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Related Concept Videos

Censoring Survival Data01:09

Censoring Survival Data

Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different reasons...
Kaplan-Meier Approach01:24

Kaplan-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,...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Median01:08

Median

Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured by arranging the data elements in an increasing or decreasing order. Since this middle value is not affected by the precise numerical values of the outliers or fluctuations, it is insensitive to them. Hence, in cases where a data set may have outliers or the extreme values are not known, the median is a better measure of the central tendency...
Midrange01:07

Midrange

A somewhat easy to compute quantitative estimate of a data set’s central tendency is its midrange, which is defined as the mean of the minimum and maximum values of an ordered data set.
Simply put, the midrange is half of the data set’s range. Similar to the mean, the midrange is sensitive to the extreme values and hence the prospective outliers. However, unlike the mean, the midrange is not sensitive to all the values of the data set that lie in the middle. Thus, it is prone to outliers and...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...

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Related Experiment Video

Updated: Jun 11, 2026

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
12:18

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment

Published on: January 11, 2020

Sparse Estimation and Inference for Censored Median Regression.

Justin Hall Shows1, Wenbin Lu, Hao Helen Zhang

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA.

Journal of Statistical Planning and Inference
|July 8, 2010
PubMed
Summary

This study introduces a novel sparse estimation method for censored median regression, enhancing analysis of high-dimensional survival data with heteroscedastic variance or outliers. The procedure offers robust and computationally efficient median estimation with proven statistical properties.

Related Experiment Videos

Last Updated: Jun 11, 2026

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
12:18

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment

Published on: January 11, 2020

Area of Science:

  • Biostatistics
  • Statistical modeling
  • Survival analysis

Background:

  • Censored median regression is valuable for complex survival data, particularly with heteroscedastic variance or outliers.
  • High-dimensional survival data analysis presents challenges, necessitating robust and sparse estimation techniques.

Purpose of the Study:

  • To develop a sparse estimation procedure for censored median regression models.
  • To address the needs of high-dimensional survival data analysis with improved robustness and sparsity.

Main Methods:

  • A novel procedure minimizing inverse-censoring-probability weighted least absolute deviation loss.
  • Incorporation of an adaptive LASSO penalty for sparse and robust median estimation.
  • Development of a resampling method for variance estimation of the proposed estimator.

Main Results:

  • The proposed procedure consistently identifies underlying sparse models.
  • The method demonstrates desirable large-sample properties, including root-n consistency and asymptotic normality.
  • The entire solution path is obtained efficiently, indicating computational advantages.

Conclusions:

  • The developed sparse estimation procedure is effective for censored median regression in high-dimensional settings.
  • The method provides a robust, computationally efficient, and statistically sound approach for survival data analysis.
  • The procedure's performance is validated through simulations and real-world applications, including microarray gene expression data.