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Stat Methods Med Res. 2019 Aug 26:962280219869742. doi: 10.1177/0962280219869742. [Epub ahead of print]

Inverse probability weighted Cox model in multi-site studies without sharing individual-level data.

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1 Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, USA.
2 Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, USA.
3 Division of Research, Kaiser Permanente Northern California, Oakland, USA.


The inverse probability weighted Cox proportional hazards model can be used to estimate the marginal hazard ratio. In multi-site studies, it may be infeasible to pool individual-level datasets due to privacy and other considerations. We propose three methods for making inference on hazard ratios without the need for pooling individual-level datasets across sites. The first method requires a summary-level eight-column risk-set table to produce the same hazard ratio estimate and robust sandwich variance estimate as those from the corresponding pooled individual-level data analysis (reference analysis). The second and third methods, which are based on two bootstrap re-sampling strategies, require a summary-level four-column risk-set table and bootstrap-based risk-set tables from each site to produce the same hazard ratio and bootstrap variance estimates as those from their reference analyses. All three methods require only one file transfer between the data-contributing sites and the analysis center. We justify these methods theoretically, illustrate their use, and demonstrate their statistical performance using both simulated and real-world data.


Cox model; distributed data networks; inverse probability weighting; multi-site study; privacy protection; risk set


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