ASA Connect

In the literature on competing risks, I've come across two slightly different definitions of a competing risk event: 

1) A competing risk event is one that precludes the event of interest from ocurring; 

2) A competing risk event either modifies the probability of occurrence of the event of interest or prevents the event of interest from ocurring. 

My questions are: 

A. Are both definitions acceptable? 

B. Should one definition be preferred over the other and why?

Many thanks, 

Isabella

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Isabella Ghement
Ghement Statistical Consulting Company Ltd.
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You hypothesize that A is a causal factor for C but any uncontrolled B is a competing risk. That is, A and B are correlated. E.g., SIDS is associated with mother being a smoker but smoking is associated with various socio-economic factors (e.g., education level) any of which is a competing risk for SIDS. In non-experimental research, an effort is made to control competing risks by selection, adjustment, post-stratification (propensity score analysis), etc. Note that the competing risk may or may not nullify the effect of A but may modify it (up or down). For example, with a suppressor variable, the effect of A may only be detected in the presence of B. True experiments achieve control by randomization (that is, A and B are correlated by chance alone).

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Chauncey Dayton

Original Message:
Sent: 12-03-2015 18:15
From: Isabella Ghement
Subject: Definitions of competing risks

In the literature on competing risks, I've come across two slightly different definitions of a competing risk event: 

1) A competing risk event is one that precludes the event of interest from ocurring; 

2) A competing risk event either modifies the probability of occurrence of the event of interest or prevents the event of interest from ocurring. 

My questions are: 

A. Are both definitions acceptable? 

B. Should one definition be preferred over the other and why?

Many thanks, 

Isabella

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Isabella Ghement
Ghement Statistical Consulting Company Ltd.
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Both definitions are acceptable, but are obviously different. Competing risks as per the first definition are "classical competing risks."  A great example is the study of causes of mortality in demography.  Death from stroke would preclude death from cancer, for example.  The second definition is obviously broader and includes the first. A good example is the illness-death model, where there are 3 states: healthy, ill, dead.  A person who becomes ill has a different probability of death than the person who is healthy.  This is also known as "semi-competing risks" in the sense that illness alters the probability of death, whereas if a person dies from a healthy state, he/she cannot become ill (at least, not in this life!).

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Ravi Varadhan
Johns Hopkins University

Original Message:
Sent: 12-04-2015 10:09
From: Chauncey Dayton
Subject: Definitions of competing risks

You hypothesize that A is a causal factor for C but any uncontrolled B is a competing risk. That is, A and B are correlated. E.g., SIDS is associated with mother being a smoker but smoking is associated with various socio-economic factors (e.g., education level) any of which is a competing risk for SIDS. In non-experimental research, an effort is made to control competing risks by selection, adjustment, post-stratification (propensity score analysis), etc. Note that the competing risk may or may not nullify the effect of A but may modify it (up or down). For example, with a suppressor variable, the effect of A may only be detected in the presence of B. True experiments achieve control by randomization (that is, A and B are correlated by chance alone).

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Chauncey Dayton

I do not care for the second definition, at least not as described by Chauncey Dayton.  I can argue with myself, but I prefer to separate "confounding", which seems to be more what Chauncey describes, from classical competing risks which Ravi describes.

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Raoul Burchette
Biostatistician III
Kaiser Permanente, Pasadena, CA USA

Original Message:
Sent: 12-04-2015 10:09
From: Chauncey Dayton
Subject: Definitions of competing risks

You hypothesize that A is a causal factor for C but any uncontrolled B is a competing risk. That is, A and B are correlated. E.g., SIDS is associated with mother being a smoker but smoking is associated with various socio-economic factors (e.g., education level) any of which is a competing risk for SIDS. In non-experimental research, an effort is made to control competing risks by selection, adjustment, post-stratification (propensity score analysis), etc. Note that the competing risk may or may not nullify the effect of A but may modify it (up or down). For example, with a suppressor variable, the effect of A may only be detected in the presence of B. True experiments achieve control by randomization (that is, A and B are correlated by chance alone).

