To identify positive selection in cancer genomes, it is essential to build an accurate background mutation rate model that corrects for covariates (features) that impact regional mutation rate variation, such as local sequence context and chromatin profiles. We considered a range of genetic and epigenetic features that could be correlated with GC somatic mutation rates. The features included 33 general and 36 gastric-specific chromatin features, 133 transcription factor binding profiles, and DNA replication timing profiles (Supplementary Data 2; Methods). To model the effect of local sequence context on mutation rate, previous studies have considered the single or tri-nucleotide sequence context of each mutation5,6,8,9. However, as mutation rates may also be influenced by wider sequence contexts33, we thus used an expanded sequence context model that considers the effects of tri-nucleotide (1 bp flanks) and penta-nucleotide (2 bp flanks) contexts on the mutation probability of each base. Least absolute shrinkage and selection operator (LASSO) logistic regression was used to identify the most predictive epigenetic and sequence context features (Supplementary Fig. 2). We used these features to estimate sample-specific background mutation probabilities, and to identify individual focal regions (21 bp) exhibiting mutational recurrence across samples beyond chance expectation (Fig. 2a; Methods). Overlapping significantly mutated regions were merged to obtain a list of unique hotspots.Fig. 2Genome-wide analysis of non-coding indel recurrence. a Workflow of the method to detect recurrently mutated non-coding regions. b Genome-wide negative log P-values of indel recurrence of 21 bp regions with at least one indel. The horizontal line marks the Bonferroni adjusted P-value of 0.01. c Negative log P-value of indel recurrence in merged non-coding regions of each gene. The top three significantly mutated genes are highlighted. The horizontal line marks the Bonferroni adjusted P-value of 0.01. d–f Gene expression of LIPF (d), PGC (e), and MUC6 (f) in normal gastric samples, tumors wildtype for the gene of interest, and tumors with non-coding indels in the gene of interest