Chapter 3 Hernán & Robins Observational Studies

1. Chapter 3 Hernán & RobinsObservational Studies Johannes A. Landsheer, Utrecht University

2. Three (or six) conditions for identifying causality when correlation exists (p. 26) • Consistency: Well defined and consistent interventions or treatments • Exchangeability: Subjects receiving the interventions are exchangeable • Positivity: All probabilities of interventions are > 0 But true experiment also guarantees that: • Each subject receives a single intervention or an unique combination of interventions • The cause precedes the effect • Some of the alternative causes are excluded by experimental control (subjects cannot influence each other) SUTVA assumption: Stable Unit-Treatment value

3. Exchangeability Randomized selection + fully exchangeable Randomized assignment Cannot be combined in an ethical way! Observational studies: lack of internal validity • RS often no problem  external validity • RA big problem  approx.: “controlling” by covariates Experimental studies: lack of external validity • RA often no problem  internal validity • RS big problem  approx.: repeated experiments

4. Exchangeability 1 (within an experiment) Experiments • True experimental design is fully exchangeable Exchangeability also holds for unmeasured variables (p.29) Experiments may have limited exchangeable results • Conditional exchangeable within well defined groups (grouping variable L)  randomized block design Exchangeability does not hold for other groupings • Conditional exchangeability when RA does not hold (covariates L)  quasi experimental design Exchangeability is assumed

5. Exchangeability 2 (within an observational study) • Receiving treatment may be associated with outcome predictors • In that case: conditional exchangeability given covariates may hold Observational studies • Necessary covariates are not well defined, i.e., there may be other relevant covariates. Conditional exchangeability is assumed. Argumentation is important. (p. 28) Furthermore: • It may be hard to guarantee that the intervention precedes the result • It is difficult to exclude other possible causes, not covered by covariate control (or random assignment). For instance: subjects may influence each other. SUTVA should be argued!

6. Positivity: Probability being assigned to each condition > 0 (p 30) • Experiments: • Positivity guaranteed by design • Observational studies: • Positivity not guaranteed • Positivity can often be verified • Only required for variables that are needed for exchangeability • But what are these variables ?? Remark: low positivity is also a problem

7. Consistency of cause: well defined treatments (p 31-34) Consistency: Ya = Y when A = a • Treatments A have to be defined precisely • When treatments are ill defined, the counterfactual outcomes are ill defined Minimal criteria: • Valid and substantial association • Other observations offer consistency and plausibility • Specificity • Cause needs to precede the outcome • Interventions have predictable outcomes

8. Why is this causal relationship vague: Obesity  Mortality (p 33) • Temporality: Obesity is a long-term risk factor • Unspecific: Obesity itself has multiple underlying causes • Direct manipulation of obesity is not possible Describing the relationship as association is sufficient Causal inference is more useful when the cause can be removed or implemented

9. Consistency: link to the data (p 35-36) Hernán & Robins recommendations: • Restrict to versions of treatment that are well-defined and interesting • Criterion: no remaining vagueness remains p.34 (How?? When??) • Assume treatment-variation irrelevance (SUTVA) • Ensure matching data (positivity)

10. Imagine a (hypothetical) experiment (p 36) • Resort to observational data when the target trial is not feasible, ethical or timely • Calculate the attributable fraction (fine point 3.4) • Make groups conditionally exchangeable, using covariates

11. Conclusions • Exchangeability in observational data • Random assignment, can be approximated using covariates • It may be difficult to guarantee sufficient exchangeability • Large amounts of data are needed • Experiments have sufficient positivity by design • Observational data may require selection • Consistency • Experiments may use various methods of control • to guarantee correct assignment • to guarantee the value of each intervention This may be difficult to achieve when using observational data • Temporality can be difficult to guarantee when using observational data

12. Further reading Little, R. J., & Rubin, D. B. (2000). Causal effects in clinical and epidemiological studies via potential outcomes: concepts and analytical approaches. Annual Review of Public Health, 21(1), 121–145.

13. For discussion: Example of true experiment: Low blood-sugar decreases attention span Simple experimental design: • Ensure low blood sugar by asking subjects to skip breakfast • Control: Measure low blood sugar, exclude subjects with high levels • Controlled Intervention: Random assignment to two conditions • Breakfast • No Breakfast • Measure blood sugar • Dependent variable: Measure attention span

14. Observational study: Skipping breakfast decreases attention during class • Measure “Independent predictor”: Ask respondent whether they have eaten breakfast • Covariates: Measure background variables to allow control for possible group differences • Measure “Dependent variable”: attention during class • Ask respondent or teacher, or • Administer an attention test Problem: lack of control • Independent predictor is not equal to a controlled treatment • Covariates do not guarantee full exchangeability • Lack of control over alternative causes

15. True experiment • Has well defined k > 1 interventions (often including no-intervention) • Has the subjects random assigned and each subject receives one intervention or a unique combination of interventions • Is preferably balanced: probabilities near 1/k • All interventions precede results by design • Some alternative causes are excluded by experimental control As subjects are truly randomly assigned, most other causes would have equal effects in all intervention groups

16. History of a causal inference: