Alternative Conditional Estimation of Time-Dependent and Nonlinear Effects of Covariates on the Hazard

• Activity Number: 350
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Willy Wynant*+ and Michal Abrahamowicz and Amel Mahboubi
• Companies: McGill University and McGill University and McGill University
• Keywords: survival analysis ; non-linear effect ; time-dependent effect ; simulations ; constraints ; spline

Abstract

Survival data are often analyzed using the Cox's PH model which relies on two assumptions: (i) the effects of continuous covariates are linear on the logarithm of the hazard and (ii) covariate effects do not change over time. To account for possibly violations of both assumptions, we use a flexible spline-based model that estimates simultaneously the non-linear (NL) and the time-dependent (TD) effects of covariates. However, we need to impose some constraints on the parameters to avoid identifiability problems. We propose the use of an alternating conditional estimation algorithm which involves an iterative 2-step procedure. At each step, one of the functions (e.g.NL) is estimated, conditional on the previous estimates of the other function (TD). Convergence is declared if the change in the log likelihood, relative to the previous iteration, is lower than a given threshold. We validate this algorithm trough a series of extensive simulations and apply it to a real data set.