We present the phase-rectified signal averaging (PRSA) method as an efficient technique for the study of quasi-periodic oscillations in noisy, nonstationary signals. It allows the assessment of system dynamics despite phase resetting and noise and in relation with either increases or decreases of the considered signal. We employ the method to study the quasi-periodicities of the human heart rate based on long-term ECG recordings. The center deflection of the PRSA curve characterizes the average capacity of the heart to decelerate (or accelerate) the cardiac rhythm. It can be measured by a central wavelet coefficient which we denote as deceleration capacity (DC). We find that decreased DC is a more precise predictor of mortality in survivors of heart attack than left ventricular ejection fraction, the current "gold standard" risk predictor. In addition, we discuss the dependence of the DC parameter on age and on diabetes.