Table 1.

Mathematical formulae for cortisol measures.

Formulas	Symbol	Equation
Total cortisol level during awakening responsea	AUCAG	${\displaystyle \sum _{i=0}^{I-1}}\frac{(s_i+s_{i+1})\times (t_{i+1}-t_i)}{2}$
Dynamic increase of awakening responsea	AUCI	${\text{AUC}}_{\text{AG}}-s_0\times {\displaystyle \sum _{i=0}^{I-1}}(t_{i+1}-t_i)$
Total cortisol level during the daya	AUCTG	${\displaystyle \sum _{k=1}^{K-1}}\frac{(s_k+s_{k+1})\times (t_{k+1}-t_k)}{2}$
Diurnal slope anchored to awake using regression	slopeawake regression	$\frac{(-t_{\text{avg}})(s_0-s_{\text{avg}})+{\sum }_{k=1}^K((t_k-t_0)-t_{\text{avg}})(s_k-s_{\text{avg}})}{t_{\text{avg}}^2+{\sum }_{k=1}^K{((t_k-t_0)-t_{\text{avg}})}^2}$
Diurnal slope anchored to awake using rise over run	slopeawake to last	$\frac{s_l-s_0}{t_l-t_0}$
Diurnal slope anchored to maximum using regression	slopemax regression	$\frac{(-t_{\text{avg.m}})(s_{max}-s_{\text{avg.m}})+{\sum }_{k=1}^K((t_k-t_{imax})-t_{\text{avg.m}})(s_k-s_{\text{avg.m}})}{t_{\text{avg.m}}^2+{\sum }_{k=1}^K{((t_k-t_{imax})-t_{\text{avg.m}})}^2}$
Diurnal slope anchored to maximum using rise over run	slopemax to last	$\frac{s_l-s_{max}}{t_l-t_{max}}$

Note: i denotes cortisol samples within 1 h post-awakening; s denotes cortisol sample; s₀ denotes awake cortisol sample; t denotes time sample taken in hours; k denotes all samples taken (excluding cortisol samples within 1 h post-awakening); $t_{\text{avg}}=({\sum }_{k=0}^K(t_k-t_0))/K$; S_avg denotes average cortisol of S_k, where the first sample is S₀; l denotes the last sample taken; s_max denotes maximum cortisol sample within 1 h post-awakening; $t_{\text{avg.m}}=({\sum }_{k=0}^K(t_k-t_{imax}))/K$; S_avg.m denotes average cortisol of S_k, where the first sample is s_max.

^aFormulas based on Pruessner et al. (2003).