Chapter 3 Hernán & Robins Observational Studies Johannes A. Landsheer, Utrecht University

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

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

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

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!

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

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

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

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)

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

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

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.

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

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

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

History of a causal inference: