Stefan Hansen
@stefanforfan.bsky.social
Mission accomplished 🫠
August 21, 2025 at 12:44 PM
Mission accomplished 🫠
Thanks, I'll give it a read.
May 28, 2025 at 9:28 AM
Thanks, I'll give it a read.
This is the relevant SWIG with different notation (A: exposure, R: selection/pregnancy, V: frailty/whatever, Y: outcome):
May 28, 2025 at 9:09 AM
This is the relevant SWIG with different notation (A: exposure, R: selection/pregnancy, V: frailty/whatever, Y: outcome):
Not according to SWIG-logic. The paper linked by @zshahn.bsky.social in another comment (doi.org/10.1093/aje/...) has this scenario in Figure 1.D and their Table 1 shows the condition is fulfilled.
May 28, 2025 at 9:08 AM
Not according to SWIG-logic. The paper linked by @zshahn.bsky.social in another comment (doi.org/10.1093/aje/...) has this scenario in Figure 1.D and their Table 1 shows the condition is fulfilled.
It's actually even simpler. When there's no arrows into E, you immediately have Y(e) _||_ E | G(e), so you don't have to go via Z but immediately have E(Y(e) | G(e) = 1) = E(Y | E=e,G=1).
May 28, 2025 at 8:25 AM
It's actually even simpler. When there's no arrows into E, you immediately have Y(e) _||_ E | G(e), so you don't have to go via Z but immediately have E(Y(e) | G(e) = 1) = E(Y | E=e,G=1).
"Importantly, if the treatment affects selection, the net treatment difference does not, in general, represent a causal treatment effect because it does not compare potential outcomes for a fixed set of individuals"
May 28, 2025 at 8:04 AM
"Importantly, if the treatment affects selection, the net treatment difference does not, in general, represent a causal treatment effect because it does not compare potential outcomes for a fixed set of individuals"
Just leaving a couple of quotes from the paper:
"... in this example the company might prefer to estimate a 'net treatment difference' that captures not only causal effects of the treatment on specific individuals but also effects of the treatment on who is in the selected sample."
"... in this example the company might prefer to estimate a 'net treatment difference' that captures not only causal effects of the treatment on specific individuals but also effects of the treatment on who is in the selected sample."
May 28, 2025 at 8:04 AM
Just leaving a couple of quotes from the paper:
"... in this example the company might prefer to estimate a 'net treatment difference' that captures not only causal effects of the treatment on specific individuals but also effects of the treatment on who is in the selected sample."
"... in this example the company might prefer to estimate a 'net treatment difference' that captures not only causal effects of the treatment on specific individuals but also effects of the treatment on who is in the selected sample."
This is it - thank you! Their Figure 1.D is exactly my case, and their "net treatment difference" is what I was interested in.
May 28, 2025 at 8:04 AM
This is it - thank you! Their Figure 1.D is exactly my case, and their "net treatment difference" is what I was interested in.
Hm, but wouldn't this suffice?
May 27, 2025 at 2:10 PM
Hm, but wouldn't this suffice?
One of the estimands they're not considering is E(Y(1) | D(1) = 0)) - E(Y(0) | D(0) = 0) but instead they want to condition on the principal stratum D(1)=D(0)=0 in their notation which requires strong assumptions to identify. I guess noone is interested in a contrast that conditions differently.
May 27, 2025 at 11:27 AM
One of the estimands they're not considering is E(Y(1) | D(1) = 0)) - E(Y(0) | D(0) = 0) but instead they want to condition on the principal stratum D(1)=D(0)=0 in their notation which requires strong assumptions to identify. I guess noone is interested in a contrast that conditions differently.
The independence assumption is needed to derive the equality between E(Y(e)|G(e)=1) and E(Y|E=e,G=1) but Z is not needed to make the estimation! So we can think of Z as just about anything relevant and the result would still hold and I wouldn't even need to measure Z.
May 27, 2025 at 11:23 AM
The independence assumption is needed to derive the equality between E(Y(e)|G(e)=1) and E(Y|E=e,G=1) but Z is not needed to make the estimation! So we can think of Z as just about anything relevant and the result would still hold and I wouldn't even need to measure Z.
Thanks, Jack. Their example is exactly identical to mine, so very useful information in this context.
May 27, 2025 at 11:04 AM
Thanks, Jack. Their example is exactly identical to mine, so very useful information in this context.
Ah, sorry, messed up the notation. G was supposed to be P (pregnancy) and Z is the frailty variable.
May 27, 2025 at 11:03 AM
Ah, sorry, messed up the notation. G was supposed to be P (pregnancy) and Z is the frailty variable.
In the identification I've used that Y(e) _||_ E | G(e), Z and that G(e) _||_ E | Z.
May 27, 2025 at 10:53 AM
In the identification I've used that Y(e) _||_ E | G(e), Z and that G(e) _||_ E | Z.
I've given this some thought, and let me redefine my estimand as the contrast between E(Y(e)|P(e) = 1) for e=0,1. These can be identified as E(Y|E=e,G=1) in this DAG. Seems to be there is no Type 1 selection bias here, so no issues with internal validity?
May 27, 2025 at 10:53 AM
I've given this some thought, and let me redefine my estimand as the contrast between E(Y(e)|P(e) = 1) for e=0,1. These can be identified as E(Y|E=e,G=1) in this DAG. Seems to be there is no Type 1 selection bias here, so no issues with internal validity?
Also, if we adjust for frailty, then we're presumably targeting E(Y(1)) - E(Y(0)), but does the counterfactuals here even make sense without making it explicit that a pregnancy/delivery has taken place?
May 27, 2025 at 8:57 AM
Also, if we adjust for frailty, then we're presumably targeting E(Y(1)) - E(Y(0)), but does the counterfactuals here even make sense without making it explicit that a pregnancy/delivery has taken place?
I'm just still not convinced that this is the effect I'll see in my population because if I expose everyone I do change my population as well as I get an effect of the exposure. So why shouldn't policies about the population take this into account?
May 27, 2025 at 8:54 AM
I'm just still not convinced that this is the effect I'll see in my population because if I expose everyone I do change my population as well as I get an effect of the exposure. So why shouldn't policies about the population take this into account?
Thanks, Peter (and sorry about the mess I made with my posts - I saw you commented on my previous post). Never heard about "index event bias" before, but now I have something to search for. Appreciate it.
May 27, 2025 at 8:46 AM
Thanks, Peter (and sorry about the mess I made with my posts - I saw you commented on my previous post). Never heard about "index event bias" before, but now I have something to search for. Appreciate it.
This is more or less the same setting as presented in "The hazard of hazard ratios", so it appears that conditional measures, where we condition on descendants of the exposure, are inherently non-causal. Yet I can't stop thinking about them as "effects". What gives?
May 27, 2025 at 8:36 AM
This is more or less the same setting as presented in "The hazard of hazard ratios", so it appears that conditional measures, where we condition on descendants of the exposure, are inherently non-causal. Yet I can't stop thinking about them as "effects". What gives?
Yet, my estimand is what I would see in my population if I were to expose everyone vs. noone. Is there a name for such an estimand? Can it be useful for policy making despite not being causal?
May 27, 2025 at 8:36 AM
Yet, my estimand is what I would see in my population if I were to expose everyone vs. noone. Is there a name for such an estimand? Can it be useful for policy making despite not being causal?