When utilizing observational knowledge, task to a remedy group is non-random and causal inference could also be tough. One frequent strategy to addressing that is propensity rating weighting the place the propensity rating is the likelihood 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 obtained the remedy or not. Propensity scores are sometimes used that to by making use of inverse likelihood 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 strategy might result in an overestimate of the pseudo-sample measurement and enhance the chance of a kind I error (i.e., rejecting the null speculation when it’s really true). The authors declare that strong variance estimators can deal with this drawback however solely work properly with massive pattern sizes. As an alternative, Xu and co-authors proposed utilizing standardized weights within the IPTW as a easy and straightforward to implement technique. Right here is how this works.
The IPTW strategy 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 individuals handled and N is the full pattern measurement. Let z=1 if the particular person is handled within the knowledge and z=0 if the particular person isn’t 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 likelihood of remedy as:
Below customary IPTW, the weights used can be:
Xu and co-authors create a simulation to indicate that the kind 1 error is simply too excessive–usually 15% to 40%. To right this, one might 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 below the standardized weights, the speed of kind 1 errors is roughly 5% as meant. In actual fact, the authors additionally present that standardized weighting usually outperforms strong variance estimators as properly for estimating fundamental results.
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