1. Chapter 3 Hernán & Robins Observational 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: