A comparative study of Cox proportional hazards and parametric survival models using residual diagnostics and shrinkage estimation

Parametric regression models allow for comparison with the widely used Cox proportional hazards model in survival analysis, yet they remain underutilized in practice. While the Cox model is well regarded for its minimal distributional assumptions, fully parametric models can provide meaningful advantages—including improved estimation efficiency, more direct interpretation of covariate effects, and improve predictive accuracy when their distributional assumptions are appropriate. In this paper, we examine the performance of three parametric survival models—Weibull, log-normal, and log-logistic—in comparison with the Cox model. Using Cox–Snell residuals, we evaluate the goodness of fit for each model and identify conditions under which parametric approaches yield performance comparable to the Cox model, as well as situations where they offer modest improvements. After determining the most suitable model, we further refine estimation through pretest and shrinkage estimation techniques, which optimally combine information from restricted and unrestricted models. A comprehensive Monte Carlo simulation study and two real-data applications demonstrate that parametric models can match, and in some settings surpass, the Cox model in terms of mean squared error and model fit. Overall, our findings suggest that parametric survival models—particularly when combined with pretest or shrinkage estimation—serve as alternatives to the Cox model, offering competitive performance across a variety of scenarios.