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Modern longitudinal data, for example from wearable devices, measuresbiological signals on a fixed set of participants at a diverging number of timepoints. Traditional statistical methods are not equipped to handle thecomputational burden of repeatedly analyzing the cumulatively growing dataseteach time new data is collected. We propose a new estimation and inferenceframework for dynamic updating of point estimates and their standard errorsacross serially collected dependent datasets. The key technique is adecomposition of the extended score function of the quadratic inferencefunction constructed over the cumulative longitudinal data into a sum ofsummary statistics over data batches. We show how this sum can be recursivelyupdated without the need to access the whole dataset, resulting in acomputationally efficient streaming procedure with minimal loss of statisticalefficiency. We prove consistency and asymptotic normality of our streamingestimator as the number of data batches diverges, even as the number ofindependent participants remains fixed. Simulations highlight the advantages ofour approach over traditional statistical methods that assume independencebetween data batches. Finally, we investigate the relationship between physicalactivity and several diseases through the analysis of accelerometry data fromthe National Health and Nutrition Examination Survey.

Statistical Inference for Streamed Longitudinal Data