Penalized Semiparametric Estimation for Causal Inference with Possibly Invalid Instruments

Inferring causal effects with unmeasured confounder is a main challenge in causal inference. Many researchers impose parametric assumptions on the distribution of unmeasured confounder. However, due to the unobservable nature of the unmeasured confounder, it is more reasonable to leave its distribution unrestricted. Another key challenge in causal inference is the involvement of invalid instrumental variables, which may lead to biased inference and possibly misleading scientific conclusions. To this end, we employ a flexible semiparametric model that allows for possibly invalid instruments without specifying the distribution of unmeasured confounder in this work. A penalized semiparametric estimator for causal effects is constructed and its oracle and asymptotic properties are well established for statistical inference. We evaluate the performance of the estimator through simulation studies, revealing that our proposed estimator exhibits asymptotic unbiasedness and robustness in estimating causal effects, along with consistent selection of invalid instruments. We also demonstrate its application using Atherosclerosis Risk in Communities Study data set, which further validates its robustness in the presence of invalid instruments. Additionally, we have implemented the proposed method in R, and the corresponding R code is available for free download. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This research was supported partially by the National Key R&D Program of China [2023YFF1205101]. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Fudan University gave ethical approval for this work I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced are available online at https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000090.v1.p1