Objective: The clinical significance of QT interval adaptation to heart rate changes has been poorly investigated in atrial fibrillation (AF), since QT delineation in the presence of f-waves is challenging. Therefore, the objective of the present study is to investigate new techniques for QT adaptation estimation in permanent AF. Methods: A multilead strategy based on generalized periodic component analysis is proposed for QT delineation, involving a spatial, linear transformation which emphasizes Twave periodicity and attenuates f-waves. QT adaptation is modeled by a linear, time-invariant filter, whose impulse response describes the dependence between the current QT interval and the preceding RR intervals, followed by a memoryless, possibly nonlinear, function. The QT adaptation time lag is determined from the estimated impulse response. Results: Using simulated ECGs in permanent AF, the transformed lead was found to offer more accurate QT delineation and time lag estimation than did the original ECG leads for a wide range of f-wave amplitudes (the time lag estimation error was found to be -0.2+/-0.6 s for SNR = 12 dB). In a population with chronic heart failure and permanent AF, the time lag estimated from the transformed lead was found to have the strongest, statistically significant association with sudden cardiac death (SCD) (hazard ratio = 3.49), whereas none of the original, orthogonal leads had any such association. Conclusions: Periodic component analysis provides more accurate QT delineation and improves time lag estimation in AF. A prolonged adaptation time of the QT interval to heart rate changes is associated with a high risk for SCD. Significance: This study demonstrates that SCD risk markers, originally developed for sinus rhythm, can also be used in AF, provided that Twave periodicity is emphasized. The time lag is a potentially useful marker for identifying patients at high risk for SCD, guiding clinicians in adopting effective therapeutic decisions.