Joint marginal structural models to estimate the causal effects of multiple longitudinal treatments in continuous time with application to COVID-19

To draw real-world evidence about the comparative effectiveness of complex time-varying treatment regimens on patient survival, we develop a joint marginal structural proportional hazards model and novel weighting schemes in continuous time to account for time-varying confounding and censoring. Our methods formulate complex longitudinal treatments with multiple "start/stop" switches as the recurrent events with discontinuous intervals of treatment eligibility. We derive the weights in continuous time to handle a complex longitudinal dataset on its own terms, without the need to discretize or artificially align the measurement times. We further propose using machine learning models designed for censored survival data with time-varying covariates and the kernel function estimator of the baseline intensity to efficiently estimate the continuous-time weights. Our simulations demonstrate that the proposed methods provide better bias reduction and nominal coverage probability when analyzing observational longitudinal survival data with irregularly spaced time intervals, compared to conventional methods that require aligned measurement time points. We apply the proposed methods to a large-scale COVID-19 dataset to estimate the causal effects of several COVID-19 treatment strategies on in-hospital mortality or ICU admission, and provide new insights relative to findings from randomized trials.