LAUSR

Despite apnea-hypopnea index (AHI) being the gold standard in diagnosing obstructive sleep apnea, AHI can be further optimized if AHI is differentiated according to sleep stages/positions, then integrated with weighted time. The primary aim of this study is to demonstrate the mathematical modeling process from which ‘projected AHI’ (pAHI) can be calculated. With the hypothesis of the nth projected AHI, expressed as AHI_n, being the gold standard and AHI_0 being test results, using AHI of 5 as cutoffs, subjects were grouped into a confusion matrix of TN_n, FP_n, FN_n and TP_n. Through recursive optimization, information obtained from AHI_0 and AHI_n was used to calculate AHI_(n + 1). The coefficients of the equation to calculate AHI_(n + 1) consisted of A_(n + 1), B_(n + 1), C_(n + 1), and D_(n + 1), each representing the % of total time of each of the four types of sleep (REM supine, REM non-supine, NREM supine, NREM non-supine) out of the people in the groups TN_n and FP_n. We tested a closed polysomnographic dataset of 337 subjects to determine the point at which all four coefficients would stay constant, producing the ideal pAHI of the dataset. Each of the four coefficients of the equation converged at n = 3. At n = 3, A_3 = 0.090, B_3 = 0.087, C_3 = 0.433, and D_3 = 0.390. The patients in the groups TN_2 and FP_2 turned out to be the same patients that were in the groups TN_3 and FP_3, explaining why each of the four coefficients of the equation converged at n = 3, and continuously onwards. As a result, it logically follows that for all n > 2, the formulas of AHI_n were determined to be equal in this closed dataset. Ideal pAHI is not a fixed formula. Instead, a recursive optimization model can generate an ideal formula in a big data set when each coefficient of the equation converges. In addition, the recursive optimization model used in our pAHI can be particularly useful in machine learning as new data sets are prospectively added to the existing data. n/a