# Lowering the bias from on the inverse chance of remedy weighting (IPTW) – Healthcare Economist

When utilizing observational information, task to a remedy group is non-random and causal inference could also be tough. One widespread strategy 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 usually 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 chance of remedy weighting (IPTW) estimators to acquire remedy results adjusting for recognized confounders.

A paper by Xu et al. (2010) reveals that utilizing the IPTW strategy could result in an overestimate of the pseudo-sample dimension and enhance the probability of a kind I error (i.e., rejecting the null speculation when it’s really true). The authors declare that sturdy variance estimators can handle this downside however solely work nicely with massive pattern sizes. As a substitute, 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 folks handled and *N* is the overall pattern dimension. Let *z*=1 if the particular person is handled within the information and *z*=0 if the particular person just isn’t handled. Assume that every particular person has a vector of affected person traits, *X*, that influence the probability of receiving remedy. Then one calculate the chance of remedy as:

Below commonplace IPTW, the weights used could be:

Xu and co-authors create a simulation to indicate that the kind 1 error is just too excessive–usually 15% to 40%. To right 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 supposed. The truth is, the authors additionally present that standardized weighting usually outperforms sturdy variance estimators as nicely for estimating essential results.

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