  Modern longitudinal data, for example from wearable devices, measures
biological signals on a fixed set of participants at a diverging number of time
points. Traditional statistical methods are not equipped to handle the
computational burden of repeatedly analyzing the cumulatively growing dataset
each time new data is collected. We propose a new estimation and inference
framework for dynamic updating of point estimates and their standard errors
across serially collected dependent datasets. The key technique is a
decomposition of the extended score function of the quadratic inference
function constructed over the cumulative longitudinal data into a sum of
summary statistics over data batches. We show how this sum can be recursively
updated without the need to access the whole dataset, resulting in a
computationally efficient streaming procedure with minimal loss of statistical
efficiency. We prove consistency and asymptotic normality of our streaming
estimator as the number of data batches diverges, even as the number of
independent participants remains fixed. Simulations highlight the advantages of
our approach over traditional statistical methods that assume independence
between data batches. Finally, we investigate the relationship between physical
activity and several diseases through the analysis of accelerometry data from
the National Health and Nutrition Examination Survey.
