Rui Duan1, Chongliang Luo1, Martijn J Schuemie2, Jiayi Tong1, C Jason Liang3, Howard H Chang4, Mary Regina Boland1, Jiang Bian5,6, Hua Xu7, John H Holmes1, Christopher B Forrest8, Sally C Morton9, Jesse A Berlin10, Jason H Moore1, Kevin B Mahoney11, Yong Chen1. 1. Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA. 2. Janssen Research and Development LLC, Titusville, New Jersey, USA. 3. Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, Maryland, USA. 4. Department of Biostatistics and Bioinformatics, Emory University, Atlanta, Georgia, USA. 5. Department of Health Outcomes and Biomedical Informatics, College of Medicine, University of Florida, Gainesville, Florida, USA. 6. Cancer Informatics and eHealth Core, University of Florida Health Cancer Center, Gainesville, Florida, USA. 7. School of Biomedical Informatics, The University of Texas Health Science Center at Houston, Houston, Texas, USA. 8. Applied Clinical Research Center, Children's Hospital of Philadelphia, Philadelphia, Pennsylvania, USA. 9. Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA. 10. Johnson & Johnson, Titusville, NJ, USA. 11. University of Pennsylvania Health System, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
Abstract
OBJECTIVE: We developed and evaluated a privacy-preserving One-shot Distributed Algorithm to fit a multicenter Cox proportional hazards model (ODAC) without sharing patient-level information across sites. MATERIALS AND METHODS: Using patient-level data from a single site combined with only aggregated information from other sites, we constructed a surrogate likelihood function, approximating the Cox partial likelihood function obtained using patient-level data from all sites. By maximizing the surrogate likelihood function, each site obtained a local estimate of the model parameter, and the ODAC estimator was constructed as a weighted average of all the local estimates. We evaluated the performance of ODAC with (1) a simulation study and (2) a real-world use case study using 4 datasets from the Observational Health Data Sciences and Informatics network. RESULTS: On the one hand, our simulation study showed that ODAC provided estimates nearly the same as the estimator obtained by analyzing, in a single dataset, the combined patient-level data from all sites (ie, the pooled estimator). The relative bias was <0.1% across all scenarios. The accuracy of ODAC remained high across different sample sizes and event rates. On the other hand, the meta-analysis estimator, which was obtained by the inverse variance weighted average of the site-specific estimates, had substantial bias when the event rate is <5%, with the relative bias reaching 20% when the event rate is 1%. In the Observational Health Data Sciences and Informatics network application, the ODAC estimates have a relative bias <5% for 15 out of 16 log hazard ratios, whereas the meta-analysis estimates had substantially higher bias than ODAC. CONCLUSIONS: ODAC is a privacy-preserving and noniterative method for implementing time-to-event analyses across multiple sites. It provides estimates on par with the pooled estimator and substantially outperforms the meta-analysis estimator when the event is uncommon, making it extremely suitable for studying rare events and diseases in a distributed manner.
OBJECTIVE: We developed and evaluated a privacy-preserving One-shot Distributed Algorithm to fit a multicenter Cox proportional hazards model (ODAC) without sharing patient-level information across sites. MATERIALS AND METHODS: Using patient-level data from a single site combined with only aggregated information from other sites, we constructed a surrogate likelihood function, approximating the Cox partial likelihood function obtained using patient-level data from all sites. By maximizing the surrogate likelihood function, each site obtained a local estimate of the model parameter, and the ODAC estimator was constructed as a weighted average of all the local estimates. We evaluated the performance of ODAC with (1) a simulation study and (2) a real-world use case study using 4 datasets from the Observational Health Data Sciences and Informatics network. RESULTS: On the one hand, our simulation study showed that ODAC provided estimates nearly the same as the estimator obtained by analyzing, in a single dataset, the combined patient-level data from all sites (ie, the pooled estimator). The relative bias was <0.1% across all scenarios. The accuracy of ODAC remained high across different sample sizes and event rates. On the other hand, the meta-analysis estimator, which was obtained by the inverse variance weighted average of the site-specific estimates, had substantial bias when the event rate is <5%, with the relative bias reaching 20% when the event rate is 1%. In the Observational Health Data Sciences and Informatics network application, the ODAC estimates have a relative bias <5% for 15 out of 16 log hazard ratios, whereas the meta-analysis estimates had substantially higher bias than ODAC. CONCLUSIONS: ODAC is a privacy-preserving and noniterative method for implementing time-to-event analyses across multiple sites. It provides estimates on par with the pooled estimator and substantially outperforms the meta-analysis estimator when the event is uncommon, making it extremely suitable for studying rare events and diseases in a distributed manner.
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