ADVANCED RESEARCH METHODS 23/24 – M HEALTH ECONOMICS,
POLICY AND LAW
WEEK 1 - CAUSALITY AND DIRECTED ACYCLIC GRAPHS
CAUSAL INFERENCES
Causal inference we consider the assumptions, study designs and estimation strategies that allow to draw
causal conclusions based on data. In causal inference we are not interested in the outcome per se but are
interested in the influence that a factor has in achieving an outcome.
Causal effect is described by Hernàn and Robins as: “In an individual, a treatment has a causal effect if the
outcome under treatment 1 would be different from the outcome under treatment 2”. To asses this,
information is needed on: What would have happened? And: What will happen?
The formal notation of a causal effect is: - Y = outcome
- a = treatment
- 1 = yes (received treatment)
- 0 = no (received no treatment)
- i = individual
- ≠ does not equal
Counterfactual outcome: the potential outcome is not observed, because the subject did not experience the
treatment (controls)
IDENTIFIABILITY CONDITIONS
Average causal effect can be determined if, and only if, three identifiability conditions are met in a study:
1. Positivity
- Each individual has to have a ‘positive probability’ of being assigned to each of the treatment
arms (i.e., Pr(A=a)>0 for all treatment arms)
2. Consistency
- The treatment (or intervention, exposure) has to be well-defined
3. Exchangeability
- The individuals assigned to the different treatment arms have to be similar
- It does not matter who gets treatment A and who gets treatment B
a
- Formal notation Y i ⊥ A , meaning that the potential outcomes are independent of the treatment
that was actually received
If all conditions are met (and a association is found in the data) the association between exposure and outcome
is an unbiased estimate of a causal effect
, MEETING THE EXCHANGEABILITY CONDITIONS
Various ways are possible
1. Randomized controlled trial (RCT) – Golden standard, because typically all identifiability conditions are
met in RCT
- Individuals are randomly assigned to one of each treatment arms
- Differences between individuals in the different treatment arms are cancelled out on the sample
level
- Differences are independent from the treatment and outcome
- Differences are random, not systematic
2. Matching
- For each individual with characteristics x, y, and z who gets treatment A, there is an individual
with characteristics x, y, and z who gets treatment B
- Statistical methods can be applied when perfect matching (i.e., use identical twins, triplets, …) is
not possible (e.g., propensity score matching
3. Stratification
- Randomly select individuals from different subsets (i.e. strata) of the larger population
- Difficult to meet the positivity condition (i.e. individuals in all strata)
- Stratification quicly becomes infeasible, the more strata are added
4. Adjustment
- Control for factors that influence (i.e. bias) the association between the treatment and outcome
in regression analysis
- Individuals are assigned to all treatment arms within all levels of adjustment factors
- Can also be combined with an RCT, stratification, and matching
- Complete and correct adjustment leads to exchangeability (use of the tool DAG)
STUDY TYPES, RCT VS OBSERVATIONAL
RCTs considered ‘golden standard’ however:
- Limited external validity (e.g., controlled setting, efficacy of treatment)
- Ethical and practical considerations
Observational (non-randomised) studies:
- Real-world outcomes (effectiveness of treatment)
- Availability of data (e.g., patient registries)
- Positivity and consistency need close attention
- Internal validity threatened by lack of exchangeability
POLICY AND LAW
WEEK 1 - CAUSALITY AND DIRECTED ACYCLIC GRAPHS
CAUSAL INFERENCES
Causal inference we consider the assumptions, study designs and estimation strategies that allow to draw
causal conclusions based on data. In causal inference we are not interested in the outcome per se but are
interested in the influence that a factor has in achieving an outcome.
Causal effect is described by Hernàn and Robins as: “In an individual, a treatment has a causal effect if the
outcome under treatment 1 would be different from the outcome under treatment 2”. To asses this,
information is needed on: What would have happened? And: What will happen?
The formal notation of a causal effect is: - Y = outcome
- a = treatment
- 1 = yes (received treatment)
- 0 = no (received no treatment)
- i = individual
- ≠ does not equal
Counterfactual outcome: the potential outcome is not observed, because the subject did not experience the
treatment (controls)
IDENTIFIABILITY CONDITIONS
Average causal effect can be determined if, and only if, three identifiability conditions are met in a study:
1. Positivity
- Each individual has to have a ‘positive probability’ of being assigned to each of the treatment
arms (i.e., Pr(A=a)>0 for all treatment arms)
2. Consistency
- The treatment (or intervention, exposure) has to be well-defined
3. Exchangeability
- The individuals assigned to the different treatment arms have to be similar
- It does not matter who gets treatment A and who gets treatment B
a
- Formal notation Y i ⊥ A , meaning that the potential outcomes are independent of the treatment
that was actually received
If all conditions are met (and a association is found in the data) the association between exposure and outcome
is an unbiased estimate of a causal effect
, MEETING THE EXCHANGEABILITY CONDITIONS
Various ways are possible
1. Randomized controlled trial (RCT) – Golden standard, because typically all identifiability conditions are
met in RCT
- Individuals are randomly assigned to one of each treatment arms
- Differences between individuals in the different treatment arms are cancelled out on the sample
level
- Differences are independent from the treatment and outcome
- Differences are random, not systematic
2. Matching
- For each individual with characteristics x, y, and z who gets treatment A, there is an individual
with characteristics x, y, and z who gets treatment B
- Statistical methods can be applied when perfect matching (i.e., use identical twins, triplets, …) is
not possible (e.g., propensity score matching
3. Stratification
- Randomly select individuals from different subsets (i.e. strata) of the larger population
- Difficult to meet the positivity condition (i.e. individuals in all strata)
- Stratification quicly becomes infeasible, the more strata are added
4. Adjustment
- Control for factors that influence (i.e. bias) the association between the treatment and outcome
in regression analysis
- Individuals are assigned to all treatment arms within all levels of adjustment factors
- Can also be combined with an RCT, stratification, and matching
- Complete and correct adjustment leads to exchangeability (use of the tool DAG)
STUDY TYPES, RCT VS OBSERVATIONAL
RCTs considered ‘golden standard’ however:
- Limited external validity (e.g., controlled setting, efficacy of treatment)
- Ethical and practical considerations
Observational (non-randomised) studies:
- Real-world outcomes (effectiveness of treatment)
- Availability of data (e.g., patient registries)
- Positivity and consistency need close attention
- Internal validity threatened by lack of exchangeability
