Sequence alignment is a powerful technique to compare and analyze sequential data, with applications in bioinformatics and signal processing. Traditional multiple sequence alignment (MSA) methods have a number of limitations that make them unsuitable for applications such as apnea detection in sleep medicine. First, the sequences need to be numerical or they are one-dimensional sequences of events. Apnea detection requires patterns across multiple dimensions of event sequences. Second, existing approaches are based on pairwise alignments. This puts too much focus on the alignment of all possible events in a pair of sequences. In apnea detection, however, the sequences contain many extraneous events, leading to a sparse set of relevant events. Furthermore, relevant events only manifest themselves when considering all sequences jointly. We present a novel multiple sequence alignment method that lifts these limitations. Our approach iteratively moves events across all sequences simultaneously to group identical events together. The direction in which to move events is based on the insight that event occurrences represent a density function and that a set of aligned sequences represents a sharply peaked density function. New sequences can be warped to a reference pattern using this density function. The efficacy of our new alignment method is shown in the apnea and hypopnea application.