Semiparametric Causal Inference for Right-Censored Outcomes with Many Weak Invalid Instruments
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911190102310912 |
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| author | Bu, Qiushi Su, Wen Zhao, Xingqiu Liu, Zhonghua |
| author_facet | Bu, Qiushi Su, Wen Zhao, Xingqiu Liu, Zhonghua |
| contents | We propose a semiparametric framework for causal inference with right-censored survival outcomes and many weak invalid instruments, motivated by Mendelian randomization in biobank studies where classical methods may fail. We adopt an accelerated failure time model and construct a moment condition based on augmented inverse probability of censoring weighting, incorporating both uncensored and censored observations. Under a heteroscedasticity-based condition on the treatment model, we establish point identification of the causal effect despite censoring and invalid instruments. We propose GEL-NOW (Generalized Empirical Likelihood with Non-Neyman Orthogonal and Weak moments) for valid inference under these conditions. A divergent number of Neyman orthogonal nuisance functions is estimated using deep neural networks. A key challenge is that the conditional censoring distribution is a non-Neyman orthogonal nuisance, contributing to the first-order asymptotics of the estimator for the target causal effect parameter. We derive the asymptotic distribution and explicitly incorporate this additional uncertainty into the asymptotic variance formula. We also introduce a censoring-adjusted over-identification test that accounts for this new variance component. Simulation studies and UK Biobank applications demonstrate the method's robustness and practical utility. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semiparametric Causal Inference for Right-Censored Outcomes with Many Weak Invalid Instruments Bu, Qiushi Su, Wen Zhao, Xingqiu Liu, Zhonghua Methodology Statistics Theory We propose a semiparametric framework for causal inference with right-censored survival outcomes and many weak invalid instruments, motivated by Mendelian randomization in biobank studies where classical methods may fail. We adopt an accelerated failure time model and construct a moment condition based on augmented inverse probability of censoring weighting, incorporating both uncensored and censored observations. Under a heteroscedasticity-based condition on the treatment model, we establish point identification of the causal effect despite censoring and invalid instruments. We propose GEL-NOW (Generalized Empirical Likelihood with Non-Neyman Orthogonal and Weak moments) for valid inference under these conditions. A divergent number of Neyman orthogonal nuisance functions is estimated using deep neural networks. A key challenge is that the conditional censoring distribution is a non-Neyman orthogonal nuisance, contributing to the first-order asymptotics of the estimator for the target causal effect parameter. We derive the asymptotic distribution and explicitly incorporate this additional uncertainty into the asymptotic variance formula. We also introduce a censoring-adjusted over-identification test that accounts for this new variance component. Simulation studies and UK Biobank applications demonstrate the method's robustness and practical utility. |
| title | Semiparametric Causal Inference for Right-Censored Outcomes with Many Weak Invalid Instruments |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2509.13176 |