title: Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters.
abstract: Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time-dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real-life analyses to estimate nonlinear and time-dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real-life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure.
authors.affiliation: Department of Epidemiology and Biostatistics, McGill University, Montreal, Quebec, H3A 1A2, Canada.
authors.forename: Willy
authors.initials: W
authors.lastname: Wynant
authors.affiliation: Department of Epidemiology and Biostatistics, McGill University, Montreal, Quebec, H3A 1A2, Canada. michal.abrahamowicz@mcgill.ca.|Division of Clinical Epidemiology, McGill University Health Centre, Montreal, Quebec, H3A 1A1, Canada. michal.abrahamowicz@mcgill.ca.
authors.forename: Michal
authors.initials: M
authors.lastname: Abrahamowicz
mesh_terms: D000465:Algorithms; D003110:Colonic Neoplasms / Q000175:diagnosis / Q000401:mortality; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D011379:Prognosis; D016016:Proportional Hazards Models; D016019:Survival Analysis
keywords: Constrained optimization; Cox's proportional hazards model; Nonidentifiability; Nonlinear effects; Time-varying effects