scholarly journals Unified Least Squares Methods for the Evaluation of Diagnostic Tests With the Gold Standard

2017 ◽  
Vol 16 ◽  
pp. 117693511668606 ◽  
Author(s):  
Liansheng Larry Tang ◽  
Ao Yuan ◽  
John Collins ◽  
Xuan Che ◽  
Leighton Chan
Keyword(s):  
Least Squares ◽  
Diagnostic Tests ◽  
Ordinal Data ◽  
Least Squares Method ◽  
Test Results ◽  
Finite Sample ◽  
Monotonic Transformation ◽  
Model Framework ◽  
Response Variable ◽  
Continuous Test

The article proposes a unified least squares method to estimate the receiver operating characteristic (ROC) parameters for continuous and ordinal diagnostic tests, such as cancer biomarkers. The method is based on a linear model framework using the empirically estimated sensitivities and specificities as input “data.” It gives consistent estimates for regression and accuracy parameters when the underlying continuous test results are normally distributed after some monotonic transformation. The key difference between the proposed method and the method of Tang and Zhou lies in the response variable. The response variable in the latter is transformed empirical ROC curves at different thresholds. It takes on many values for continuous test results, but few values for ordinal test results. The limited number of values for the response variable makes it impractical for ordinal data. However, the response variable in the proposed method takes on many more distinct values so that the method yields valid estimates for ordinal data. Extensive simulation studies are conducted to investigate and compare the finite sample performance of the proposed method with an existing method, and the method is then used to analyze 2 real cancer diagnostic example as an illustration.

Value Prediction of Design Parameters Based on Weighting Least Squares

2014 ◽  
Vol 909 ◽  
pp. 379-385 ◽  
Author(s):  
Sheng Li ◽  
Hong Sheng Jia
Keyword(s):  
Least Squares ◽  
Design Parameter ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Design Parameters ◽  
Test Results ◽  
Original Design ◽  
Unknown Parameters ◽  
Value Prediction ◽  
Weighted Least Squares Method

Parametric equipments or standard parts usually have many different types of original design parameters. So when designing some new specifications, it requires a lot of estimation or trial and error to determine the value trends and intervals of other unknown design parameters. Based on a finite number of historical examples of design parameter groups, the paper gives an algorithm to fit value trend line using multivariate linear weighted least squares method, whose weights are designed by using distance-proximity coefficient and correlation coefficient. The algorithm uses a small amount of new design parameters, fits value trend lines of other unknown parameters, predicts all other design parameters, finally makes up a design parameter group for a new specification. Two test results of standard parts from home and abroad show that, the accuracy of value prediction is able to meet the requirements of engineering applications.

Software Processing of the Test Results of Building Materials

2019 ◽  
Vol 828 ◽  
pp. 121-128 ◽  
Author(s):  
Narine Pirumyan ◽  
Mihran Stakyan ◽  
Gagik Galstyan
Keyword(s):  
Least Squares ◽  
Building Materials ◽  
Least Squares Method ◽  
Test Results ◽  
Technological Parameters ◽  
Physicomechanical Characteristics ◽  
Functional Connections ◽  
Functional Relationships ◽  
Processing Data

A method for processing data from tests of building materials is proposed in order to identify the optimal functional relationships between the physicomechanical characteristics and the technological parameters of building materials. The least squares method (MLS) was used and to improve the accuracy of calculations, a three-level optimization of calculations was introduced using groups of transforming functions (180 items). Taking into account the increased volume of statistical computations, computer subroutines have been developed, which, together with standard MLS computational programs, make it possible to realize the choice of the indicated optimal functional connections.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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