Stochastic relaxation for building some classes of piecewise linear regression functions

2000 ◽  
Vol 6 (2) ◽  
Author(s):  
B.A. Zalesky
Keyword(s):  
Linear Regression ◽  
Piecewise Linear ◽  
Piecewise Linear Regression ◽  
Regression Functions ◽  
Stochastic Relaxation

Fitting piecewise linear regression functions to biological responses

1989 ◽  
Vol 67 (1) ◽  
pp. 390-396 ◽  
Author(s):  
E. Vieth
Keyword(s):  
Linear Regression ◽  
Piecewise Linear ◽  
Regression Line ◽  
Regression Function ◽  
Linear Functions ◽  
Separation Point ◽  
Piecewise Linear Regression ◽  
Biological Variables ◽  
Biological Responses ◽  
Regression Functions

An iterative approach was achieved for fitting piecewise linear functions to nonrectilinear responses of biological variables. This algorithm is used to estimate the parameters of the two (or more) regression functions and the separation point(s) (thresholds, sensitivities) by statistical approximation. Although it is often unknown whether the response of a biological variable is adequately described by one rectilinear regression function or by piecewise linear regression function(s) with separation point(s), an F test is proposed to determine whether one regression line is the optimal fitted function. A FORTRAN-77 program has been developed for estimating the optimal parameters and the coordinates of the separation point(s). A few sets of data illustrating this kind of problem in the analysis of thermoregulation, osmoregulation, and the neuronal responses are discussed.

Identifying changes in trends in the age standardized incidence of melanoma in Australia

2019 ◽  
Vol 3 (4) ◽  
pp. 250-252 ◽  
Author(s):  
David M Hille
Keyword(s):  
Public Health ◽  
Linear Regression ◽  
Iterative Process ◽  
Linear Trend ◽  
Piecewise Linear ◽  
Health Issue ◽  
Public Health Issue ◽  
Piecewise Linear Regression ◽  
Significant Public Health ◽  
Males And Females

ObjectiveTo identify changes in the linear trend of the age-standardized incidence of melanoma in Australia for all persons, males, and females. MethodsA two-piece piecewise linear regression was fitted to the data. The piecewise breakpoint varied through an iterative process to determine the model that best fits the data.ResultsStatistically significant changes in the trendof the age-standardized incidence of melanoma in Australia were found for all persons, males, and females. The optimal breakpoint for all persons and males was at 1998. For females, the optimal breakpoint was at 2005. The trend after these breakpoints was flatter than prior to the breakpoints, but still positive.ConclusionMelanoma is a significant public health issue in Australia. Overall incidence continues to increase. However, the rate at which the incidence is increasing appears to be decreasing.

U-Shaped Association Between the Triglycerides-Glucose index and the Risk of Incident Diabetes in Apparently Healthy Population: A Population-based Cohort Study

2020 ◽  
Author(s):  
Xiuping Xuan ◽  
Masahide Hamaguchi ◽  
Qiuli Cao ◽  
Okamura Takuro ◽  
Yoshitaka Hashimoto ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Piecewise Linear ◽  
Incident Diabetes ◽  
Smoothing Function ◽  
Healthy Population ◽  
Piecewise Linear Regression ◽  
Tyg Index ◽  
Apparently Healthy

Abstract Background Although the triglycerides-glucose (TyG) index was thought to be a practical predictor of incident diabetes, the association between them has not been well characterized. The study aimed to further examine the association between the TyG index and incident diabetes in Japanese adults. Methods The cases were extracted of the individual participating in the NAGALA (NAfld in the Gifu Area, Longitudinal Analysis) study at Murakami Memorial Hospital from 2004 to 2015, and 14297individuals apparently healthy at baseline were included in the study. Cox proportional hazards models were used to evaluate the associations between baseline TyG levels and incident of T2DM, and a two-piecewise linear regression model was use to examine the threshold effect of the baseline TyG on incident diabetes using a smoothing function. The threshold level (i.e., turning point) was determined using trial and error. A log likelihood ratio test was also conducted to compare the one-line linear regression model with a two-piecewise linear model. Results During a median follow-up period of 5.26 (women) and 5.88 (men) years, 47 women and 182 men developed Type 2 diabetes. The risk of diabetes was strongly associated with the baseline TyG index in the fully adjusted model in men but not in women, and no dose-dependent positive relationship between incident diabetes and TyG was observed across TyG tertiles. Intriguingly, two-piecewise linear regression analysis showed a U-shaped association between the TyG index and incident T2DM. The risk of incident diabetes decreased by around 90% in women with TyG < 7.27 (HR: 0.09; P = 0.0435) and 80% in men with TyG < 7.97 (HR 0.21, P = 0.002) with each increment of the TyG index after adjusting for confounders. In contrast, the risk of incident T2DM significantly elevated with the increase in TyG index in men with TyG > 7.97 (HR: 2.42, P < 0.001) and women with TyG > 7.29 (HR 2.76, P = 0.0166). Conclusions A U-shaped association was observed between the TyG index and incident T2DM among healthy individuals, with the TyG threshold of 7.97 in men and 7.27 in women. This information may be useful for reducing incident diabetes by maintaining the TyG index near these thresholds.

scholarly journals Piecewise Linear Regression Based on Plane Clustering

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 29845-29855 ◽  
Author(s):  
Xubing Yang ◽  
Hongxin Yang ◽  
Fuquan Zhang ◽  
Li Zhang ◽  
Xijian Fan ◽  
...  
Keyword(s):  
Linear Regression ◽  
Piecewise Linear ◽  
Piecewise Linear Regression

scholarly journals Network-based piecewise linear regression for QSAR modelling

2019 ◽  
Vol 33 (9) ◽  
pp. 831-844
Author(s):  
Jonathan Cardoso-Silva ◽  
Lazaros G. Papageorgiou ◽  
Sophia Tsoka
Keyword(s):  
Virtual Screening ◽  
Linear Regression ◽  
Predictive Accuracy ◽  
Piecewise Linear ◽  
Chemical Properties ◽  
Structural Similarity ◽  
Quantitative Structure Activity Relationship ◽  
Support Vector ◽  
Piecewise Linear Regression ◽  
Qsar Models

Abstract Quantitative Structure-Activity Relationship (QSAR) models are critical in various areas of drug discovery, for example in lead optimisation and virtual screening. Recently, the need for models that are not only predictive but also interpretable has been highlighted. In this paper, a new methodology is proposed to build interpretable QSAR models by combining elements of network analysis and piecewise linear regression. The algorithm presented, modSAR, splits data using a two-step procedure. First, compounds associated with a common target are represented as a network in terms of their structural similarity, revealing modules of similar chemical properties. Second, each module is subdivided into subsets (regions), each of which is modelled by an independent linear equation. Comparative analysis of QSAR models across five data sets of protein inhibitors obtained from ChEMBL is reported and it is shown that modSAR offers similar predictive accuracy to popular algorithms, such as Random Forest and Support Vector Machine. Moreover, we show that models built by modSAR are interpretatable, capable of evaluating the applicability domain of the compounds and serve well tasks such as virtual screening and the development of new drug leads.

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