for individual risk (i.e., the units may be counties, for example), or even if it is, the goal of the analysis is to compute the effect of a variable on subpopulation-level risk (e.g., using a multilevel model).

One may also be interested in individual causal effects. Designs like interrupted time series or synthetic control get at individual causal effects, and some big data analysis methods allow you to estimate individual causal effects from standard treatment-outcome data (with many covariates observed). Some causal inference techniques are also concerned only with the existence of a causal effect in a sample (e.g., randomization inference-based methods), with no population to generalize to. It's still coherent to ask these kinds of causal questions that don't refer to populations.

I would not say the primary distinction between predictive and causal methods is on whether the target of inference is an individual or a population. Although many predictive methods are particularly well suited for making predictions at the level of the individual and many causal inference techniques focus on making population-level inferences, these are not the only applications of these methods, and either can make claims about individuals or populations.

Answer 2

I find McElreath's explanation in Statistical Rethinking 2nd edition completely satisfying (and helpful to understand why these two are so commonly conflated). Essentially, both predictive and explanatory models are addressing two different meanings, or problems, of prediction.

• The first, associated with predictive models, addresses the 'raw' problem of prediction (what will happen next?).
• The second, associated with explanatory models, addresses a causal identification prediction problem (what will happen if we intervene, or a variable in the causal pathway is otherwise altered).

This wonderfully sets the stage for linking the challenge of overfitting with the raw prediction problem, and linking erroneous/spurious association with the causal identification predictive problem.

The original question was hung up on a perception of ambiguity in the language, "Effect on risk" versus "predictors of risk." While this language seems clear now, I think McElreath's explanation more explicitly helps readers (who are so used to the terms being interchangeable) delineate the difference by initially describing them as two problems of prediction (avoiding use of the conflated terms themselves in the description). Then learners (like me) can better map the understanding back onto other terms. This problem runs deep and is long-standing.