Causal models and learning from data: integrating causal modeling and statistical estimation

Abstract

The practice of epidemiology requires asking causal questions. Formal frameworks for causal inference developed over the past decades have the potential to improve the rigor of this process. However, the appropriate role for formal causal thinking in applied epidemiology remains a matter of debate. We argue that a formal causal framework can help in designing a statistical analysis that comes as close as possible to answering the motivating causal question, while making clear what assumptions are required to endow the resulting estimates with a causal interpretation. A systematic approach for the integration of causal modeling with statistical estimation is presented. We highlight some common points of confusion that occur when causal modeling techniques are applied in practice and provide a broad overview on the types of questions that a causal framework can help to address. Our aims are to argue for the utility of formal causal thinking, to clarify what causal models can and cannot do, and to provide an accessible introduction to the flexible and powerful tools provided by causal models.

FIGURE 1

A general roadmap for approaching causal questions.

FIGURE 2

Causal graphs and corresponding structural equations representing alternative data generating processes. (A), Assumes that W may have affected A, both A and W may have affected Y, and W, A, and Y may all share unmeasured common causes. (B), Assumes that subjects were randomly assigned to an exposure arm R with probability 0.5 and that assigned exposure arm R does not affect the outcome Y other than via uptake of the exposure A. (C), Figure 2A after a hypothetical intervention in which all subjects in the target population are assigned exposure level 0 (however this is defined). (D) and (E), Figure 2A augmented with additional assumptions to ensure identifiability of the distribution of Y_a (and thus target quantities such as the average treatment effect) given observed data (W,A,Y). (F), Assumes that Z does not affect A or Y, that A shares no common causes with W or Y, and that W shares no common causes with Y or Z. Figures 2A, 2D, and 2E have no testable implications with W,A,Y observed, and thus imply non-parametric statistical models for the distribution of (W,A,Y). In contrast, Figure 2B implies that R is independent of W, and thus implies a semi-parametric statistical model for the distribution of (W,R,A,Y).

FIGURE 3

Translating a scientific question into a target causal quantity.

FIGURE 4

Interpreting the results of a data analysis: a hierarchy. The use of a statistical model known to contain the true distribution of the observed data and of an estimator that minimizes bias and provides a valid measure of statistical uncertainty helps to ensure that analyses maintain a valid statistical interpretation. Under additional assumptions, this interpretation can be augmented.