Uitwerking van alle colleges en werkgroepen van het vak Advanced Research Methods (GW4003MV). Door enkel het leren van deze aantekeningen het vak met een mooi cijfer kunnen afronden (7.3) Notes of all the lectures and working groups of the course Advanced Research Methods (GW4003MV).
Lecture 1: causal inference
Problems of the l'oreal study:
Small sample of 41 woman: is a small sample always a problem? If everybody died, you don’t
say “it is a small sample”. It depends on the strength of the effect and the variability.
Study performed or financed by commercial company: It could be a problem but university
work with commercial partners all the time. You need safeguards to protect the
independence of the research. It is a potentially problem, not always. You should use an
independent person.
No control group: this is an essential omission. What would happen with
patients without treatment? If you have a bad skin, there is a chance your skin
will be better in a few weeks without any products.
Causation: Formal definition (Hernan and Robins): In an individual, a treatment has a causal effect if
the outcome under treatment 1 would be different from the outcome under treatment 2.
You ask two questions:
What would have happened?
What will happen?
,A causal effect is there if the outcome of treatment with A is different than the outcome of no
treatment.
You can see in this picture what the outcome is when a patient does and when a patient doesn’t use
the treatment.
But you do not always know what would happen if the patient doesn’t use the treatment. Then you
will call the outcome a counterfactual outcome: potential outcome that is not observed because the
subject did not experience the treatment (counter the fact).
For patient K the outcome without treatment is counterfactual.
For patient M the outcome with treatment is counterfactual.
Counter-factuality is a fundamental problem of causal inference!
We have missing data. Individual causal effect cannot be observed. Except under extremely strong
(and generally unreasonable assumptions -> when someone is blind, you give a pill and someone can
see again). But generally when you don’t give the medication, you will not know what would have
happened.
Therefore we need a different approach!
It is still possible to know what would have happened if certain conditions apply. Not on individual
cases but in average -> the average causal effect, to 'observe' the counterfactual.
Based on population averages, causal effects can be estimated if three identifiability conditions
hold:
Positivity
Consistency
Exchangeability
If we meet these conditions, then association of exposure and outcome is unbiased estimate of
causal effect.
For example: you ask in the city centre who has a cigarette lighter. You come back after twenty years
and see who is healthier. The causal question is: What is the effect of carrying a cigarette lighter on
health?
It is all about observing: what would have happened if…
Positivity means that there is a chance that someone with a lighter could also not have had a lighter
and vice versa. Positivity is not possible when you do research in gender -> it is not possible that you
couldn’t have been a woman. In the Loreal example there was also no positivity -> it wasn’t possible
to not use the product
,Consistency is about defining. How do you define if? For example, you can ask: is broccoli healthy?
But how much broccoli? And what do you eat when you don’t eat broccoli?
You have to compare it with something very specific as well. But also for example, the effect of
obesity on health. How do the obesity people got obesity, with unhealthy food or DNA mutations?
This is not the same, the one will be unhealthier than the other one. But you have a consistent
concept when you do research if there is an effect of obesity on job prospects. The reason of the
obesity doesn’t matter. In the case of the lighter, it is consistent: You have a lighter or you haven’t a
lighter.
Exchangeability is about 'What would happen if you give all the lighters of the people who had them,
to the people who not had them' Would the outcome be different? Treatment groups are
exchangeable if it doesn’t matter who gets treatment A and who gets treatment B.
Potential outcomes are independent of the treatment that was actually received.
In the case of the lighter, there is no exchangeability. Someone without a lighter is probably not a
smoker.
But there is a solution for this: it may be necessary to take other factors into account (adjustment for
smokers and non-smokers: 2 groups). Within smoking group, are people with and without lighter
exchangeable? Within non-smoking group, are people with and without lighter exchangeable?
But you need more positivity. Units are assigned to all relevant treatment within levels of adjustment
factors. You need:
Smokers with cigarette lighter
Smokers without lighter
Non-smokers with lighter
Non-smokers without lighter
You can do stratification. You can make two groups: with lighter and without lighter. You see a
different in health after twenty years. With lighter 57% is healthy and without 87% is healthy -> but
you cannot conclude that carrying a lighter is bad for you!
You need some stratification and make a difference between smokers with lighter and without
lighter and then you will see that carrying a lighter makes no difference in health!
, You see unadjusted results and adjusted results. We have positivity, it is possible to have of don’t
have a lighter. Probably we have consistency; it is clear what we mean with having a lighter and don’t
having a lighter. And after having adjusted for smoking status, the groups are exchangeable with
regards to smoking status. You can put someone with a cigarette lighter in the group without lighter.
Meeting the conditions: RCT
If you do a randomised controlled trial it is easy to achieve these conditions. You select patients and
randomly assign them to treatment groups:
Random: exchangeability, because you can change the patients because of the
randomly assign
Random: positivity, everybody in the sample had the chance or getting treatment 1 or
2
Because of we are assigning people to a treatment, we have to know what the
treatment means so we also have consistency.
Sometimes you can’t do a RCT or you don’t want to do this (ethical reasons). There are limited
generalisability (external validity) due to treatment protocol and patient selection.
Than you have to look at observational studies. Those are from the real-world. Than you have a
threat of internal validity by lack of exchangeability. And positivity and consistency need also explicit
attention.
Segment 3 exchangeability and DAG
In many cases we are interested in causal effects, not just associations
Causal conclusions can be drawn if identifiability conditions are true (positivity, exchangeability,
consistency)
To see what assumptions are required we use: theory/subject knowledge, causal structure and we
design the analysis accordingly.
You can do several adjustments to improve exchangeability:
Stratification when you have small number of factors
Matching
Weighting
Regression analysis
What you should adjust for? There are traditional selection strategies:
Correlation matrix: select variables with significant association with outcome and put
them in regression model.
Stepwise backward selection:
Start with all variables in regression model
Remove the variable that is the least statistically significant
Repeat steps
Or: retrain variable if removal leads to substantial change in effect estimate (PC lab)
Adjust for confounders, which are defined as being
Associated with the exposure
Conditionally associated with the outcome, given the exposure
It is not in the causal pathway between exposure and outcome
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