In observational clinic registries, time to treatment is often of interest, but treatment can be given at any time during follow-up and there is no structure or intervention to ensure regular clinic visits for data collection. To address these challenges, we introduce the time-dependent propensity process as a generalization of the propensity score. We show that the propensity process balances the entire time-varying covariate history which cannot be achieved by existing propensity score methods and that treatment assignment is strongly ignorable conditional on the propensity process. We develop methods for estimating the propensity process using observed data and for matching based on the propensity process. We illustrate the propensity process method using the Emory Amyotrophic Lateral Sclerosis (ALS) Registry data.
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