Maximum Likelihood Estimation for Shape-restricted Single-index Hazard Models

Single-index models are becoming increasingly popular in many scientific applications as they offer the advantages of flexibility regression modeling well interpretable covariate effects. In context survival analysis, single-index hazards natural extensions Cox proportional models. this paper, we propose a novel estimation procedure for hazard under monotone constraint index. We apply profile likelihood method to obtain semiparametric maximum estimator, where novelty lies estimating unknown link function by embedding problem isotonic with exponentially distributed random variables. The consistency proposed estimator is established suitable regularity conditions. Numerical simulations conducted examine finite-sample performance method. An analysis breast cancer data presented illustration.