Systematic perturbation screens provide comprehensive resources for the elucidation of cancer driver genes. The perturbation of many genes in relatively few cell lines in such functional screens necessitates the development of specialized computational tools with sufficient statistical power. Here we developed APSiC (Analysis of Perturbation Screens for identifying novel Cancer genes) to identify genetic and non-genetic drivers in perturbation screens even with few samples. Applying APSiC to the shRNA screen Project DRIVE, APSiC identified well-known, pan-cancer genetic drivers, novel putative genetic drivers known to be dysregulated in specific cancer types and the context dependency of mRNA-splicing between cancer types. Additionally, APSiC discovered a median of 28 and 35 putative non-genetic oncogenes and tumor suppressor genes, respectively, for individual cancer types, including genes involved in genome stability maintenance and cell cycle. We functionally demonstrated that LRRC4B, a putative novel non-genetic tumor suppressor gene, suppresses proliferation by delaying cell cycle and modulates apoptosis in breast cancer. We demonstrate APSiC is a robust statistical framework for discovery of novel cancer genes through analysis of large-scale perturbation screens. The analysis of DRIVE using APSiC is provided as a web portal and represents a valuable resource for the discovery of novel cancer genes.