The absence/presence logic of an "existing hazard" fails to explain the temporal ambiguity of toxicity and its slow and invisible diffusion into the environment, whether that environment is residential, rural, or urban.
The first example concerns a prostate cancer trial, well known in competing risks literature, to show a situation where proportional hazard fail to model the treatment effect during the whole follow-up.
The logistic regression model with 5-year mortality as the dependent outcome was chosen over the Cox survival model because the assumption of proportional hazards failed to hold.
The multivariate stepwise Cox's proportional regression hazard model failed to identify independent prognostic factors for OS.
A Cox proportional hazard analysis failed to show a significant influence of ECOG performance status, elevation of LDH, number of involved sites, and liver involvement on survival.
Survival analyses were conducted by using Kaplan-Meier plots, log-rank test, and adjusted Cox regression when proportional hazard assumption passed (assessed globally by using a Wald goodness-of-fit χ2 test for each cohort and outcome multivariate model) or adjusted Weibull regression when proportional hazard assumption failed (SAS v9.2; SAS Institute, Cary, NC, USA).
Cox proportional hazards models failed to show adverse effects of increasing mitral gradient on outcomes analyzed: survival hazard ratio = 0.95 (95% confidence interval: 0.82 to 1.11, p = 0.527) and survival/heart failure hospitalization hazard ratio = 1.04 (95% confidence interval: 0.93 to 1.17, p = 0.488).
Although the test of the proportional hazards assumption failed (P < 0.001), elevated depressive symptoms and antidepressant use were found to be significantly associated with diabetes risk in accelerated failure time models that allowed nonproportional hazards over time.
Moreover, even when the PH assumption is satisfied, because the Cox model does not postulate a direct relationship between the covariate (treatment) and the survival time, the hazard ratio fails to measure the extent to which the treatment is clinically valuable [ 38, 70].
"Should one of the high-hazard dams fail, and there is a risk of that happening, we could have fatalities," he added.
