Inference for proportional hazard model with propensity score |
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| Authors: | Bo Lu Luheng Wang Xingwei Tong Huiyun Xiang |
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| Institution: | 1. College of Public Health, Division of Biostatistics, The Ohio State University, Columbus, Ohio, USA;2. School of Mathematical Sciences, Beijing Normal University, Beijing, China;3. School of Statistics, Beijing Normal University, Beijing, China;4. Center for Pediatric Trauma Research, The Research Institute at Nationwide Childrens Hospital, The Ohio State University College of Medicine, Columbus, Ohio, USA |
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| Abstract: | Since the publication of the seminal paper by Cox (1972), proportional hazard model has become very popular in regression analysis for right censored data. In observational studies, treatment assignment may depend on observed covariates. If these confounding variables are not accounted for properly, the inference based on the Cox proportional hazard model may perform poorly. As shown in Rosenbaum and Rubin (1983), under the strongly ignorable treatment assignment assumption, conditioning on the propensity score yields valid causal effect estimates. Therefore we incorporate the propensity score into the Cox model for causal inference with survival data. We derive the asymptotic property of the maximum partial likelihood estimator when the model is correctly specified. Simulation results show that our method performs quite well for observational data. The approach is applied to a real dataset on the time of readmission of trauma patients. We also derive the asymptotic property of the maximum partial likelihood estimator with a robust variance estimator, when the model is incorrectly specified. |
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| Keywords: | Partial likelihood propensity score proportional hazard model robust inference |
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