Online Causal Inference with Application to Near Real-Time Post-Market Vaccine Safety Surveillance

Streaming data routinely generated by mobile phones, social networks, e-commerce, and electronic health records present new opportunities for near real-time surveillance of the impact of an intervention on an outcome of interest via causal inference methods. However, as data grow rapidly in volume and velocity, storing and combing data become increasingly challenging. The amount of time and effort spent to update analyses can grow exponentially, which defeats the purpose of instantaneous surveillance. Data sharing barriers in multi-center studies bring additional challenges to rapid signal detection and update. It is thus time to turn static causal inference to online causal learning that can incorporate new information as it becomes available without revisiting prior observations. In this paper, we present a framework for online estimation and inference of treatment effects leveraging a series of datasets that arrive sequentially without storing or re-accessing individual-level raw data. We establish estimation consistency and asymptotic normality of the proposed framework for online causal inference. In particular, our framework is robust to biased data batches in the sense that the proposed online estimator is asymptotically unbiased as long as the pooled data is a random sample of the target population regardless of whether each data batch is. We also provide an R package for analyzing streaming observational data that enjoys great computation efficiency compared to existing software packages for offline analyses. Our proposed methods are illustrated with extensive simulations and an application to sequential monitoring of adverse events post COVID-19 vaccine.