Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/21/4459 |
| _version_ | 1797631685069635584 |
|---|---|
| author | Yi He Linzhi Zheng Peng Luo |
| author_facet | Yi He Linzhi Zheng Peng Luo |
| author_sort | Yi He |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T11:25:46Z |
| format | Article |
| id | doaj.art-e05fc978ef7442da83cbea82388e9609 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:46Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e05fc978ef7442da83cbea82388e96092023-11-10T15:07:56ZengMDPI AGMathematics2227-73902023-10-011121445910.3390/math11214459Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or TreatmentYi He0Linzhi Zheng1Peng Luo2School of Mathematics and Statistics, Shenzhen University, Shenzhen 518061, ChinaSchool of Mathematics and Statistics, Shenzhen University, Shenzhen 518061, ChinaSchool of Mathematics and Statistics, Shenzhen University, Shenzhen 518061, ChinaThe 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.https://www.mdpi.com/2227-7390/11/21/4459nonignorable missingtreatment harm ratestreatment benefit ratescausal inferencenonparametric estimation |
| spellingShingle | Yi He Linzhi Zheng Peng Luo Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment Mathematics nonignorable missing treatment harm rates treatment benefit rates causal inference nonparametric estimation |
| title | Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment |
| title_full | Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment |
| title_fullStr | Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment |
| title_full_unstemmed | Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment |
| title_short | Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment |
| title_sort | treatment benefit and treatment harm rates with nonignorable missing covariate endpoint or treatment |
| topic | nonignorable missing treatment harm rates treatment benefit rates causal inference nonparametric estimation |
| url | https://www.mdpi.com/2227-7390/11/21/4459 |
| work_keys_str_mv | AT yihe treatmentbenefitandtreatmentharmrateswithnonignorablemissingcovariateendpointortreatment AT linzhizheng treatmentbenefitandtreatmentharmrateswithnonignorablemissingcovariateendpointortreatment AT pengluo treatmentbenefitandtreatmentharmrateswithnonignorablemissingcovariateendpointortreatment |