# Causation- Exacerbating factor

The last three types of causal inference to be discussed diverge from the previous two in a critical way. Exacerbating factor, possible elimination and definite elimination all refer to causes that must interact with effects that are also occur due to other causes; and they either exacerbate the effect of the primary cause, or are possibly eliminating or definitely eliminating the effect from the primary cause. So with these last three types we are really talking about the beginning considerations of causal networks and how a second cause interacts in the relationship between a primary cause and effect.

Generally for Z to be an exacerbating factor the following must be true of X, Y and Z:

P(Y | X and Z) > P(Y | X) |

I can think of at least three minimal forms of an exacerbating factor. They all require a third factor (the exacerbating factor) which we will call Z.

In the first form X is a probable cause of Y (must be probable because if X was a definite cause then the definition of an exacerbating factor Z could not hold (P(Y | X and Z) > P(Y | X)) at the most P(Y | X and Z) = P(Y | X)). The assumption with this first form is that there is no association between X and Z, but if present Z increases the probability of (or the response of) Y. In other words, Z exacerbates the effect. There are implications for this network that need to be considered in both induction and abduction. In both cases, generalize the causal association between X and Y, or Z and Y you need to account for the other (X or Z). So whether making observations of X and Y and attempting to say they are causally associated you would need to know about Z; or whether you are observing Y and trying to say X is the cause you need to rule out Z. In the use of graphical causal models, this is referred to as conditioning, we would say we need to condition on Z to know whether X causes Y or whether Y abducts X. |

The second form is more complicated as X is a cause of Z and Z then causes Y, but X is also a direct cause of Y. With this form we would again need X to be a probable cause of Y. If you think through it you will realize that for Z to be an exacerbating factor here either X to Z or Z to Y needs to be probable. If they are both definite (X to Z and Z to Y) then there is a definite causal chain between X and Y through Z making Z part of the causal chain, not an exacerbating factor.

The final form I can think of is the classic definition of confounding. So an exacerbating factor may be a confounder, and a confounder may be an exacerbating factor (but confounders may also be eliminators, that is they may eliminate not exacerbate the effect). With this form of an exacerbating factor, Z causes X and Y. In the next post I will consider when this model meets the definition of an exacerbating factor.

For those following along, it would be very helpful for others to consider examples of these generalized networks in physical therapy practice. I have found myself with less time lately for that more practical extension of this work. If you have an example please share it with me and we can discuss having you write it up as a post with a graphic and explanation.

In my last post I wrote: “ In the next post I will consider when this model meets the definition of an exacerbating factor.” The model I was considering was that of classical confounding. For the definition of an exacerbating factor: P(Y | X and Z) > P(Y | X) to be true the only condition required with this causal model is that the 0<P(Y | X) <1 (in other words, a probable cause not a definite cause). If X to Y was a definite cause then Z could not exacerbate the effect Y. It could cause Y by causing X, but then it is not an exacerbating factor. |

Before signing off of this post and starting one on definite elimination I just want to point out that so far all of our considerations are testable based on observations with induction leading to generalizations (universals). I have not started to consider the considerations of these forms for abduction where things get more complicated.

The last three types of causal inference to be discussed diverge from the previous two in a critical way. Exacerbating factor, possible elimination and definite elimination all refer to causes that must interact with effects that are also occur due to other causes; and they either exacerbate the effect of the primary cause, or are possibly eliminating or definitely eliminating the effect from the primary cause. So with these last three types we are really talking about the beginning considerations of causal networks and how a second cause interacts in the relationship between a primary cause and effect.

Generally for Z to be an exacerbating factor the following must be true of X, Y and Z:

P(Y | X and Z) > P(Y | X) |

I can think of at least three minimal forms of an exacerbating factor. They all require a third factor (the exacerbating factor) which we will call Z.

In the first form X is a probable cause of Y (must be probable because if X was a definite cause then the definition of an exacerbating factor Z could not hold (P(Y | X and Z) > P(Y | X)) at the most P(Y | X and Z) = P(Y | X)). The assumption with this first form is that there is no association between X and Z, but if present Z increases the probability of (or the response of) Y. In other words, Z exacerbates the effect. There are implications for this network that need to be considered in both induction and abduction. In both cases, generalize the causal association between X and Y, or Z and Y you need to account for the other (X or Z). So whether making observations of X and Y and attempting to say they are causally associated you would need to know about Z; or whether you are observing Y and trying to say X is the cause you need to rule out Z. In the use of graphical causal models, this is referred to as conditioning, we would say we need to condition on Z to know whether X causes Y or whether Y abducts X. |

The second form is more complicated as X is a cause of Z and Z then causes Y, but X is also a direct cause of Y. With this form we would again need X to be a probable cause of Y. If you think through it you will realize that for Z to be an exacerbating factor here either X to Z or Z to Y needs to be probable. If they are both definite (X to Z and Z to Y) then there is a definite causal chain between X and Y through Z making Z part of the causal chain, not an exacerbating factor.

The final form I can think of is the classic definition of confounding. So an exacerbating factor may be a confounder, and a confounder may be an exacerbating factor (but confounders may also be eliminators, that is they may eliminate not exacerbate the effect). With this form of an exacerbating factor, Z causes X and Y. In the next post I will consider when this model meets the definition of an exacerbating factor.

For those following along, it would be very helpful for others to consider examples of these generalized networks in physical therapy practice. I have found myself with less time lately for that more practical extension of this work. If you have an example please share it with me and we can discuss having you write it up as a post with a graphic and explanation.

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