Z-score analysis for comorbidity profiles

We assess whether the comorbidity profile of interest is uniquely expressed or suppressed in a certain sepsis state. We compute the corresponding Z-score:

where μ_j is the rate of presence of comorbidity j among all the patients in the cohort, σ_j is its corresponding standard deviation, and wji is the reference point, calculated as the rate of the presence of comorbidity i among patients who have passed through sepsis state j. Here, zji measures how far the reference point wji is from the population mean for the sepsis state i. If zji is positive, wji is expressed in sepsis state i, and vice versa.