Area under the curve on a graph with cumulative y-axis
(Apologies if this is in the wrong forum)
I'm doing an project in which I am measuring snoring (objectively) under two different conditions, inactive and active treatment, to see whether it improves during active treatment. One of the snoring variables I am measuring is snoring time, which is the % of the night spent above a chosen decibel (dB) threshold. Based on previous work, we decided to use a threshold of 55 dB for snoring time (assuming anything less is background noise) - this showed no significant difference between inactive and active treatment. However, we also wanted to look at the results using various other dB thresholds to assess the consistency of the findings, resulting in the attached graph.
I believe that there are multiple ways of analysis these data, including multiple comparisons-adjusted paired t-tests, linear mixed model analysis, and area under the curve analysis. Considering how the graph is set out, I thought it would be nice to include a comparison of the area under the curves for inactive vs active treatment.
I know how to calculate the area under the curve using both the trapezoid rule and integration. But given that the y-axis is cumulative, I was wondering whether AUC analysis is meaningful in this case? Also, what would the units of AUC be in this case?