A JOINT HAZARD AND TIME SCALING MODEL TO COMPARE SURVIVAL CURVES

To provide a more general method for comparing survival experience, we propose a model that independently scales both hazard and time dimens ions. To test the curve shape similarity of two time-dependent hazards , h(t)(t) and h(2)(t), we apply the proposed hazard relationship, h(12 )(tK(t))/h(1)(t) = K-h, to h(1). This relationship doubly scales h(1) by the constant hazard and time scale factors, K-h and K-t, producing a transformed hazard, h(12), with the same underlying curve shape as h (1). We optimize the match of h(12) to h(2) by adjusting K-h and K-t. The corresponding survival relationship S-12(tK(t)) = [S-1(t)]KtKh tra nsforms S-1 into a new curve S-12 of the same underlying shape that ca n be matched to the original S-2. We apply this model to the curves fo r regional and local breast cancer contained in the National Cancer In stitute's End Results Registry (1950-1973), Scaling the original regio nal curves, h(1) and S-1 with K-t = 1.769 and K-h = 0.263 produces tra nsformed curves h(12) and S-12 that display congruence with the respec tive local curves, h(2) and S-2. This similarity of curve shapes sugge sts the application of the more complete curve shapes for regional dis ease as templates to predict the longterm survival pattern for local d isease, By extension, this similarity raises the possibility of scalin g early data for clinical trial curves according to templates of regis try or previous trial curves, projecting long-term outcomes and reduci ng costs, The proposed model includes as special cases the widely used proportional hazards (K-t = 1) and accelerated life (KtKh = 1) models .