It has proven exceedingly difficult to ascertain rare copy number alterations (CNAs) that may have strong effects in individual tumors. We show that a regulatory network inferred from gene expression and gene copy number data of 768 human cancer cell lines can be used to quantify the impact of patient-specific CNAs on survival signature genes. A focused analysis of tumors from six tissues reveals that rare patient-specific gene CNAs often have stronger effects on signature genes than frequent gene CNAs. Further comparison to a related network-based approach shows that the integration of indirectly acting gene CNAs significantly improves the survival analysis.