Accelerated failure time versus proportional hazards

03 June 2018

Research question and background

  • in patients with acute heart failure (AHF), patients do poorly if they have 1) co-existing renal disease (aka CKD) 2) worsening renal failure (aka WRF)
  •  current definitions are focused on magnitude of change, but not underlying severity of CKD
  • evaluate a new definition that incorporates both baseline renal function and change in renal function while in hospital
  • evaluate the association between these definitions and short and long-term clinical outcomes in patients with AHF
  • 696 patients with eGFR calculable at admission and discharge
  • definitions: preserved (P) > 45 at admission and discharge; reduced (R) < 45 at admission or discharge; worsening (WRF), stable (SRF), improved (IRF) renal function based on 20% change
  • 6 'treatment' groups: P-WRF, P-SRF, P-IRF, R-WRF, R-SRF, R-IRF
  • hypotheses: R vs P,  IRF vs SRF vs WRF

Comparison of survival among groups

P-WRF shows a high early death rate while P-IRF has a steady death rate causing the survival curves to cross. We queried the validity of the proportional hazards assumption. (Note that we used the Wilcoxon test instead of the more common log-rank test for this reason.)

Evaluating the proportional hazards assumption

There are a number of ways to test the PH assumption, as follows (note: -logS(T) will have a unit exponential distribution, the cumulative hazard function thus increases linearly against time):

Accelerated failure time (AFT) model

  • the AFT model is an alternative to the common proportional hazards (PH) model
  • Cox PH model: in terms of HR (= constant if proportional hazards)
  • AFT: in terms of S(t), relates to Kaplan-Meier plot (above)
  • S1(t)=S2(t), ⍬ = acceleration factor, e.g. ratio of medians (see the figure below which illustrates the concept)
  • Example: dog years, ⍬ = 7 
  • HR > 1: exposure harmful to survival; HR < 1: exposure benefits survival
  • ⍬ > 1: exposure benefits survival; ⍬ < 1: exposure harmful to survival
  • ⍬ = HR = 1: no effect from exposure

We used an AFT model with an extended generalised gamma distribution: 


Model checking

To examine the model fit, the fitted survivor function is plotted against the Kaplan-Meier estimates:


Notable sources:

Comparing proportional hazards and accelerated failure time models: an application in influenza
Collett, Modelling Survival Data in Medical Research 
Modelling survival data with parametric regression models (includes SAS code)