Hi all,
I am currently researching on waiting time of passengers (the time passengers stay at the stop) in an urban station with hazard models. Results show that the best hazard model is Weibull with univariate frailty. The individual hazard is monotonically increasing in time, while the population hazard rises and then falls. I am confused about interpreting the effect of frailty conflict between population and individual hazard, although I studied many references (like "An Introduction to survival analysis using Stata"). In the literature (especially medical research), Some authors explain the conflict between the individual and population hazard by dividing the population into two parts. Some individuals are susceptible to failure/ infection/ disease, and some are not. But indeed, this would not be the case in my research because all individuals are susceptible to failure (I am sure about that). I would like to ask which of these two statements are valid to explain frailty? (Assume that frailty is greatly significant and can not be neglected)
1- With respect to the available variables in the model, the hazard is monotonically increasing, but we have not considered enough variables to describe the waiting time. The frailty term plays the role of unmeasured variables and changes the shape of individual hazard to the population (changing the level of individual susceptibility). In this regard, the correct hazard function is the population one. (The population hazard functions can merely be true hazard function)
2- We should separate the levels of study. On an individual level, the hazard function is monotonically increasing in time, while for some unknown reasons (captured by frailty term), the population hazard function rises and then falls. (Both hazard functions are valid, but we should separate the individual and population levels)
Thanks for your consideration in advance.