A Flexible and Robust Approach to Analyze Survival Systems in the Presence of Extreme Observations

Survival systems are difficult to analyze in the presence of extreme observations and multicollinearity. Finding appropriate models that provide a robust description of such survival systems and that address the smooth hazards in the context of covariates can be challenging given the sheer number of possibilities. Survival time algorithms that evaluate the efficiency of models in the presence of extreme observations over different datasets provide an effective tool to identify robust systems. However, the existing algorithms addressing the analysis of survival systems are limited in long-term evaluations. Therefore, an algorithm that can analyze survival time response on high-dimensional complex survival systems having extreme observations is developed which explores large margins dynamically. This algorithm is developed as a conjugate of flexible parametric models and partial least squares to estimate smooth, flexible, and robust functions to extrapolate the survival model in long-term evaluations in the presence of extreme observations. The algorithm is tested and validated using four distributions based on a simulated dataset generated from the Weibull distribution and compared with partial least squares-Cox regression. The comparison shows its flexibility and efficiency in handling different survival systems in the presence of extreme values. The algorithm is also used to analyze four real datasets of breast cancer survival time, each containing seven gene signatures. The coefficients of significant genes for each dataset are estimated. The flexibility in handling various distributions as parametric survival models supports the application of the algorithm to a large variety of different survival problems and represents a robust statistical framework for survival analysis in the presence of extreme observations.