Evaluation and Modeling of 24-hour Profiles of Medical Data Considering the Circadian Rhythm

The assessment of such models is performed based on a mixture of both time series analysis and spectral analysis. So for the statisticians, the degree of difficulty involved in the implementation of finding the right dynamic parameters, can sometimes be beyond their power. Anyway to cut the long story short, the following procedures might be applied sequentially:

– Spline Method (Regression Splines, Smoothing Splines)

– Exponential Smoothing (Periodogram and Correlogram)

– Simple Cosine Model

– Cosine Model with Autoregressive Error Process of Order 1

For example, the periodic regression analysis for modelling of 24-hour blood pressures (SBP/DBP) taking in account the circadian rhythm has provided a cosine model:

                                 y= M + A[Cos(0.25) t + φ] + et  for  t = 1,…,n  where

M: the mesor or middle line where the function yt fluctuates up and down

A: the amplitude (i.e. The maximum swing)

Cos(0,25) :  the angular frequency, which is proportional to the period

 φ : phase shift angle, (zero phase)

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