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Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Regression Toward the Mean01:52

Regression Toward the Mean

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 researchers try to extrapolate results...
Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
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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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Regression calibration with heteroscedastic error variance.

Donna Spiegelman1, Roger Logan, Douglas Grove

  • 1Harvard School of Public Health, USA.

The International Journal of Biostatistics
|August 1, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for covariate measurement error with heteroscedastic variance, finding standard regression calibration often sufficient. The proposed estimator showed minimal differences in real-world data analysis.

Keywords:
heteroscedasticitylogistic regressionmeasurement errorregression calibration

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An R-Based Landscape Validation of a Competing Risk Model
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An R-Based Landscape Validation of a Competing Risk Model

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Covariate measurement error is a common issue in epidemiological studies.
  • Standard regression calibration methods assume homoscedastic measurement error variance.
  • Heteroscedasticity in measurement error variance complicates standard approaches.

Purpose of the Study:

  • To develop and evaluate an estimator for regression coefficients that accounts for heteroscedastic measurement error variance.
  • To compare the performance of the new estimator against standard regression calibration.

Main Methods:

  • Proposed a closed-form estimator for regression coefficients correcting for heteroscedastic covariate measurement error.
  • Utilized validation data with gold standard measurements.
  • Applied the estimator to logistic and Cox proportional hazards models.
  • Illustrated with occupational (ACE study) and nutritional (Nurses' Health Study) epidemiology data.

Main Results:

  • The proposed estimator showed little difference from standard regression calibration in applied datasets, despite moderate heteroscedasticity.
  • Theoretical analysis suggests standard regression calibration is often adequate unless relative risk is large or measurement error is severe.
  • Simulation studies indicated standard regression calibration performed as well as or better than the new estimator.

Conclusions:

  • Standard regression calibration is generally adequate for handling moderate heteroscedasticity in covariate measurement error.
  • The new estimator may offer benefits in specific scenarios, but standard methods are often preferred due to simplicity and performance.
  • For rare diseases, normally distributed errors, or moderate measurement error, standard regression calibration remains the recommended approach.