Survival estimation through the cumulative hazard function with monotone natural cubic splines

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Censoring is a common challenge in survival analysis, complicating the estimation of survival probabilities.
• Existing methods like Kaplan-Meier and logspline estimators have limitations in certain scenarios.

Purpose of the Study:

• To develop a smoothed survival function for accurate survival probability estimation with censored data.
• To evaluate the performance of the proposed method against established techniques.
• To extend the method for handling covariates and left censoring.

Main Methods:

• Utilizing natural cubic splines on the cumulative hazard function under constraints.
• Formulating the estimation problem as a restricted least squares problem, leading to convex optimization.
• Comparing the proposed approach with Kaplan-Meier and logspline estimators via simulations.

Main Results:

• The proposed smoothed survival function provides a viable alternative for survival probability estimation.
• The method demonstrates competitive performance in simulations compared to existing estimators.
• The approach is adaptable for survival analysis with covariates under the proportional hazards model and for left-censored data.

Conclusions:

• The smoothed survival function offers a robust and extendable method for survival analysis.
• The technique simplifies complex estimation problems into convex optimization.
• The approach shows promise for broader applications in biostatistics and related fields.