The ends of cell-free DNA fragments may be used for analysis of a biological sample. In some embodiments, DNA from a urine sample may be analyzed. Cell-free DNA fragments often include jagged ends, where one end of one strand of double-stranded DNA extends beyond the other end of the other strand. The length and amount of these jagged ends may be used to determine a level of a condition of an individual. The density of ends of fragments in certain regions may also be used in classifying the level of a condition. Additionally, DNA fragments may show a periodic pattern with the amount of DNA fragments corresponding to a length of the overhang. The periodicity may be analyzed to determine properties of a biological sample. Jagged ends may also be analyzed with a technique that avoids trimming overhanging 3′ ends of a double-stranded DNA.