Polynomial regression with heteroscedastic measurement errors in both axes: Estimation and hypothesis testing

2018 ◽  
Vol 28 (9) ◽  
pp. 2681-2696
Author(s):  
Chi-Lun Cheng ◽  
Jia-Ren Tsai ◽  
Hans Schneeweiss
Keyword(s):  
Hypothesis Testing ◽  
Simulation Study ◽  
Measurement Errors ◽  
Polynomial Regression ◽  
Least Squares Method ◽  
Structural Models ◽  
Point Estimation ◽  
Equation Error ◽  
Adjusted Least Squares ◽  
Polynomial Regression Model

This article investigates point estimation and hypothesis testing in a polynomial regression model with heteroscedastic measurement errors present in both response and regressor variables. For point estimation, the adjusted least squares method and its modifications are developed. These methods can treat both functional and structural models, and models with or without an equation error. For hypothesis testing, the Wald-type and score-type tests are discussed. Their performance is investigated in a simulation study. Applications of these methods are also illustrated with real datasets.

scholarly journals Fetal Biparietal Diameter and Abdominal Circumference Ratio in Bangladesh

1970 ◽  
Vol 39 (1) ◽  
pp. 24-27
Author(s):  
Sabrina Q Rashid
Keyword(s):  
Polynomial Regression ◽  
Cross Sectional Study ◽  
Abdominal Circumference ◽  
Accurate Assessment ◽  
Sectional Study ◽  
Cross Sectional ◽  
Biparietal Diameter ◽  
First Time ◽  
Polynomial Regression Model ◽  
Growth Abnormality

This study was conducted to determine fetal biparietal diameter and abdominal circumference ratio in Bangladesh. There is still no table of this ratio in our country. A prospective, cross-sectional study was conducted on well dated, singleton fetuses of healthy pregnant women. One table and two graphs were prepared by fitting Polynomial regression model. Percentiles, mean and two standard deviations were derived of the ratio. Fetal charts of the raw data with superimposed fitted curves were constructed. The model showed a good fit to the data of 1223 subjects. It covered 95% of the population and gave 3rd, 10th, 50th, 90th and 97th percentiles. This chart can be useful for accurate assessment of fetal biparietal diameter and abdominal circumference ratio to determine the type of fetal growth abnormality, symmetrical or asymmetrical. This is the first time that this ratio has been studied in Bangladesh. Key words: Biparietal diameter; abdominal circumference. DOI: 10.3329/bmj.v39i1.6229 Bangladesh Medical Journal 2010; 39(1): 24-27

scholarly journals Polynomial Regression Model Analysis of Abdominal Wall Tension and Intra-abdominal Pressure in Critically ill Patients

2021 ◽  
Author(s):  
Hao Tang ◽  
Dongchu Zhao ◽  
Chuan Zhang ◽  
Xiaoying Huang ◽  
Dong Liu ◽  
...  
Keyword(s):  
Risk Factors ◽  
Regression Model ◽  
Critically Ill ◽  
Critically Ill Patients ◽  
Polynomial Regression ◽  
Prognostic Indicators ◽  
Wall Tension ◽  
Abdominal Hypertension ◽  
Abdominal Compliance ◽  
Polynomial Regression Model

Abstract BackgroundAbdominal wall tension (AWT) plays an important role in the pathogenesis of abdominal compliance (AC). This study uses a polynomial regression model to analyze the correlation between intra-vesical pressure(IVP) and AWT in critically ill patients and provides new ideas for the diagnosis and treatment of critically ill patients with intra-abdominal hypertension（IAH）.MethodsA retrospective analysis was conducted in critically ill patients who met the inclusion criteria and were admitted to the Department of intensive care unit of Daping Hospital of Army Medical University from March 14, 2019, to May 23, 2020. According to the IVP on the first day of ICU admission and death within 28 days, the patients were divided into the IAH group (IVP ≥12 mmHg), the non-IAH group, the survival group and the nonsurvival group. The demographic and clinical data, prognostic indicators, AWT and IVP on days 1-7 after entering the ICU, IAH risk factors, and 28-day death risk factors were collected.ResultsA total of 100 patients were enrolled, with an average age of 45.59±11.4 years. There were 55 males (55%), 30 patients from departments of internal medicine (30%), 43 patients from surgery departments (43%), and 27 trauma patients (27%). In the IAH group, there were 50 patients (29 males, 58%), with an average age of 45.28±12.27 years; there were 50 patients (26 males, 52%) in the non-IAH group, with an average age of 45.90±10.58 years. The IVP on the 1st day and the average IVP within 7 days of the IAH group was 18.99（17.52，20.77）mmHg and 19.43（16.87，22.25）mmHg, respectively, which was higher than that of the non-IAH group [ 6.14（3.48，8.70）mmHg, 6.66（2.74，9.08）mmHg], p＜0.001. The AWT on the 1st day and the average AWT within 7 days of the IAH group was 2.89±0.32 N/mm and 2.82±0.46 N/mm, respectively, which was higher than that of the non-IAH group [(2.45±0.29)N/mm,(2.43±0.39)N/mm],p＜0.001.The polynomial regression models showed that the average AWT and IVP on the 1st day and within 7 days were AWTday1 = -2.450×10-3IVP2+9.695×10-2 IVP+2.046，r=0.667（p＜0.0001），and AWTmean = -2.293×10-3IVP2+9.273×10-2 IVP+2.081, respectively. The logistic regression analysis showed that AWTday1 of 2.73-2.97 N/mm increased the patient's 28-day mortality risk (OR: 6.834; 95%: 1.105-42.266, p=0.010).ConclusionsThere is a nonlinear correlation between AWT and IVP in critically ill patients, and a high AWT may indicate poor prognosis.

