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An R-Based Landscape Validation of a Competing Risk Model

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Residual-Based Sieve Maximum Full Likelihood Estimation for the Proportional Hazards Model.

Taehwa Choi^1,2, Susan Halabi¹, Hyotae Kim¹

¹Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA.

Communications in Statistics: Theory and Methods

|May 21, 2026

Summary

A new sieve maximum full likelihood method improves proportional hazards model estimation. This robust approach enhances accuracy, especially with outliers or high censoring, outperforming standard partial likelihood methods.

Keywords:

Deviance full likelihood profile likelihood proportional hazards score residual sieve estimation survival analysis variance estimation

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Area of Science:

Biostatistics
Survival Analysis
Statistical Modeling

Background:

Partial likelihood is standard for proportional hazards models but lacks robustness.
Issues arise with model mis-specification, outliers, or high censoring rates.

Purpose of the Study:

Propose a sieve maximum full likelihood estimation method for proportional hazards models.
Enhance robustness and efficiency compared to partial likelihood methods.

Main Methods:

Approximate cumulative hazard function using piecewise polynomials in a two-step procedure.
Utilize full likelihood for simultaneous parameter estimation.
Employ profile likelihood for variance estimation and an information criterion for sieve space selection.

Main Results:

Simulations show superior performance over partial and existing full likelihood methods.
Demonstrated effectiveness in both proportional and non-proportional hazards settings.
Successful application in real-world bladder and breast cancer data.

Conclusions:

The proposed sieve maximum full likelihood method offers a flexible and robust alternative for survival analysis.
This approach is particularly beneficial when standard methods fail due to outliers or assumption violations.