Study Length Over-Estimating Hazard Ratio? Are cox model studies over too long a time-scale at risk of over estimating (or under estimating) a covariate's effect on hazard?
I'm studying inbreeding in a captive animal population. Some individuals are 30+ years old. The oldest year of age, in this model's terms, is our longest (or latest) year of study. But there's the possibility that only a few animals live to be this long (perhaps <5%).
Could the hazard ratio outputs from my mixed effect Cox models be over-estimates due to the study period being too long and only a few individuals living to an old age (i.e., does having only a few of one group of interest - say inbred individuals - present for a long period in a study bias hazard ratio estimates)?
Any help, advice, or discussion would be greatly appreciated. Thank you. 
 A: I think the most important question is if the proportional hazards assumption holds. If this holds then you have little problem with long-term follow-up. The proportional hazards assumption is usually investigated using Schoenfeld residuals. These should align along a straight line for each estimate. In R you simply specify your model with the x=TRUE and y=TRUE, i.e. coxph(Surv(time, event) ~ var1 + var2, data=my_data, x=TRUE, y=TRUE) and then you pass the fitted model to the cox.zph(). Here is a tutorial.
My intuition has always been that generally a non-prooportional hazard should bias the results towards null but Ranstam et al. write in this article that: 

The consequence of non-PH 
If the PH assumption is violated, by hazard
  ratios increasing over time, the overall hazard ratio for the risk
  factor will be overestimated. Decreasing hazard ratios will lead to
  underestimation (Schemper 1992).

My personal experience is that the effect can be completely obliterated by non-proportional hazards. It is also important to not that a few cases at the end will not have the same impact as the bulk of the early cases, i.e. a negative risk early on may be relatively small but it may cancel out an increased risk later due to that there are so many of them. 
So in short, the risk that < 5% of cases impact the results should be negligible.
