When utilizing observational knowledge, task to a therapy group is non-random and causal inference could also be troublesome. One widespread strategy to addressing that is propensity rating weighting the place the propensity rating is the likelihood that an individual is assigned to the therapy 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 therapy or not. Propensity scores are sometimes used that to by making use of inverse likelihood of therapy weighting (IPTW) estimators to acquire therapy results adjusting for recognized confounders.
A paper by Xu et al. (2010) reveals that utilizing the IPTW strategy might result in an overestimate of the pseudo-sample measurement and improve the chance of a sort I error (i.e., rejecting the null speculation when it’s really true). The authors declare that strong variance estimators can handle this downside however solely work effectively with giant pattern sizes. Instead, Xu and co-authors proposed utilizing standardized weights within the IPTW as a easy and straightforward to implement technique. 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 whole pattern measurement. Let z=1 if the individual is handled within the knowledge and z=0 if the individual is just not handled. Assume that every individual has a vector of affected person traits, X, that affect the chance of receiving therapy. Then one calculate the likelihood of therapy as:
Under normal IPTW, the weights used could be:
Xu and co-authors create a simulation to indicate that the sort 1 error is just too excessive–usually 15% to 40%. To appropriate this, one might use standardized weights (SW) as follows:
The former 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 beneath the standardized weights, the speed of kind 1 errors is roughly 5% as meant. In truth, the authors additionally present that standardized weighting usually outperforms strong variance estimators as effectively for estimating most important results.
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