The Swift satellite made a real break through with measuring simultaneously the gamma X-ray and optical data of GRBs, effectively. Although, the satellite measures the gamma, X-ray and optical properties almost in the same time a significant fractions of GRBs remain undetected in the optical domain. In a large number of cases only an upper bound is obtained. Survival analysis is a tool for studying samples where a part of the cases has only an upper (lower) limit. The obtained survival function may depend on some other variables.
The Cox regression is a way to study these dependencies. We studied the dependence of the optical brightness (obtained by the UVOT) on the gamma and X-ray properties, measured by the BAT and XRT on board of the Swift satellite. We showed that the gamma peak flux has the greatest impact on the afterglow's optical brightness while the gamma photon index and the X-ray flux do not. This effect probably originates in the energetics of the jet launched from the central engine of the GRB which triggers the afterglow.