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Abstract Background Traditional mediation analysis typically examines the relations among an intervention, a time-invariant mediator, and a time-invariant outcome variable. Although there may be a total effect of the intervention on the outcome, there is a need to understand the process by which the intervention affects the outcome (i.e., the indirect effect through the mediator). This indirect effect is frequently assumed to be time-invariant. With improvements in data collection technology, it is possible to obtain repeated assessments over time resulting in intensive longitudinal data. This calls for an extension of traditional mediation analysis to incorporate time-varying variables as well as time-varying effects. Methods We focus on estimation and inference for the time-varying mediation model, which allows mediation effects to vary as a function of time. We propose a two-step approach to estimate the time-varying mediation effect. Moreover, we use a simulation-based approach to derive the corresponding point-wise confidence band for the time-varying mediation effect. Results Simulation studies show that the proposed procedures perform well when comparing the confidence band and the true underlying model. We further apply the proposed model and the statistical inference procedure to data collected from a smoking cessation study. Conclusions We present a model for estimating time-varying mediation effects that allows both time-varying outcomes and mediators. Simulation-based inference is also proposed and implemented in a user-friendly R package. 

Understanding the nature and origin of errors in satellite precipitation products is important for applications and product improvement. Here we propose a new error decomposition scheme incorporating precipitation event (continuous rainy periods) information to characterize satellite errors. Under this framework, the errors are attributed to the inaccuracies in event occurrence, timing (event start/end time), and intensity. The Integrated MultisatellitE Retrieval for Global Precipitation Measurement (IMERG) is used as our test product to apply the method over CONUS. The above‐listed factors contribute approximately 30%, 20%, and 50% to the total bias, respectively. Significant asymmetry exists in the temporal distribution of biases throughout events: early event endings cause threefold more precipitation amount bias than late event beginnings, while early event beginnings cause fourfold more bias than late event endings. Dominant contributors vary across seasons and regions. The proposed error decomposition provides insight into sources of error for improved retrievals.