Inverse-Probability-of-Treatment-Weighted (IPTW) estimators are becoming a popular analysis tool in causal inference. It is well known that these estimators suffer from high variability if some treatment probabilities are estimated to be close to zero. While it is a common recommendation for such situations to truncate the weights in order to reduce the mean squared error of the estimator, the current literature gives little guidance on how to select an appropriate truncation level. In this article, we develop a closed-form estimate for the mean squared error of a truncated IPTW estimator that can be used to select this truncation level data-adaptively. While the resulting estimator requires an estimate of an additional nuisance parameter, we show that its consistency does not rely on a consistent estimate of that nuisance parameter. For the case of a binary treatment variable, we present an approach for obtaining an estimate of this nuisance parameter that does not require the user to specify an appropriate parametric model.
We illustrate the practical performance of the proposed estimator in a number of simulation studies that show consistent gains in efficiency relative to more ad-hoc truncation approaches currently in use, with typical gains lying in the range from 1 to 15%. In fact, the estimator is seen to perform on par with an infeasible benchmark estimator that relies on knowledge of the true data-generating distribution. In an applied data analysis, the proposed methodology is estimated to achieve a 7% gain in efficiency relative to the non-truncated IPTW estimator, with truncation resulting in a non-significant finding becoming statistically significant. The methodology presented here has been implemented in an R package called tIPTW that can be downloaded at http://www.stat.berkeley.edu/~laan/Software/.
Bembom, Oliver and van der Laan, Mark J., "Data-adaptive selection of the truncation level for Inverse-Probability-of-Treatment-Weighted estimators" (March 2008). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 230.