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Causal inference is the science of attributing a particular outcome (or effect) to one or more particular causes. In addition to concluding that there is an association between two variables, causal inference implies that the effect is the direct result of a measurable cause. In medical research, the cause is often an intervention or treatment, and the outcome is often a disease or complication. Outcomes from those receiving the intervention, perhaps a particular drug, are often compared with those of a control group. When the difference in outcomes between the experimental and control groups is attributed to the intervention, causal inference is being made.

Causal inference is made most cleanly in a randomized, blinded study. However, even in a non-randomized setting, some degree of qualified causal inference may be possible. This depends on the extent of thorough understanding of the relationships involved, careful design, and data collection and analysis. Causal inference relationships can be visualized and clarified using causal diagrams—modern tools that use arrows to visualize the purported relationships between causal variables, outcome variables, and confounding variables in both randomized and nonrandomized studies.

Randomized Studies

In a randomized research study, each subject is randomly assigned to receive one of the interventions to be compared. At randomization, but before receiving intervention, randomized groups are very similar to each other with respect to baseline predictors of outcome, the only systematic difference being the assigned intervention. Unless the process of randomization has been systematically altered, other baseline differences would be due to chance.

Thus, in a properly conducted randomized study, there is no selection bias or treatment assignment bias; neither patients nor doctors choose which intervention an individual will receive. Because a confounder is a variable that is associated with both intervention and outcome, and because there is usually no association between treatment assignment and baseline predictors of outcome in a randomized study, confounding does not usually exist. Differences in outcome between randomized groups are correctly interpreted as cause-effect.

Fundamental Problem of Causal Inference

Causal inference is a missing-data problem. It has its basis in individuals, not group averages. Let Y1 and Y0 represent an individual's potential (or hypothetical) response on treatment and control, respectively. An individual causal effect is defined as the difference between these two potential outcomes at the same point in time, or δ = Y1Y0. The average of the individual causal effects, or the average causal effect (ACE), can be written as E[Y1Y0] = E [δ], where E is the expectation sign, indicating the average of all subjects. Causal effects may well differ across individuals.

However, individual causal effects are never observable because more than one intervention cannot be independently given to the same individual at the same time. In a parallel-group randomized study, each patient receives only one intervention, either treatment or control, and so the outcome is observed for only one of the potential outcomes for that patient. Causal inference is thus a huge missing data problem, in which half of the data for each individual is unobserved. How, then, can causal inference be made? This is the Fundamental Problem of Causal Inference.

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