ARM samenvatting
tentamen
Week 1: lectures and workgroups
Causal inference: the study of causal effects. Its about asking the ‘what if’ question. We observe what
happens and ask ourselves ‘what would have happened if’.
Causal effect: in an individual, a treatment has a causal effect if the outcome under treatment 1 would be
different from the outcome under treatment 2.
Counterfactual outcomes: outcomes that have not been observed. This is often a fundamental problem in
research: you don’t know what would have happened if someone did not get the treatment.
These missing data is a fundamental problem because individual causal effects cannot be observed,
except under extremely strong assumptions. But this is generally unreasonable. The average causal effect
cannot be inferred/concluded from individual estimates. So we need a different approach to causal
effects identifiability conditions.
Average causal effects can still be determined under certain conditions, not individual cases, but in groups
we can still observe the counterfactual outcomes. Based on population averages, the causal effects can be
estimated if three identifiability conditions hold:
1. Positivity: about the sample and the way it was composed. There has to be a positive probability
to get assigned to one of the treatments. There has to be a control group. We must have results
for all treatment groups in order to make the analysis possible. More exactly: results for all
treatment groups in all strata of the adjustment variables. Problems might be: lack of control
group, observations being unavailable
2. Consistency: the definition of the exposure and the alternative needs to be well-defined and can
always be expected to lead to the same results (on average). For example SES: someone with
high education and low income has the same SES as someone with a low education and high
income. So ‘giving’ someone a SES has different meanings and is not consistent.
3. Exchangeability: treatment groups need to be exchangeable: it does not matter who get
treatment A and who gets treatment B. Exchangeability means that the results of the analysis
would be the same if the treatment groups were swapped, after possible statistical adjustment.
There might be problems when there is unresolved confounding.
If these three conditions are present: association of exposure and outcome is an unbiased estimate of
causal effect Randomized controlled trial (RCT)
Example: when you are researching if carrying a cigarette lighter has an effect on your health, people are
not exchangeable. But they are once you adjust for smoking. Then you only observe people who smoke
and then identify if carrying a cigarette lighter has an effect on their health. So adjustment can improve
exchangeability. When you have a small number of factors you can do stratification: matching, weighting
or regression analysis.
An association does not equal causation. In many cases we are interested in causal effects, not just
associations. To see what assumptions are required we design the analysis according: theory/subject
knowledge and causal structure.
,There are some traditional strategies for adjustment that are problematic: correlation matrix, stepwise
backward selection, adjustment for confounders. These are problematic because they rely on the
observed data rather than any theory/subject knowledge. They are applied after the data collection and
important variables may be missed in this way. They may lead to underestimation of statistical uncertainty
and they may increase bias rather than reduce it. Solution graphical presentation of assumed/underlying
causal structure (DAGs).
In a DAG you don’t only see associations but you also see
connections: transmit association. DAG example:
Each connection is an arrow (directed)
A path of arrows does not come back to its origin
(acyclic).
Each arrow represents a possible causal effect
No arrow means that there is certainly no causal effect. So if
you are uncertain, draw an arrow. It sounds easy to stay on the safe side and just draw arrows
everywhere, but you should always have a reason why you should draw an arrow. In a DAG you cannot
have an arrow that is connected between two factors (see red arrow), this might be the case, but it is not
allowed in a DAG.
Path: route between exposure and outcome, it has not have to follow the direction of the arrows.
Causal path: follows the direction of the arrows.
Backdoor path: does not follow the direction of the path.
All paths are open unless there is a collider somewhere. We call something a collider when arrows collide
at one point, example:
W is a collider, so there are no open paths that go through W.
Open paths transmit association: the association of X and Y is the combination of all open paths between
them. An open path can be blocked when we adjust for a variable along the path.
Blocking: removing a backdoor path from an association by adjusting for a variable on that path.
Unblocking: opening a backdoor path by adjusting for a collider on that path.
Collider bias: bias caused by adjustment for a collider. Adjusting for a collider opens a backdoor path,
which introduces a non-causal element to the association of exposure and outcome. This generates an
association that is not there. This happens because you select the wrong two things. It is hard to identify
this without using a DAG!
Simple example:
Weight loss is a collider in this case. When you
‘open’ this backdoor path, diet may cause the
disease… that is not the case.
Colliders do not necessarily ‘happen’ after the
exposure and the outcome. It is very hard to understand this without a DAG.
Traditional definition of confounder: associated with the exposure and outcome, given the exposure. Not
in a causal pathway between exposure and outcome.
Structural definition of confounder: variables that can be used to remove confounding.
, Structural definition confounding: bias caused by common cause of exposure and outcome (lighter and
health are associated because of smoking).
So, the difference is that a confounder can cause confounding (the problem). Following the traditional
definition may lead to adjust for a collider (collider-bias)!
Healthy user bias (page 125): ‘People who take vitamins regularly are likely to be healthy –
because they are the kind of people who take vitamins regularly!’ – Confounding bias
Selection bias (collider bias): conditioning on/ adjusting for common effect.
There is confusion about selection bias and confounding. Confounding is sometimes called selection bias.
Selection bias sometimes means ‘sample not representative’. Confounding, collider bias and reverse
causality are sometimes called ‘endogeneity’. This doesn’t have to be a problem, as long as you are aware
of it.
Conclusion lectures: theory is important, you need it for developing an assumed causal structure and a
DAG. Deciding on adjustments in analysis: always for confounders and never for colliders. Causal
analysis cannot be data-driven. Draw your assumptions before you draw your conclusions!
It might happen that a variable is in some paths a collider and in some paths a confounder. When that
happens you should adjust for it because it is a confounder. The problem that it is in some paths it is a
confounder is than also tackled, because you open the backdoor path, but you close them again.
Week 2: lectures and workgroups
How to adjust: Stratification
Splitting up sample into strata, according to one confounder or a combination of confounders. For
example: smokers and non-smokers. Then you analyse each stratum separately and compare outcomes
with and without exposure in people with same characteristics (exchangeability).
Advantage: easy, intuitively interpretable
Disadvantage: only possible for limited number of confounders, confounders have to be categorized (for
instance age, you have to make groups)
How to adjust: Regression
Here you can adjust for several confounders at the same time (and/or intermediate variables). Regression
describes the (mathematical) relationship between outcome and one or more variables, while adjusting
for other variables.
Ordinary least square (OLS) regression
It is called like this because you are minimizing (squared)
distances between fitted line and observations.
Equation linear regression (OLS): Y = a + b*x
Example: weight (kg) = -61,2 + 0,80*height (cm)
What do the coefficients mean in this example? Coefficients
have a weight, in this case it is +0,8 kg for every centimetre in
height. With this equation you can predict somebody’s
weight. This prediction is the average for people with the
same characteristics.
OLS regression: adjusting for confounders
When you have confounders, you want to block these paths (remove parts from the association) to isolate
the causal effect between X and Y. When you want to do this, you add an extra term to the regression
each time.
