Related Experiment Video
Updated: May 22, 2026
05:37
An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Residual-Based Sieve Maximum Full Likelihood Estimation for the Proportional Hazards Model
Taehwa Choi1,2, 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.
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.
Related Concept Videos
01:11Hazard Rate
The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
01:24Kaplan-Meier Approach
The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
01:14Parametric Survival Analysis: Weibull and Exponential Methods
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
01:15Assumptions of Survival Analysis
Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
01:18Introduction To Survival Analysis
Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
The primary goal of survival analysis is to estimate survival time—the time until a...
The primary goal of survival analysis is to estimate survival time—the time until a...
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...