  Amidst rising appreciation for privacy and data usage rights, researchers
have increasingly recognized the principle of data minimization, which holds
that the accessibility, collection, and retention of subjects' data should be
kept to the minimum necessary to answer focused research questions. Applying
this principle to randomized controlled trials (RCTs), this paper presents
algorithms for drawing precise inferences from RCTs under stringent data
retention and anonymization policies. In particular, we show how to use
recursive algorithms to construct running estimates of treatment effects in
RCTs, thereby allowing individualized records to be deleted or anonymized
shortly after collection. Devoting special attention to the case of non-i.i.d.
data, we further demonstrate how to draw robust inferences from RCTs by
combining recursive algorithms with bootstrap and federated strategies.
