Proximal causal inference for complex longitudinal studies

Abstract A standard assumption for causal inference about the joint effects of time-varying treatment is that one has measured sufficient covariates to ensure within covariate strata, subjects are exchangeable across observed values, also known as ‘sequential randomization (SRA)’. SRA often criticized it requires accurately measure all confounders. Realistically, can rarely capture confounders with certainty. Often measurements at best proxies confounders, thus invalidating inferences under SRA. In this paper, we extend proximal (PCI) framework Miao, Geng, et al. (2018. Identifying proxy variables an unmeasured confounder. Biometrika, 105(4), 987–993. https://doi.org/10.1093/biomet/asy038) longitudinal setting a semiparametric marginal structural mean model (MSMM). PCI offers opportunity learn in settings where based on fails, by formally accounting imperfect underlying confounding mechanisms. We establish nonparametric identification pair and provide corresponding characterization regular asymptotically linear estimators parameter indexing MSMM, including rich class doubly robust estimators, efficiency bound MSMM. Extensive simulation studies data application illustrate finite sample behaviour proposed methods.