Mathematics, Vol. 11, Pages 4459: Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment

Mathematics, Vol. 11, Pages 4459: Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment

Mathematics doi: 10.3390/math11214459

Authors: Yi He Linzhi Zheng Peng Luo

The average treatment effect is an important concept in causal inference. However, it fails to capture variation in response to treatment due to heterogeneity at many levels among patients in the target population. To study the heterogeneity in the treatment effect, researchers proposed the concepts of treatment benefit rate (TBR) and treatment harm rate (THR). Howerver, in practice, missing data often occurs in treatment, endpoints, and covariates. In these cases, the conditions given by them are not enough to identify treatment benefit rate. In this article, we address the problem of identifying the treatment benefit rate and treatment harm rate when treatment or endpoints or covariates are missing. Different types of missing data mechanisms are assumed, including several situations of nonignorable missingness. We prove that the treatment benefit rate and treatment harm rate are identifiable under very mild conditions, and then construct estimators based on methods of the EM algorithm. The performance of the proposed inference procedure is evaluated via simulation studies. Lastly, we illustrate our method by real data sets.