Table 4 Description of hypnodensity features. Here, H represents the hypnodensity of length N and S symbols the most certain sleep stages in H

From: Sleep stage mixing is associated with poor prognosis in early Parkinson’s disease

Hypnodensity features

Formula

Global Sleep Stage Uncertainty

Computed across all stages

\(100\cdot \frac{1}{N}\mathop{\sum }\limits_{i=1}^{N}[\max \left({H}_{i}\right) < 0.9]\)

Sleep Stage Dependent Uncertainty

Computed for stage \({{\boldsymbol{s}}}_{{\boldsymbol{1}}}\)

\(100\cdot \frac{1}{{|S}={s}_{1}|}\mathop{\sum}\limits_{i\in ({S}_{i}={s}_{1})}[{H}_{i,s} < 0.9]\)

Global Sleep Stage Mixing Prevalence

Computed between stages \({{\boldsymbol{s}}}_{{\boldsymbol{1}}}\) and \({{\boldsymbol{s}}}_{{\boldsymbol{2}}}\)

\(100\cdot \frac{1}{N}\mathop{\sum }\limits_{i=1}^{N}2\cdot {\left({H}_{i,{s}_{1}}\cdot {H}_{i,{s}_{2}}\right)}^{\frac{1}{2}}\)