Cancer treatment effectiveness is often quantified by analyzing time from treatment initiation to the occurrence of a particular event. Very commonly studies report data on overall survival (OS), where the event is death from any cause, and on progression-free survival (PFS), where the event is death from any cause or disease progression, whichever occurred first. Both OS and PFS can inform decision making. Separate meta-analyses of OS and of PFS data ignore the correlation between the outcomes.  We introduce a method for the joint meta-analysis of OS and PFS that is based on a tri-state transition model with time-varying hazard rates modeled with fractional polynomials.  In English, we assume that, at any time, patients can be in one of three health states: “alive but not progressed”, “alive and progressed”, and “dead”. PFS corresponds to time spent in the first state, and OS to time spent in the two alive states.  The proposed approach allows the joint network meta-analysis of OS and PFS, relaxes the proportional hazards assumption, extends to a network of more than two treatments, and simplifies the parameterization of decision and cost-effectiveness analyses. The data needed to run these analyses can be extracted directly from published survival curves.  We demonstrate use by applying the methodology to a network of trials for the treatment of non-small cell lung cancer.