Systems, apparatus, and methods are provided for determining genetic or molecular aberrations in a biological sample. Biological samples including cell-free DNA fragments are analyzed to identify imbalances in chromosomal regions, e.g., due to deletions and/or amplifications in a tumor. Multiple loci are used for each chromosomal region. Such imbalances can be used to diagnose (screen) a patient for cancer, as well as prognosticate a patient with cancer, or to detect the presence or to monitor the progress of a premalignant condition in a patient. Severity of an imbalance and the number of regions exhibiting an imbalance can be used. A systematic analysis of non-overlapping genomic segments can provide a general screening tool. A patient can be tested over time to track severity of each of one or more chromosomal regions and a number of chromosomal regions to enable screening and prognosticating, as well as monitoring of progress (e.g. after treatment).