Penalised method of sieves for semi-parametric AFT model with right-censored survival data

The accelerated failure time (AFT) model is an important alternative semi-parametric survival model apart from the commonly used Cox proportional hazard (Cox) model. The function form of the AFT model is analogous to the classical linear regression model, which directly links survival time to the regression coefficients. However, unlike the Cox model, an estimation of the non-parametric component is always required in the AFT model. Estimation of the non-parametric component is computational challenge. In this thesis we extend the approach of Ma [1] and develop a penalised method of sieves to estimate the regression coefficients as well as the non-parametric component of the AFT model. Inspired by the method of sieves [2] [3], we adopt the M-spline family to construct an approximating function for the non-parametric component. To facilitate the approach, we set up the relevant constrained maximisation problem. The combination of a modified Newton's method and the multiplicative algorithm is used to solve the optimisation problem. A simulation study is conducted to compare our proposed method with a penalised likelihood method [4] and a rank-based method [5].