Nonparametric regression models for right-censored data using Bernstein polynomials

2011 ◽  
Author(s):  
Muhtarjan Osman ◽  
Sujit K. Ghosh
Keyword(s):  
Nonparametric Regression ◽  
Censored Data ◽  
Regression Models ◽  
Bernstein Polynomials ◽  
Right Censored Data

scholarly journals The comparison of censored quantile regression methods in prognosis factors of breast cancer survival

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Akram Yazdani ◽  
Mehdi Yaseri ◽  
Shahpar Haghighat ◽  
Ahmad Kaviani ◽  
Hojjat Zeraati
Keyword(s):  
Breast Cancer ◽  
Quantile Regression ◽  
Survival Time ◽  
Censored Data ◽  
Regression Models ◽  
Cancer Survival ◽  
Breast Cancer Survival ◽  
Right Censored Data ◽  
Censored Quantile Regression ◽  
Covariate Effects

AbstractThe Cox proportional hazards model is a widely used statistical method for the censored data that model the hazard rate rather than survival time. To overcome complexity of interpreting hazard ratio, quantile regression was introduced for censored data with more straightforward interpretation. Different methods for analyzing censored data using quantile regression model, have been introduced. The quantile regression approach models the quantile function of failure time and investigates the covariate effects in different quantiles. In this model, the covariate effects can be changed for patients with different risk and is a flexible model for controlling the heterogeneity of covariate effects. We illustrated and compared five methods in quantile regression for right censored data included Portnoy, Wang and Wang, Bottai and Zhang, Yang and De Backer methods. The comparison was made through the use of these methods in modeling the survival time of breast cancer. According to the results of quantile regression models, tumor grade and stage of the disease were identified as significant factors affecting 20th percentile of survival time. In Bottai and Zhang method, 20th percentile of survival time for a case with higher unit of stage decreased about 14 months and 20th percentile of survival time for a case with higher grade decreased about 13 months. The quantile regression models acted the same to determine prognostic factors of breast cancer survival in most of the time. The estimated coefficients of five methods were close to each other for quantiles lower than 0.1 and they were different from quantiles upper than 0.1.

scholarly journals A-Spline Regression for Fitting a Nonparametric Regression Function with Censored Data

Stats ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 120-136
Author(s):  
Ersin Yılmaz ◽  
Syed Ejaz Ahmed ◽  
Dursun Aydın
Keyword(s):  
Nonparametric Regression ◽  
Censored Data ◽  
Kernel Smoothing ◽  
Synthetic Data ◽  
Regression Function ◽  
Data Transformation ◽  
Smoothing Splines ◽  
Spline Regression ◽  
Real World Data ◽  
Right Censored Data

This paper aims to solve the problem of fitting a nonparametric regression function with right-censored data. In general, issues of censorship in the response variable are solved by synthetic data transformation based on the Kaplan–Meier estimator in the literature. In the context of synthetic data, there have been different studies on the estimation of right-censored nonparametric regression models based on smoothing splines, regression splines, kernel smoothing, local polynomials, and so on. It should be emphasized that synthetic data transformation manipulates the observations because it assigns zero values to censored data points and increases the size of the observations. Thus, an irregularly distributed dataset is obtained. We claim that adaptive spline (A-spline) regression has the potential to deal with this irregular dataset more easily than the smoothing techniques mentioned here, due to the freedom to determine the degree of the spline, as well as the number and location of the knots. The theoretical properties of A-splines with synthetic data are detailed in this paper. Additionally, we support our claim with numerical studies, including a simulation study and a real-world data example.

scholarly journals Weighted expectile regression for right‐censored data

2021 ◽  
Author(s):  
Alexander Seipp ◽  
Verena Uslar ◽  
Dirk Weyhe ◽  
Antje Timmer ◽  
Fabian Otto‐Sobotka
Keyword(s):  
Censored Data ◽  
Right Censored Data ◽  
Expectile Regression
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