Related Experiment Video
Updated: Jan 22, 2026
04:57
Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
10.8K
Stein-type shrinkage estimators in gamma regression model with application to prostate cancer data
Saumen Mandal1, Reza Arabi Belaghi2, Akram Mahmoudi2
1Department of Statistics, University of Manitoba, Winnipeg, Canada.
Statistics in Medicine
|July 19, 2019
Summary
New Stein-type shrinkage estimators (SEs) improve coefficient estimation in gamma regression, outperforming maximum likelihood (ML) estimators. These advancements are validated through simulations and applied to prostate cancer data analysis.
Area of Science:
- Statistics
- Biostatistics
- Survival Analysis
Background:
- Gamma regression is widely used in diverse fields including life testing, cancer incidence forecasting, genomics, and quality control.
- Gamma regression models are essential for survival analysis, accommodating monotone and non-constant hazard rates.
Purpose of the Study:
- To propose novel and improved methods for estimating coefficients in gamma regression models.
- To introduce Stein-type shrinkage estimators (SEs) by combining unrestricted maximum likelihood (ML) and restricted estimators.
Main Methods:
- Development of an asymptotic theory for the proposed Stein-type shrinkage estimators (SEs).
- Conducting Monte Carlo simulations to evaluate the performance and relative efficiencies of the estimators.
- Application and appraisal of the developed estimators using real-world prostate cancer data.
Main Results:
- The proposed Stein-type shrinkage estimators (SEs) demonstrate superior performance compared to standard maximum likelihood (ML) estimators.
- Asymptotic quadratic risks for the SEs were derived and analyzed.
- Simulation studies confirmed the enhanced efficiency of the SEs.
Conclusions:
- The novel Stein-type shrinkage estimators offer a significant improvement for gamma regression coefficient estimation.
- The findings are supported by theoretical derivations, simulation results, and a practical application to prostate cancer data.
Related Concept Videos
01:52Regression Toward the Mean
6.9K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.9K
01:19Data: Types and Distribution
1.5K
In biostatistics, data are the observations collected for analysis. There are two main types: parametric and non-parametric. Parametric data, which include continuous (e.g., weight) and discrete numerical data (e.g., number of tablets), assume a particular distribution pattern, often the normal distribution. Non-parametric data do not adhere to a specific distribution and typically comprise nominal (e.g., gender) and ordinal categorical data (e.g., pain scale ratings).
Distributions in...
Distributions in...
1.5K
01:27Shrinkage in Concrete
380
Shrinkage in concrete is primarily due to water loss from evaporation, hydration of cement, or carbonation, leading to a reduction in volume. The volumetric contraction results in volumetric strain in concrete. However, in practice, shrinkage is measured as linear strain, which is one-third of the volumetric strain.
When concrete is still in its plastic state, it can undergo a decrease in volume by about 1% of its absolute volume. This decrease is known as plastic shrinkage. It arises either...
When concrete is still in its plastic state, it can undergo a decrease in volume by about 1% of its absolute volume. This decrease is known as plastic shrinkage. It arises either...
380
01:21Drying Shrinkage
364
When hardened concrete is exposed to air with a relative humidity of less than 100 percent, it begins to lose the free water within its capillaries. As this water evaporates, the water initially adsorbed onto the calcium silicate hydrates migrates towards these now empty spaces and eventually evaporates as well. Over time, as more water leaves, the volume of the concrete decreases, a phenomenon known as drying shrinkage.
A portion of this drying shrinkage can be reversed; if the concrete is...
A portion of this drying shrinkage can be reversed; if the concrete is...
364
01:24Carbonation Shrinkage
451
Atmospheric CO2 penetrates the concrete's pores and, in the presence of moisture, forms carbonic acid, which then reacts with calcium hydroxide in the hydrated cement, forming calcium carbonate. This process reduces the concrete's volume and is termed carbonation shrinkage.
The concrete's permeability is slightly reduced as calcium carbonate produced during the reaction fills its pores. Furthermore, its strength is slightly enhanced as the water released during the reaction...
The concrete's permeability is slightly reduced as calcium carbonate produced during the reaction fills its pores. Furthermore, its strength is slightly enhanced as the water released during the reaction...
451
01:25Multiple Regression
3.8K
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
3.8K