Multiple mechanisms are involved in the pathogenesis of obstructive sleep apnea (OSA). Elevated loop gain is a key target for precision OSA care and may be associated with treatment intolerance when the upper airway is the sole therapeutic target. Morphological or computational estimation of LG is not yet widely available or fully validated - there is a need for improved phenotyping/endotyping of apnea to advance its therapy and prognosis. This study proposes a new algorithm to assess self-similarity as a signature of elevated loop gain using respiratory effort signals and presents its use to predict the probability of acute failure (high residual event counts) of continuous positive airway pressure (CPAP) therapy. Effort signals from 2145 split-night polysomnography studies from the Massachusetts General Hospital were analyzed for SS and used to predict acute CPAP therapy effectiveness. Logistic regression models were trained and evaluated using 5-fold cross-validation. Receiver operating characteristic (ROC) and precision-recall (PR) curves with AUC values of 0.82 and 0.84, respectively, were obtained. Self-similarity combined with the central apnea index (CAI) and hypoxic burden outperformed CAI alone. Even in those with a low CAI by conventional scoring criteria or only mild desaturation, SS was related to poor therapy outcomes. The proposed algorithm for assessing SS as a measure of expressed high loop gain is accurate, non-invasive, and has the potential to improve phenotyping/endotyping of apnea, leading to more precise sleep apnea treatment strategies.