The goals of this paper wereto provide a set of conditions for inverse probability weights (IPW) to target a subpopulation of the patients who have clinical equipose, establish a
relationship between matching weights and overlap weight estimators, and use
the beta distribution to help determine the appropriate weights. Whenever distributions of covariates betweentwo treatment groups were very different, this can result in limited overlap of
distribution of the propensity scores and violations of the positivity
assumptions which they called lack of adequate positivity. Difference propensity score methods haveshown to be affected differently by insufficient overlap of distribution of the
propensity scores or by the lack of the adequate positivity.
They discussed per creationof propensity score weights, creating balancing weight estimators. The authors then went into an incredible amount of detail regarding their estimators
extending into all possible realms until they finally got to their simulations
section. They found that overall, OW(overlap weight), MW (matching weight), and EW (entropy weight) were more efficient than IPW, despite the fact that the latter is doubly robust. Out of
the three, OW, MW, and EW, the OW estimator had the best RMSE in most of the
scenarios we considered under the homogeneous treatment effect, while MW is the
best under the heterogeneous treatment effect.
They demonstrated that the beta family canalso approximate the matching weights and entropy weights very well. This is for those who desire to expand their statistical toolsets as the equipoise
estimators (OW, MW, EW, and BW) to explore complex studies where the lack of
adequate positivity is not just by happenstance. Although they mainly focused
on continuous outcomes, the methods presented in this paper can be extended to
other types of outcomes and can easily be implemented using the PSweight
R-package (Zhou, Tong, et al., 2020).
Written by,
UshaGovindarajulu
References:
Matsouaka RAand Zhou Y (2024). “Causal inference in the absence of positivity: The role of
overlap weights.” Biometrical Journal.https://onlinelibrary.wiley.com/doi/full/10.1002/bimj.202300156?campaign=woletoc
Zhou, T., Tong, G., Li, F., & Thomas, L. E. (2020). Psweight: An rpackage for propensity score weighting analysis. arXiv. https://doi.org/10.48550/arXiv.2010.08893
