Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions

Area of Science:

• Biostatistics
• Survival Analysis
• Nonparametric Statistics

Background:

• Estimating survivor functions with right-censored data is challenging.
• Existing methods lack satisfactory properties for censored data under stochastic ordering constraints.
• Stochastic ordering is a common assumption in comparative survival studies.

Purpose of the Study:

• To develop a novel, pointwise constrained nonparametric maximum likelihood estimator for survivor functions.
• To address limitations of existing methods when dealing with censored data and stochastic ordering.
• To provide an efficient computational method for the proposed estimator.

Main Methods:

• Proposed a pointwise constrained nonparametric maximum likelihood estimator (MLE).
• The estimator is defined by constraints applied only at each specific time point *t*.
• Developed an efficient algorithm for computing the MLE.

Main Results:

• The proposed estimator is nonincreasing in time *t*.
• Consistency and asymptotic distribution of the estimator were established.
• Simulation studies indicated superior small and large sample properties compared to existing estimators.

Conclusions:

• The developed method offers a statistically sound and computationally efficient approach for survival function estimation under stochastic ordering with censored data.
• The estimator demonstrates robust performance, outperforming alternatives in simulations.
• The method is applicable to real-world scenarios, as shown with prostate cancer data.