scholarly journals Forecasting COVID-19 cases in Algeria using logistic growth and polynomial regression models

2021 ◽  
Author(s):  
Mohamed LOUNIS ◽  
Babu Malavika
Keyword(s):  
Regression Model ◽  
Logistic Model ◽  
Polynomial Regression ◽  
Logistic Growth ◽  
The Novel ◽  
Logistic Growth Model ◽  
Polynomial Regression Models ◽  
Using Data ◽  
Novel Coronavirus ◽  
Polynomial Regression Model

Abstract The novel Coronavirus respiratory disease 2019 (COVID-19) is still expanding through the world since it started in Wuhan (China) on December 2019 reporting a number of more than 84.4 millions cases and 1.8 millions deaths on January 3rd 2021.In this work and to forecast the COVID-19 cases in Algeria, we used two models: the logistic growth model and the polynomial regression model using data of COVID-19 cases reported by the Algerian ministry of health from February 25th to December 2nd, 2020. Results showed that the polynomial regression model fitted better the data of COVID-19 in Algeria the Logistic model. The first model estimated the number of cases on January, 19th 2021 at 387673 cases. This model could help the Algerian authorities in the fighting against this disease.

scholarly journals Combining Global Geopotential Models, Digital Elevation Models, and GNSS/Leveling for Precise Local Geoid Determination in Some Mexico Urban Areas: Case Study

2021 ◽  
Vol 10 (12) ◽  
pp. 819
Author(s):  
Norberto Alcantar-Elizondo ◽  
Ramon Victorino Garcia-Lopez ◽  
Xochitl Guadalupe Torres-Carillo ◽  
Guadalupe Esteban Vazquez-Becerra
Keyword(s):  
Regression Model ◽  
Numerical Integration ◽  
Urban Areas ◽  
Polynomial Regression ◽  
Geodetic Network ◽  
Geoid Undulation ◽  
Geopotential Model ◽  
Commission Error ◽  
Standard Deviations ◽  
Polynomial Regression Model

This work shows improvements of geoid undulation values obtained from a high-resolution Global Geopotential Model (GGM), applied to local urban areas. The methodology employed made use of a Residual Terrain Model (RTM) to account for the topographic masses effect on the geoid. This effect was computed applying the spherical tesseroids approach for mass discretization. The required numerical integration was performed by 2-D integration with 1DFFT technique that combines DFT along parallels with direct numerical integration along meridians. In order to eliminate the GGM commission error, independent geoid undulations values obtained from a set of GNSS/leveling stations are employed. A corrector surface from the associated geoid undulation differences at the stations was generated through a polynomial regression model. The corrector surface, in addition to the GGM commission error, also absorbs the GNSS/leveling errors as well as datum inconsistencies and systematic errors of the data. The procedure was applied to five Mexican urban areas that have a geodetic network of GNSS/leveling points, which range from 166 to 811. Two GGM were evaluated: EGM2008 and XGM2019e_2159. EGM2008 was the model that showed relatively better agreement with the GNSS/leveling stations having differences with RMSE values in the range of 8–60 cm and standard deviations of 5–8 cm in four of the networks and 17 cm in one of them. The computed topographic masses contribution to the geoid were relatively small, having standard deviations on the range 1–24 mm. With respect to corrector surface estimations, they turned out to be fairly smooth yielding similar residuals values for two geoid models. This was also the case for the most recent Mexican gravity geoid GGM10. For the three geoid models, the second order polynomial regression model performed slightly better than the first order with differences up to 1 cm. These two models produced geoid correction residuals with a standard deviation in one test area of 14 cm while for the others it was of about 4–7 cm. However, the kriging method that was applied for comparison purposes produced slightly smaller values: 8 cm for one area and 4–6 cm for the others.

scholarly journals Comparison of Statistical Methods for Estimating Continuous Paediatric Reference Intervals: A Simulation Study

2021 ◽  
Author(s):  
Monsurul Hoq ◽  
Susan Donath ◽  
Paul Monagle ◽  
John Carlin
Keyword(s):  
Statistical Methods ◽  
Simulation Study ◽  
Assessment Tool ◽  
Polynomial Regression ◽  
Reference Intervals ◽  
Performance Measure ◽  
Parametric Models ◽  
New Method ◽  
Sample Sizes ◽  
Generalised Additive Model

Abstract Background: Reference intervals (RIs), which are used as an assessment tool in laboratory medicine, change with age for most biomarkers in children. Addressing this, RIs that vary continuously with age have been developed using a range of curve-fitting approaches. The choice of statistical method may be important as different methods may produce substantially different RIs. Hence, we developed a simulation study to investigate the performance of statistical methods for estimating continuous paediatric RIs.Methods: We compared four methods for estimating age-varying RIs. These were Cole’s LMS, the Generalised Additive Model for Location Scale and Shape (GAMLSS), Royston’s method based on fractional polynomials and exponential transformation, and a new method applying quantile regression using power variables in age selected by fractional polynomial regression for the mean. Data were generated using hypothetical true curves based on five biomarkers with varying complexity of association with age, i.e. linear or nonlinear, constant or nonconstant variation across age, and for four sample sizes (100, 200, 400 and 1000). Root mean square error (RMSE) was used as the primary performance measure for comparison. Results: Regression-based parametric methods performed better in most scenarios. Royston’s and the new method performed consistently well in all scenarios for sample sizes of at least 400, while the new method had the smallest average RMSE in scenarios with nonconstant variation across age. Conclusions: We recommend methods based on flexible parametric models for estimating continuous paediatric RIs, irrespective of the complexity of the association between biomarkers and age, for at least 400 samples.

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