Methods, systems, and apparatus determine whether a first chromosomal region exhibits a deletion or an amplification associated with cancer in a sample from a subject (e.g., where the sample includes a mixture of cell-free DNA from tumor cells and non-malignant cells. Nucleic acid molecules of the biological sample are sequenced. Respective amounts of a clinically-relevant chromosomal region and of background chromosomal region(s) are determined from results of the sequencing. A parameter derived from these amounts (e.g. a ratio) is compared to one or more cutoff values, thereby determining a classification of whether first chromosomal region exhibits a deletion or an amplification associated with cancer.