Questions: Causal Inference Methods in Biostatistics

Question 1

The fundamental problem of causal inference states that we can never observe both potential outcomes for the same individual. Why does randomization solve this problem at the population level even though it cannot solve it at the individual level?

• A. Randomization ensures every individual is observed under both conditions
• B. Randomization ensures that the treatment and control groups are, on average, exchangeable — the treated group's observed outcomes estimate Y(1) for the population, and the control group's observed outcomes estimate Y(0), because assignment is independent of potential outcomes
• C. Randomization eliminates all confounders including those that cannot be measured
• D. Both B and C

Answer: (D)

Both B and C are correct and describe the same mechanism from different angles. Randomization makes treatment assignment independent of all subject characteristics (measured and unmeasured), ensuring exchangeability — the treated group is a random sample of the population's Y(1) values and the control group is a random sample of Y(0) values. This solves the problem at the group level (we can estimate E[Y(1)] and E[Y(0)] separately) even though each individual is only observed under one condition.

Question 2

A directed acyclic graph (DAG) shows that Socioeconomic Status (SES) causes both Exercise (treatment) and Heart Disease (outcome). A researcher adjusts for SES in a regression. According to the DAG, is this sufficient to identify the causal effect of Exercise on Heart Disease?

• A. Yes, if SES is the only confounder — adjusting for it blocks the backdoor path from Exercise to Heart Disease through SES
• B. No — adjusting for confounders is never sufficient in observational data
• C. Yes, but only if Exercise is randomized
• D. No — you should also adjust for all variables in the dataset

Answer: (A)

The backdoor criterion from DAG theory states that the causal effect is identified if all backdoor paths (non-causal paths from treatment to outcome) are blocked by conditioning on a sufficient set of variables. If SES is the only confounder, adjusting for it blocks the only backdoor path Exercise ← SES → Heart Disease, and the remaining association is causal. DAGs make the no-unmeasured-confounders assumption explicit and help determine the minimum sufficient adjustment set — adjusting for everything is actually harmful if it includes colliders or mediators.

Question 3

Adjusting for a collider (a variable caused by both treatment and outcome) in a regression introduces bias rather than removing it.

• T. True
• F. False

Answer: True

A collider is a variable that is caused by both the treatment and the outcome (or by causes of each). Conditioning on a collider opens a spurious path between treatment and outcome that was not present before adjustment. This is called collider bias or Berkson's bias. For example, if both Exercise and Heart Disease independently affect Hospital Admission (a collider), conditioning on hospitalization creates a spurious negative association between exercise and heart disease among hospitalized patients. DAGs reveal this: a path Treatment → Collider ← Outcome is blocked by default but opened by conditioning on the collider.

Question 4

Explain the SUTVA (Stable Unit Treatment Value Assumption) and give a biostatistical example of when it would be violated.

Model answer: SUTVA requires that (1) each subject's potential outcome depends only on their own treatment, not on other subjects' treatments (no interference), and (2) there is only one version of each treatment level (no hidden variations). It is violated in vaccination studies: an unvaccinated person's probability of infection depends on how many of their contacts are vaccinated (herd immunity), so one person's treatment assignment affects another person's outcome. It is also violated if the 'same' drug is administered at different doses, by different routes, or with different compliance levels across study sites.

SUTVA violations are common in infectious disease, cluster-randomized trials, and social network studies. When interference is present, the potential outcomes notation Y_i(1) and Y_i(0) is insufficient — the potential outcome depends on the full treatment vector of all subjects, not just the individual's assignment. Methods for handling interference include cluster-randomized designs and interference-aware estimands.