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Multiplicative Inverse Intensity and Probability Weights for Irregular Longitudinal Data Analysis
Longitudinal data, where observations are repeatedly taken on subjects over time, is often used to answer complex research questions in a variety of disciplines. In observational studies, we often encounter irregular longitudinal data where the timings of observations vary across individuals. Although there exist methods that can accommodate irregular longitudinal data, such as the generalized estimating equation (GEE), issues arise when data is collected at observation times that are driven by the longitudinal outcome (referred to as outcome-dependent sampling). In this setting, ignoring the observation process can lead to biased estimates of the outcome model parameters. This issue can be coupled with other sources of bias, including failing to account for non-randomized exposures or treatment assignments when estimating causal effects. Individually, there are weighting methods that can account for only one, but not both, of these sources of bias. As such, we present a new multiplicative weighting method that simultaneously accounts for both potential sources of bias and is simple to implement. We show that under certain conditions, this method can produce unbiased estimates of model parameters when assumptions of ignorability are violated in the observation timing and treatment assignment processes.