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

Abstract

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.

The Partial Least Squares Spline Model for Public Health Surveillance Data

“…The authors also employed a parametric analysis for comparison and variable selection. Another study developed an algorithm as a conjugate of the parametric model and partial least squares in the presence of extreme observations to enhance model performance [ 2 ]. In this study, the PLS-spline model is proposed to treat survival response with collinear predictors using the spline strategy based on different scales with various knots regarding better model performance and superior interpretation potential.…”

“…For the absolute measure of effect, the Weibull distribution can generally facilitate accurate predictions for a constant, monotonically decreasing or monotonically increasing hazards. However, for more complex hazard functions, the parametric survival model specifying a Weibull function will lead to inaccurate predictions [ 2 ].…”

“…Therefore, the partial least squares-Cox (PLS-Cox) regression model was developed to analyze survival systems in the presence of multicollinearity [ 7 ]. Due to several limitations of the PLS-Cox regression model, the PLS flexible parametric (PLS-FP) survival regression model is proposed to estimate smooth hazard ratios of predictors and corresponding cumulative hazard functions and to extrapolate the survival model [ 2 ]. However, the major limitation of the PLS-FP model is that it is not appropriate for all complex shapes of hazard function.…”

Complex Survival System Modeling for Risk Assessment of Infant Mortality Using a Parametric Approach

“…However, nonparametric and semiparametric survival methods can peculate model structures as unsmooth estimates are evaluated. The present study extended the PLS-FPM [ 14 ] to correlated predictors having moderate trend observations using four alternative probability distributions. The PLS-FPM extends previous survival approaches that either perform semiparametric analyses or use nonparametric methods, while analysis of all previous methods was limited due to their inflexible nature.…”

“…Within this line, the partial least squares flexible parametric model (PLS-FPM) is developed to analyze the complex survival systems in the presence of extreme observations for risk and hazard assessment [ 14 ]. The present study extended the PLS-FPM to collinear predictors having moderate trend observations using four alternative probability distributions.…”