Crossing survival curves: alternatives to the log-rank test

Crossing survival curves: alternatives to the log-rank test

Background It is not uncommon for clinical trials to present results on survival time as Kaplan-Meier survival curves that cross, indicating non-proportional hazards. A recent example was given in a pivotal trial in advanced nonsmall cell lung cancer (The ‘IPASS study’ [1]). Trials such as these present a hazard ratio and log-rank test for treatment comparison as this is their planned primary a...

A log-rank-type test to compare net survival distributions.

In population-based cancer studies, it is often interesting to compare cancer survival between different populations. However, in such studies, the exact causes of death are often unavailable or unreliable. Net survival methods were developed to overcome this difficulty. Net survival is the survival that would be observed if the disease under study was the only possible cause of death. The Poha...

Log-rank Test for Two Groups

Comparing Survival Curves Using Rank Tests

Survival times of patients can be compared using rank tests in various experimental setups, including the two-sample case and t h e cnse of paired dnta. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author’s recent work on a new and simple class of censored rank test:. Various models for tail nl...

On the rank of certain parametrized elliptic curves

In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.