Single-nucleotide polymorphisms (SNPs) contributing to interactions between regulatory elements that modulate gene transcription may explain some of the uncharacterized variation for complex traits. We explored this hypothesis among 856 adult survivors of pediatric cancer exposed to curative treatments that adversely affect bone mineral density (BMD). To restrict our search to interactions among SNPs in regulatory elements, our analysis considered 75523 SNPs mapped to putative promoter or enhancer regions. In anticipation that power to detect higher order epistasis would be low using an exhaustive search and a Bonferroni-corrected threshold for genome-wide significance (e.g., P < 5.6 × 10-14), a novel non-exhaustive statistical algorithm was implemented to detect chromosome-wide three-way regulatory interactions. We used a permutation-based evaluation statistic to identify candidate SNP interactions with stronger associations with BMD than expected. Of the six regulatory 3-SNP interactions identified as candidate interactions (P < 3.5 × 10-11) among cancer survivors exposed to treatments, five were replicated in an independent cohort of survivors (N = 1428) as modifiers of treatment effects on BMD (P < 0.05). Analyses with publicly available bioinformatics data revealed that SNPs contributing to replicated interactions were enriched for gene expressions (P = 3.6 × 10-4) and enhancer states (P < 0.05) in cells relevant for bone biology. For each replicated interaction, implicated SNPs were within or directly adjacent to 100-kb windows of genomic regions that plausibly physically interact in lymphoblastoid cells. Our study demonstrates the utility of a hypothesis-driven approach in revealing epistasis associated with complex traits.