A maximum likelihood training approach to irrelevant variability compensation based on piecewise linear transformations

2006 ◽  
Author(s):  
Qiang Huo ◽  
Donglai Zhu
Keyword(s):  
Maximum Likelihood ◽  
Piecewise Linear ◽  
Linear Transformations ◽  
Training Approach ◽  
Variability Compensation

scholarly journals Interconversion of Plasma Free Thyroxine Values from Assay Platforms with Different Reference Intervals Using Linear Transformation Methods

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 45
Author(s):  
Fanwen Meng ◽  
Jacqueline Jonklaas ◽  
Melvin Khee-Shing Leow
Keyword(s):  
Linear Transformation ◽  
Piecewise Linear ◽  
Equilibrium Dialysis ◽  
Accurate Method ◽  
Reference Intervals ◽  
Thyroid Stimulating Hormone ◽  
Free Thyroxine ◽  
Thyroid Function Tests ◽  
Linear Transformations ◽  
Transformation Methods

Clinicians often encounter thyroid function tests (TFT) comprising serum/plasma free thyroxine (FT4) and thyroid stimulating hormone (TSH) measured using different assay platforms during the course of follow-up evaluations which complicates reliable comparison and interpretation of TFT changes. Although interconversion between concentration units is straightforward, the validity of interconversion of FT4/TSH values from one assay platform to another with different reference intervals remains questionable. This study aims to establish an accurate and reliable methodology of interconverting FT4 by any laboratory to an equivalent FT4 value scaled to a reference range of interest via linear transformation methods. As a proof-of-concept, FT4 was simultaneously assayed by direct analog immunoassay, tandem mass spectrometry and equilibrium dialysis. Both linear and piecewise linear transformations proved relatively accurate for FT4 inter-scale conversion. Linear transformation performs better when FT4 are converted from a more accurate to a less accurate assay platform. The converse is true, whereby piecewise linear transformation is superior to linear transformation when converting values from a less accurate method to a more robust assay platform. Such transformations can potentially apply to other biochemical analytes scale conversions, including TSH. This aids interpretation of TFT trends while monitoring the treatment of patients with thyroid disorders.

A free group of piecewise linear transformations

2011 ◽  
Vol 125 (2) ◽  
pp. 141-146
Author(s):  
Grzegorz Tomkowicz
Keyword(s):  
Free Group ◽  
Piecewise Linear ◽  
Linear Transformations

Induction of Similarity Measures and Medical Diagnosis Support Rules through Separable, Linear Data Transformations

2006 ◽  
Vol 45 (02) ◽  
pp. 200-203 ◽  
Author(s):  
L. Bobrowski
Keyword(s):  
Medical Diagnosis ◽  
Euclidean Distance ◽  
Piecewise Linear ◽  
Similarity Measures ◽  
Case Based Reasoning ◽  
Data Sets ◽  
Linear Transformations ◽  
Data Transformations ◽  
Criterion Functions ◽  
Learning Data

Summary Objectives: To improve the medical diagnosis support rules based on comparisons of diagnosed patients with similar cases (precedents) archived in a clinical database. The case-based reasoning (CBR) or the nearest neighbors (K-NN) classifications, which operate on referencing (learning) data sets, belong to this scheme. Methods: Inducing similarity measure through special linear transformations of the referencing sets aimed at the best separation of these sets. Designing separable transformations can be based on dipolar models and minimization of the convex and piecewise linear (CPL) criterion functions in accordance with the basis exchange algorithm. Results: Separable linear transformations allow for some data sets to decrease the error rate of the K-NNclassification rule based on the Euclidean distance. Such results can be seen on the example of data sets taken from the Heparsystem of diagnosis support. Conclusions: Medical diagnosis support based on the CBRor the K-NNrules can be improved through separable transformations of the referencing sets.

Statistical Analyses of Monozygotic and Dizygotic Twinning Rates

2013 ◽  
Vol 16 (6) ◽  
pp. 1107-1111 ◽  
Author(s):  
Johan Fellman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Parameter Estimates ◽  
Published Data ◽  
Same Sex ◽  
Linear Transformations ◽  
French Mathematician ◽  
Male Birth ◽  
Asymptotically Normal ◽  
Opposite Sex

The French mathematician Bertillon reasoned that the number of dizygotic (DZ) pairs would equal twice the number of twin pairs of unlike sexes. The remaining twin pairs in a sample would presumably be monozygotic (MZ). Weinberg restated this idea and the calculation has come to be known as Weinberg's differential rule (WDR). The keystone of WDR is that DZ twin pairs should be equally likely to be of the same or the opposite sex. Although the probability of a male birth is greater than .5, the reliability of WDR's assumptions has never been conclusively verified or rejected. Let the probability for an opposite-sex (OS) twin maternity be pO, for a same-sex (SS) twin maternity pS and, consequently, the probability for other maternities 1 − pS − pO. The parameter estimates $\hat p_O$ and $\hat p_S$ are relative frequencies. Applying WDR, the MZ rate is m = pS − pO and the DZ rate is d = 2pO, but the estimates $\hat m$ and $\hat d$ are not relative frequencies. The maximum likelihood estimators $\hat p_S$ and $\hat p_O$ are unbiased, efficient, and asymptotically normal. The linear transformations $\hat m = \hat p_S - \hat p_O$ and ${\skew6\hat d} = 2\hat p_O$ are efficient and asymptotically normal. If WDR holds they are also unbiased. For the tests of a set of m and d rates, contingency tables cannot be used. Alternative tests are presented and the models are applied on published data.

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