Detecting proportional and constant bias in method comparison studies by using linear regression with errors in both axes

Martı́nez, Àngel; Río, F. Javier del; Riu, Jordi; Rius, F. Xavier

doi:10.1016/s0169-7439(99)00036-2

Cited by 28 publications

(21 citation statements)

References 16 publications

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“…A proportional bias of the measurement method existed if the estimated slope was significantly different from 1. Equivalence between the two measurement methods was tested by using the bivariate least square (BLS) regression [17]. Cyst volumes estimated manually and semiautomatically were plotted after being transformed into logarithms as a large range of volumes were present (Fig.…”

Section: Discussionmentioning

confidence: 99%

Measurement of bone cyst fluid volume using k-means clustering

Docquier

Laurent

Menten

et al. 2009

Magnetic Resonance Imaging

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Section: Discussionmentioning

confidence: 99%

Measurement of bone cyst fluid volume using k-means clustering

Docquier

Laurent

Menten

et al. 2009

Magnetic Resonance Imaging

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“…The linear relation of this dataset was studied by Martinez et al [21] and del Río et al [22] for different purposes, such as prediction. Here we are interested in establishing the confidence sets.…”

Section: And 5 Below Cwmentioning

confidence: 99%

On interval estimation in linear relationships with heteroscedastic measurement errors in both axes

Cheng

Tsai

2015

Chemometrics and Intelligent Laboratory Systems

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“…It is stated that if the errors in x i are greater than one-tenth of the errors in y i , then the overall error is significantly increased. Moreover, the regression parameters and their confidence intervals are then biased using (ordinary) weighted least squares [25]. …”

Section: Theoretical Backgroundmentioning

confidence: 99%

A New Approach in Regression Analysis for Modeling Adsorption Isotherms

Marković

Lekić

Rajaković-Ognjanović

et al. 2014

The Scientific World Journal

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Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart's percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.

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Detecting proportional and constant bias in method comparison studies by using linear regression with errors in both axes

Cited by 28 publications

References 16 publications

Measurement of bone cyst fluid volume using k-means clustering

Measurement of bone cyst fluid volume using k-means clustering

On interval estimation in linear relationships with heteroscedastic measurement errors in both axes

A New Approach in Regression Analysis for Modeling Adsorption Isotherms

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