When utilizing observational knowledge, task to a remedy group is non-random and causal inference could also be troublesome. One frequent method to addressing that is propensity rating weighting the place the propensity rating is the chance that an individual is assigned to the remedy arm given their observable traits. This propensity is commonly estimated utilizing a logistic regression of particular person traits on a binary variable of whether or not the person acquired the remedy or not. Propensity scores are sometimes used that to by making use of inverse chance of remedy weighting (IPTW) estimators to acquire remedy results adjusting for identified confounders.
A paper by Xu et al. (2010) exhibits that utilizing the IPTW method might result in an overestimate of the pseudo-sample dimension and enhance the chance of a sort I error (i.e., rejecting the null speculation when it’s truly true). The authors declare that sturdy variance estimators can deal with this drawback however solely work nicely with massive pattern sizes. As an alternative, Xu and co-authors proposed utilizing standardized weights within the IPTW as a easy and simple to implement technique. Right here is how this works.
The IPTW method merely examines the distinction between the handled and untreated group after making use of the IPTW weighting. Let the frequency that somebody is handled be:
the place n1 is the variety of folks handled and N is the full pattern dimension. Let z=1 if the particular person is handled within the knowledge and z=0 if the particular person is just not handled. Assume that every particular person has a vector of affected person traits, X, that influence the chance of receiving remedy. Then one calculate the chance of remedy as:
Beneath normal IPTW, the weights used could be:
Xu and co-authors create a simulation to point out that the kind 1 error is simply too excessive–usually 15% to 40%. To appropriate this, one may use standardized weights (SW) as follows:
The previous is used for the handled inhabitants (i.e., z=1) and the latter is used within the untreated inhabitants (z=0). The authors present that underneath the standardized weights, the speed of kind 1 errors is roughly 5% as meant. In reality, the authors additionally present that standardized weighting usually outperforms sturdy variance estimators as nicely for estimating primary results.
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