New estimation approaches in survival analysis with Aalen's additive risk model

New estimation methods for predictive risk modeling are proposed. These approaches based on the Aalen additive risk model (1980) for survival analysis are used to compute both the instantaneous and cumulative covariate effect on the hazard at each point in time.; Smoothing methods based on smoothing polynomial splines (SPS) are proposed to estimate the cumulative regression function together with its first and second derivatives. Compared to more traditional methods due to Aalen (1993), this approach has improved validity and accuracy in estimation. In addition, this method allows one to explicitly identify temporal patterns of risk via the rates of change of the cumulative regression function, regression functions, and slope of the regression functions. FORTRAN algorithms are developed to implement the SPS method.; Inequality constrained least squares (ICLS) estimation is proposed to compute the cumulative regression functions. This is typically done with ordinary least squares (Aalen 1989), however the estimated hazard function is unrestricted, which may result in implausible hazard values. The ICLS estimator uses inequality constraints that restrict the estimation so that one can obtain only plausible hazard estimates. The ICLS method was developed from the linear complementary problem of Cottle and Dantzig (1968). The problem is efficiently solved with a quadratic programming algorithm offered by Gill et al. (1995). Results from simulation studies indicated that the ICLS estimator has consistent improvements in estimation compared to the OLS method in terms of accuracy and validity. FORTRAN algorithms are developed to implement the ICLS method.; We propose new methodology in survival analysis, which is a common type of public health study. Our estimation methods proposed for Aalen's additive risk model provide improvements in accuracy and validity to help better understand risk factors associated with disease.