Apnea of prematurity, a common developmental disorder in preterm infants, is implicated in long-term neurodevelopmental deficits. Preventative clinical interventions, such as mechanosensory stimulation, would benefit from predictive knowledge of when the patient is at high risk for apnea. In this study, the predictive utility of features derived from breathing rate and heart rate is explored. Specifically, the multiscale correlation structure of interbreath intervals and heartbeat intervals is used to train a patient-specific apnea prediction algorithm. The algorithm's prediction results are significantly better than chance for three of the six patients it is evaluated on. These preliminary studies suggest that features of cardiopulmonary signals can anticipate the occurrence of clinically significant apneas in preterm infants.