Weighted Quantile Sum Regressions for Cox Proportional Hazards Model

Weighted Sum (WS) and Weighted Quantile Sum (WQS) regression model the joint effect of correlated predictors through a constrained index with nonnegative weights summing to one; WQS further applies quantile transformation and estimates weights via bootstrap aggregation. Both approaches are established for generalized linear models, yet many biomedical outcomes are time-to-event. We present WS-Cox and WQS-Cox regression, extending this framework to Cox proportional hazards regression while preserving mixture-weight interpretability through partial likelihood estimation. Weight estimation is formalized as constrained nonlinear optimization of the Cox log-partial-likelihood, with bootstrap aggregation consistent with standard WQS practice. A simulation study evaluates finite-sample performance across varying sample sizes and weight distributions. Applied to liver cirrhosis decompensation, WS-Cox regression yields an interpretable global hazard ratio and ranked contributor profile for cardiometabolic risk factors.