1. Causal Networks
Farrokh Alemi, PhD

2. Is the relationship between two variables causal?
Association
How can we decide if the relationship between two variables is causal? In order to answer this question, the relationship must meet 4 criteria. First, the two variables must be associated with each other. Lack of association indicates that the two variables are independent of each other and therefore do not have a causal effect on each other.

3. Is the relationship between two variables causal?
Association
Sequence
Causes must precede effects. Causes cannot follow the effect. A relationship is judged to be more likely to be causal if the presumed cause precedes the effect.

4. Is the relationship between two variables causal?
Association
Sequence
Mechanism
If one variable causes another, then it must have a mechanism through which this occurs. We are more willing to accept a causal interpretation if the mechanism of the effect is described and is known to produce the effect.

5. Is the relationship between two variables causal?
Association
Sequence
Mechanism
Counterfactual
When causes are absent, the effect should be less likely to occur. Counterfactual cannot be observed but says that under an unobserved scenario where the cause has not occurred we should not see the effect or see the effect to be less likely. Counterfactual modifies the notion of association. When two variables are associated, changes in the effect modifies the likelihood of observing the cause and vice versa. In causal relationship this is not true. Changes in effect do not change the frequency of the cause. Only changes in the cause affect the frequency of effects.

6. Collection of Inter-related Causes and Effects
Causal Network
Collection of Inter-related Causes and Effects
A causal network is a collection of interrelated causes and their effects. By interrelated we mean that one cause can have an effect that can cause another effect. No variable is unrelated to anything else. Variables that are not related to the network are simply ignored as they are not relevant.

7. Collection of Nodes & Directed Links
Causal Network
Collection of Nodes & Directed Links
A causal network is a collection of nodes and directed links among pairs of nodes. Each node represents one variable and each link a relationship among a pair of variables.

8. Fidelity of Causal Graphs and Independence
No Relationship No Link
Causal graphs can be drawn from independence assumptions. If two variables are directly related to each other they are shown by a directed link. If they are indirectly related to each other you can start from one variable and follow the links and reach the other. If two variables are unrelated then there should be no link between them and one cannot follow the links shown in a graph to reach from one to the other.

9. Display of Causal EffectsB C D
The cause and effect is shown by a directional arrow between the two nodes, each node designating a variable. Here we see the effect of variable A on variable B. The direction of the arrow shows the causal impact of one variable on another. The absence of the arrow indicates that the two variables are associated. The two variables C and D are associated and we do not know if there is a causal relationship among them. Finally the absence of a link between the two variables indicates that the two variables E and F are independent from each other. E F

10. Display of Causal Effects
Medication Error
Long Hospital Stay
This display shows that medication errors lead to prolonged hospital stay. There are two variables shown: medication error and long hospital stays. The link between the two shows that these two variables are associated with each other. The arrow in the link shows that medication error causes long hospital stays but not vice versa. It is not correct that long hospital stays cause medication errors.

11. Common Effect Medication Error Long Hospital Stay Severe Illness
Here we are showing two competing causes of long hospital stays. Patients may stay longer in the hospital because they have had a medication error or they are sicker than average hospitalized patient. There are two causes for the same effect and this situation is referred to as common effect. Some refer to it as the V relationship among 3 variables.

12. Severe conditions don’t have more medication errors
Long Hospital Stay
Severe Illness
Note that this graph also shows that the probability of medication errors is independent of severity of the patients’ illness. This is implied by the fact that there is no link between severe illness and medication error. If this is not true then the network as drawn is misleading.

13. Severe conditions increase rate of medication error
Long Hospital Stay
Severe Illness
If we think that this is not correct, we can insert a causal link between severity of the patient’s illness and the frequency of medication error. Now the graph shows not only an association between severity of the patient’s illness and medication error, but a causal relationship.

14. Causal Chain Provider Fatigue Medication Error Long Hospital Stay
Severe Illness
As the number of variables increases a causal network can describe the relationship among any pair of variable. Let us add provider fatigue into the network.

15. Causal Chain Provider Fatigue Medication Error Long Hospital Stay
Severe Illness
Here the provider fatigue is shown to cause medication errors and medication errors are shown to cause long hospital stays. These three variables are said to be in a causal chain. Fatigue causes errors and errors cause longer stays.

16. Direct and Indirect Causes
Provider Fatigue
Medication Error
Long Hospital Stay
Severe Illness
Provider fatigue is an indirect cause of long hospital stays.

17. Mediation Provider Fatigue Medication Error Long Hospital Stay
Severe Illness
Provider fatigue changes length of hospital stay through the mediating variable medication error. Provider fatigue is the direct cause of medication error and medication error is the direct cause of long hospital stay. Another way of saying the same thing is that provider fatigue is the indirect cause of long hospital stays and this effect is mediated by presence of medication errors.

18. Independence Provider Fatigue Medication Error Long Hospital Stay
Severe Illness
A typical network shows a lot more independence than it shows causal relationships. Here we see 5 direct causal relationships shown by 5 links between pairs of variables. What we do not see is a lot more.

19. Meaning of What Is Not Shown
Provider Fatigue
Medication Error
Long Hospital Stay
Severe Illness
We do not see a direct causal impact between provider fatigue and long hospital stay although these two variables are correlated. What is not shown has meaning and implies lack of direct causal relationship.

20. No Connection Means Independence
Provider Fatigue
Medication Error
Long Hospital Stay
Severe Illness
Here for example, we show no relationship between provider fatigue and severe illness. These two variables are independent from each other. There is no way that we can start from either variable and end in the other. The absence of a link in a network implies independence and vice versa independence implies a particular network.

21. Impact of Changes in Effect
Cause
Counterfactual modifies the notion of association. Here we see a cause and effect relationship where any time the cause decreases the effect increases. For example, any time we go into recession more people seek service sector jobs. If this relationship is causal, then increases in the effect should not necessarily lead to decreases in the cause. So if we see many people applying for health services jobs we should not assume that we are in recession. When two variables are associated, changes in the effect modifies the likelihood of observing the cause and vice versa. Think of association as seesaw. In causal relationship this is not necessarily true. Changes in effect do not change the frequency of the cause. The seesaw model does not apply as changes in the effect do not cause any change. Only changes in the cause affect the frequency of effects.

22. No Cycles B C D A
In our analysis of causal effects, we ignore cycles. This is not to say that in real life there are no cycles of causal effects. They are there.

23. No Cycles
Time breaks cycles. If we think of time increasing then as we move through a causal chain we do not end up at the place we started as now A is occurring at a later time period. Even though we do not consider causal cycles, the models and methods we develop can be used to analyze causal cycles over time. B C D A