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 dimensions. To test the curve shape similarity of two time-dependent hazards, h1(t) and h2(t), we apply the proposed hazard relationship, h12(tKt)/ h1(t) = Kh, to h1. This relationship doubly scales h1 by the constant hazard and time scale factors, Kh and Kt, producing a transformed hazard, h12, with the same underlying curve shape as h1. We optimize the match of h12 to h2 by adjusting Kh and Kt. The corresponding survival relationship S12(tKt) = [S1(t)]KtKh transforms S1 into a new curve S12 of the same underlying shape that can be matched to the original S2. We apply this model to the curves for regional and local breast cancer contained in the National Cancer Institute's End Results Registry (1950-1973). Scaling the original regional curves, h1 and S1 with Kt = 1.769 and Kh = 0.263 produces transformed curves h12 and S12 that display congruence with the respective local curves, h2 and S2. This similarity of curve shapes suggests the application of the more complete curve shapes for regional disease as templates to predict the long-term survival pattern for local disease. By extension, this similarity raises the possibility of scaling early data for clinical trial curves according to templates of registry or previous trial curves, projecting long-term outcomes and reducing costs. The proposed model includes as special cases the widely used proportional hazards (Kt = 1) and accelerated life (KtKh = 1) models.

Initiation process of earthquakes and its implications for seismic hazard reduction strategy.

For the average citizen and the public, "earthquake prediction" means "short-term prediction," a prediction of a specific earthquake on a relatively short time scale. Such prediction must specify the time, place, and magnitude of the earthquake in question with sufficiently high reliability. For this type of prediction, one must rely on some short-term precursors. Examinations of strain changes just before large earthquakes suggest that consistent detection of such precursory strain changes cannot be expected. Other precursory phenomena such as foreshocks and nonseismological anomalies do not occur consistently either. Thus, reliable short-term prediction would be very difficult. Although short-term predictions with large uncertainties could be useful for some areas if their social and economic environments can tolerate false alarms, such predictions would be impractical for most modern industrialized cities. A strategy for effective seismic hazard reduction is to take full advantage of the recent technical advancements in seismology, computers, and communication. In highly industrialized communities, rapid earthquake information is critically important for emergency services agencies, utilities, communications, financial companies, and media to make quick reports and damage estimates and to determine where emergency response is most needed. Long-term forecast, or prognosis, of earthquakes is important for development of realistic building codes, retrofitting existing structures, and land-use planning, but the distinction between short-term and long-term predictions needs to be clearly communicated to the public to avoid misunderstanding.