A method of assaying a sample to detect cells of a cancer type in a subject, the method comprising: (a) capturing converted or unconverted cell-free DNA (cfDNA) fragments from the sample or amplification products thereof with a composition comprising a plurality of different bait oligonucleotides, wherein converted cfDNA relates to cfDNA that has been treated to convert unmethylated cytosines to uracils, wherein: (i) each bait oligonucleotide in the plurality of different bait oligonucleotides is at least 45 nucleotides in length; (ii) the plurality of different bait oligonucleotides collectively hybridize to at least 200 target genomic regions; (iii) the at least 200 target genomic regions are differentially methylated in cfDNA of reference subjects with at least one cancer type relative to a different cancer type or relative to non-cancer; and (iv) the at least 200 target genomic regions comprise, for at least 80% of all possible pairs of cancer types selected from a set comprising at least 10 cancer types, at least one target genomic region that is differentially methylated between the pair of cancer types; (b) sequencing the captured cfDNA fragments or amplification products thereof to produce sequencing reads, wherein if the captured cfDNA in step (a) was unconverted then that cfDNA is converted prior to sequencing by treating the cfDNA to convert unmethylated cytosines to uracils; and (c) applying a trained classifier to the sequencing reads to determine the presence or absence of cancer, wherein: (i) the trained classifier is a classifier trained using converted cfDNA samples, wherein converted cfDNA relates to cfDNA that has been treated to convert unmethylated cytosines to uracils; (ii) the trained classifier compares a number of sequencing reads for a plurality of the at least 200 target genomic regions that are identified as hypermethylated or hypomethylated in the cfDNA fragments to a threshold for each of the at least 10 cancer types; and (iii) detection above the threshold for a respective cancer type identifies the presence of the cells of the cancer type in the subject. (a) capturing converted or unconverted cell-free DNA (cfDNA) fragments from the sample or amplification products thereof with a composition comprising a plurality of different bait oligonucleotides, wherein converted cfDNA relates to cfDNA that has been treated to convert unmethylated cytosines to uracils, wherein: (i) each bait oligonucleotide in the plurality of different bait oligonucleotides is at least 45 nucleotides in length; (ii) the plurality of different bait oligonucleotides collectively hybridize to at least 200 target genomic regions; (iii) the at least 200 target genomic regions are differentially methylated in cfDNA of reference subjects with at least one cancer type relative to a different cancer type or relative to non-cancer; and (iv) the at least 200 target genomic regions comprise, for at least 80% of all possible pairs of cancer types selected from a set comprising at least 10 cancer types, at least one target genomic region that is differentially methylated between the pair of cancer types; (i) each bait oligonucleotide in the plurality of different bait oligonucleotides is at least 45 nucleotides in length; (ii) the plurality of different bait oligonucleotides collectively hybridize to at least 200 target genomic regions; (iii) the at least 200 target genomic regions are differentially methylated in cfDNA of reference subjects with at least one cancer type relative to a different cancer type or relative to non-cancer; and (iv) the at least 200 target genomic regions comprise, for at least 80% of all possible pairs of cancer types selected from a set comprising at least 10 cancer types, at least one target genomic region that is differentially methylated between the pair of cancer types; (b) sequencing the captured cfDNA fragments or amplification products thereof to produce sequencing reads, wherein if the captured cfDNA in step (a) was unconverted then that cfDNA is converted prior to sequencing by treating the cfDNA to convert unmethylated cytosines to uracils; and (c) applying a trained classifier to the sequencing reads to determine the presence or absence of cancer, wherein: (i) the trained classifier is a classifier trained using converted cfDNA samples, wherein converted cfDNA relates to cfDNA that has been treated to convert unmethylated cytosines to uracils; (ii) the trained classifier compares a number of sequencing reads for a plurality of the at least 200 target genomic regions that are identified as hypermethylated or hypomethylated in the cfDNA fragments to a threshold for each of the at least 10 cancer types; and (iii) detection above the threshold for a respective cancer type identifies the presence of the cells of the cancer type in the subject. (i) the trained classifier is a classifier trained using converted cfDNA samples, wherein converted cfDNA relates to cfDNA that has been treated to convert unmethylated cytosines to uracils; (ii) the trained classifier compares a number of sequencing reads for a plurality of the at least 200 target genomic regions that are identified as hypermethylated or hypomethylated in the cfDNA fragments to a threshold for each of the at least 10 cancer types; and (iii) detection above the threshold for a respective cancer type identifies the presence of the cells of the cancer type in the subject.