So I'm thinking about propensity scores in general.
P is the probability that someone is in the intervention group. And p is also the measure being used to match people between the intervention and reference population.
There are multiple ways to use the propensity score to match members between the two populations, some with replacement and some without.
Either way, I would imagine that when you look at both the intervention and the reference population, you will end up having members in the intervention population with much higher p scores than in the reference population, simply by the definition of a p score.
So for p scores > 0.5 you are matching a bunch of members in the intervention population with a much smaller number of members in the reference population.
So if you use w/o replacement, you will likely have to throw out a lot of members in the intervention population (I am assuming that you will somewhat quickly exhaust your pool of reference members with high p scores) So you will run into credibility issues and will have spent all this money intervening for this members but you won't be able to assess their outcome.
On the other hand if you use w/ replacement, then your results will be very sensitive to this small reference population that have p scores > 0.5.
Also it seems that the bulk of your intervention population will have p scores > 0.5, which really exacerbates this issue.
I do think that having p represent the probability of being in the intervention is really a genuine technique for achieving comparability/equivalence b/w to the two populations. But unless the total sample is very large to account for the two issues I mentioned (having to throw out a bunch of intervention members or matching a large intervention population to a small reference population) the propensity score method seems to not be very practical and would otherwise (w/ small to moderate size population) be biased.
I can't imagine the SOA would come up with a question that would require us to consider these things, but I guess I find this part of the material more interesting.
P is the probability that someone is in the intervention group. And p is also the measure being used to match people between the intervention and reference population.
There are multiple ways to use the propensity score to match members between the two populations, some with replacement and some without.
Either way, I would imagine that when you look at both the intervention and the reference population, you will end up having members in the intervention population with much higher p scores than in the reference population, simply by the definition of a p score.
So for p scores > 0.5 you are matching a bunch of members in the intervention population with a much smaller number of members in the reference population.
So if you use w/o replacement, you will likely have to throw out a lot of members in the intervention population (I am assuming that you will somewhat quickly exhaust your pool of reference members with high p scores) So you will run into credibility issues and will have spent all this money intervening for this members but you won't be able to assess their outcome.
On the other hand if you use w/ replacement, then your results will be very sensitive to this small reference population that have p scores > 0.5.
Also it seems that the bulk of your intervention population will have p scores > 0.5, which really exacerbates this issue.
I do think that having p represent the probability of being in the intervention is really a genuine technique for achieving comparability/equivalence b/w to the two populations. But unless the total sample is very large to account for the two issues I mentioned (having to throw out a bunch of intervention members or matching a large intervention population to a small reference population) the propensity score method seems to not be very practical and would otherwise (w/ small to moderate size population) be biased.
I can't imagine the SOA would come up with a question that would require us to consider these things, but I guess I find this part of the material more interesting.
Propensity Score and Bias
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