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Chauncey Dayton

#1 is a subset of #2. (Modifying the probability can be setting it to zero.) So #2 is the choice.

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Robert Riffenburgh
Naval Medical Center

Original Message:
Sent: 12-03-2015 18:15
From: Isabella Ghement
Subject: Definitions of competing risks

In the literature on competing risks, I've come across two slightly different definitions of a competing risk event: 

1) A competing risk event is one that precludes the event of interest from ocurring; 

2) A competing risk event either modifies the probability of occurrence of the event of interest or prevents the event of interest from ocurring. 

My questions are: 

A. Are both definitions acceptable? 

B. Should one definition be preferred over the other and why?

Many thanks, 

Isabella

------------------------------
Isabella Ghement
Ghement Statistical Consulting Company Ltd.
------------------------------

Definition #2 may subsume definition #1, but it adds no clarity. How does one distinguish definition #2 from confounding (or interaction or effect modification or mediation or moderation)? 

Perhaps we need new definitions for #1 as a special case, or a different definition for #2.  Definition #1 is a particularly interesting special case.

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Raoul Burchette
Biostatistician III
Kaiser Permanente, Pasadena, CA USA

Original Message:
Sent: 12-12-2015 23:45
From: Robert Riffenburgh
Subject: Definitions of competing risks

#1 is a subset of #2. (Modifying the probability can be setting it to zero.) So #2 is the choice.

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Robert Riffenburgh
Naval Medical Center

I think definition 2 is meaningful when it is clear that the semi-competing event alters, not just the probability, but also the meaning and interpretation of the primary event of interest.  Take an instance of the illness-death model: healthy-disabled-dead.  When a person becomes physically disabled, their probability of (all-cause) death increases.  But, now the problem has also changed significantly in the sense that we may not care about the probability of death for those who are disabled. Thus, disability actually acts "as if" it is a competing event, even though it is only semi-competing in the strictest sense.  Does this make sense?    

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Ravi Varadhan
Johns Hopkins University

Original Message:
Sent: 12-14-2015 13:33
From: Raoul Burchette
Subject: Definitions of competing risks

Definition #2 may subsume definition #1, but it adds no clarity. How does one distinguish definition #2 from confounding (or interaction or effect modification or mediation or moderation)? 

Perhaps we need new definitions for #1 as a special case, or a different definition for #2.  Definition #1 is a particularly interesting special case.

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Raoul Burchette
Biostatistician III
Kaiser Permanente, Pasadena, CA USA

Dr. Vardhan's responses are the best.  In a competing risk scenario, exposure to 'A' may be affected by exposure to 'B' as follows:

1. Additive effect: Effects of the two  are simple additive i.e. Effect of ('A' +'B') = Effect of 'A' +Effect of 'B'.

2. Multiplicative or synergistic effect: Effect of ('A'+'B') = k * (Effect of 'A' +Effect of 'B'), where k>=1.

3. Antisynergistic effect: Same as 2 with k<=1.

All three of the above phenomena are well established in biomedical and environmental sciences.

Ajit K. Thakur, Ph.D.

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Ajit Thakur, Ph.D.
Associate Director, Retired

Original Message:
Sent: 12-03-2015 18:15
From: Isabella Ghement
Subject: Definitions of competing risks

In the literature on competing risks, I've come across two slightly different definitions of a competing risk event: 

1) A competing risk event is one that precludes the event of interest from ocurring; 

2) A competing risk event either modifies the probability of occurrence of the event of interest or prevents the event of interest from ocurring. 

My questions are: 

A. Are both definitions acceptable? 

B. Should one definition be preferred over the other and why?

Many thanks, 

Isabella

------------------------------
Isabella Ghement
Ghement Statistical Consulting Company Ltd.
------------------------------