We move slowly from the two-sample and k-sample cases, where the logrank test is introduced, to the general regression situation. There the logrank test is generalized to Cox regression (Cox 1972). The fundamental concept of proportional hazards is introduced.
The property of proportional hazards is fundamental in Cox regression. It is in fact the essence of Cox’s simple yet ingenious idea. The definition is as follows.
Definition 1 Proportional hazards
If h1(t) and h0(t) are hazard functions from two separate distributions, we say that they are proportional if
for some positive constant ψ and all t ≥ 0. Further, if (3.1) holds, then the same property ...