Processes and materials to detect cancer, transplant rejection, or fetal genetic abnormalities from a biopsy are described. In some cases, cell-free nucleic acids can be sequenced, and the sequencing result can be utilized to detect sequences indicative of a neoplasm, transplant rejection, or fetal genetic abnormality. Detection of somatic variants occurring in phase and/or insertions and deletions (indels) can indicate the presence of cancer, transplant rejection, or fetal genetic abnormalities in a diagnostic scan, and a clinical intervention can be performed.