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Suppose I am looking at an estimate $\hat\beta$ in a clinical trial data.

With $a=.05$, a patient with $\hat\beta>1$ is considered to have some medical condition.

A daily example could be a 24-hr blood pressure monitoring. When a person is diagnosed as pre-hypertension, then a physician usually orders a 24-hr BP monitoring to make a final call. The BP monitor usually goes on on 20-minute basis. Unfortunately, even with the 24-hr tracking, there is a lot of noise in any given patient's data.

Back to my original question: if you are looking at a threshold-value for an estimate and need to clean up the noise to reduce the probability of false-positive, what are some standard protocols? Can you provide both theory and how this is done in STATA, MATLAB, Pyhton, R, and the like? You can pick a package that you are familiar with and provide a reference if possible.

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