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Digital monitoring studies collect real-time high frequency data via mobilesensors in the subjects' natural environment. This data can be used to modelthe impact of changes in physiology on recurrent event outcomes such assmoking, drug use, alcohol use, or self-identified moments of suicide ideation.Likelihood calculations for the recurrent event analysis, however, becomecomputationally prohibitive in this setting. Motivated by this, a randomsubsampling framework is proposed for computationally efficient, approximatelikelihood-based estimation. A subsampling-unbiased estimator for thederivative of the cumulative hazard enters into an approximation oflog-likelihood. The estimator has two sources of variation: the first due tothe recurrent event model and the second due to subsampling. The latter can bereduced by increasing the sampling rate; however, this leads to increasedcomputational costs. The approximate score equations are equivalent to logisticregression score equations, allowing for standard, "off-the-shelf" software tobe used in fitting these models. Simulations demonstrate the method andefficiency-computation trade-off. We end by illustrating our approach usingdata from a digital monitoring study of suicidal ideation.

Recurrent event analysis in the presence of real-time high frequency data via random subsampling