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RATIONALE Ventilatory control instability is an important factor contributing to the pathogenesis of periodic breathing (PB) and other forms of sleep-related breathing disorders (SRBD). The development of tools for the quantification of such instabilities from non-invasive respiratory measurements during sleep could be useful to clinicians in identifying subjects that are at risk of developing SRBD. OBJECTIVES To present and compare two different mathematical modeling approaches that allow the quantification of ventilatory control stability from the ventilatory responses to spontaneous sighs. MEASUREMENTS AND METHODS Breath-by-breath measurements of normalized ventilation were derived from respiratory inductance plethysmography (RIP) traces collected during sleep from a cohort of 19 preterm infants with various degrees of periodic breathing. A hypothesis-based minimal closed-loop model consisting of a gain, time-constant and time delay; and a data-driven autoregressive model with time delay were used to fit the ventilatory responses to the spontaneous sighs. Loop gain, a quantitative measure of ventilatory control stability, was extracted from both models. RESULTS AND DISCUSSION Both approaches accurately described the ensuing responses to the sighs. Significant and robust correlations were found in the loop gain estimates extracted with the two models in the frequency range spanning 2-8 cycles min-1, which corresponds to PB cycling oscillations in infants. In addition, the hypothesis-based model showed a decreased within-subject variability of the estimated stability quantifiers, while the data-driven better resembled the experimental data. There are advantages and limitations associated with each of the modeling approaches which are discussed in the paper. CONCLUSIONS The agreement found between the two mathematical models indicates that either methodology can be used indistinctively providing reliable results and their application can expand to sigh data from other clinical cohorts of preterm infants.