Testing the Equivalence of Survival Distributions using PP- and PPP-Plots - Cox, Trevor F. (International Journal of Statistics in Medical Research, 2014)
This paper discusses the use of PP-plots for survival distributions where for a pair of survival distributions, one is plotted against the other. This is another way of visualizing the nature of the relationship between the two survival distributions along with typical Kaplan-Meier plots. For three survival distributions, the PPP-plot is introduced where the survival distributions are plotted against each other in three-dimensions. At the population level, measures of divergence between distributions are introduced based on areas and lengths associated with the PP- and PPP- plots. At the sample level, two test statistics are defined, based on these areas and lengths, to test the null hypothesis of equivalent survival curves. A simulation exercise showed that, overall, the new tests are worthy competitors to the log-rank and Wilcoxon tests and also to a Levine-type test and a Kolmogorov-Smirnov type test for the case of crossing survival curves. The paper also shows how the PP-plot can be used to estimate the hazard ratio and to assess the ratio of hazard functions if proportional hazards are not appropriate. Finally, the methods introduced are illustrated on two cancer data sets