Synthetic data based nonparametric testing of parametric mean-regression models with censored data

2007 ◽  
Author(s):  
Olivier Lopez ◽  
Valentin Patilea
Keyword(s):  
Censored Data ◽  
Regression Models ◽  
Synthetic Data ◽  
Nonparametric Testing

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 New Flexible Regression Models Generated by Gamma Random Variables with Censored Data

2016 ◽  
Vol 5 (3) ◽  
pp. 9 ◽  
Author(s):  
Elizabeth M. Hashimoto ◽  
Gauss M. Cordeiro ◽  
Edwin M.M. Ortega ◽  
G.G. Hamedani
Keyword(s):  
Regression Model ◽  
Censored Data ◽  
Survival Data ◽  
Regression Models ◽  
Empirical Distribution ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Standard Normal Distribution ◽  
Model Parameters ◽  
Linear Regression Models

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models. 

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