Bahadur-kiefer theorems for kernel smooth product-limit quantile estimator

1995 ◽  
Vol 24 (11) ◽  
pp. 2815-2828
Author(s):  
Zhou Yong
Keyword(s):  
Kernel Smooth ◽  
Product Limit

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov
Keyword(s):  
Relative Risk ◽  
Sample Size ◽  
Censored Data ◽  
Survival Function ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

scholarly journals Prognostic Autophagy-Related Genes of Gastric Cancer Patients on Chemotherapy

2021 ◽  
Author(s):  
xiaolong Liu ◽  
Zhen Ma ◽  
Lei Zhang ◽  
Yang Yu ◽  
Maswikiti Ewetse Paul ◽  
...  
Keyword(s):  
Gastric Cancer ◽  
Regression Models ◽  
Risk Group ◽  
Chemotherapy Resistance ◽  
Estimation Method ◽  
High Risk Group ◽  
Chemotherapy Administration ◽  
Clinical Complications ◽  
Product Limit ◽  
Gastric Cancer Patients

Abstract Background Gastric cancer(GC) treated with fluorouracil and cisplatin can cause chemotherapy resistance, which is one of the most common postoperative clinical complications and leads to in poor prognosis. Methods The purpose of this study is to investigate the susceptibility of patients with GC after postoperative chemotherapy based on autophagy-related genes (ATGs). Under the background of TCGA database, for patients with GC undergoing and during chemotherapy,gene expression data was integrated and analyzed. Prognostic genes were screened based on univariate and various analysis regression models. Subjects were divided into two groups: high-risk group and low-risk group. Univariate and various analytical regression models were used to screen for prognostic genes. Median risk score was used for analysis. OS and DFS were evaluated by the product limit estimation method. Subject curve analysis is used to determine the accuracy of the forecast. We also have performed appropriate analysis and conducted some detailed assessments in our work. The differential expression of ATGs was mainly associated with chemotherapy resistance.Results After chemotherapy administration, we have screened 9 ATGs outcomes in the subjects and DFS and OS were precisely predicted by the model of GEO and TCGA databases.Conclusions 9 genes were established as prognostic markers to predict the relationship between ATGs and GC chemotherapy susceptibility, suggesting a better individualized treatment in clinical practice.

scholarly journals Radiation dose-response (a Bayesian model) in the radiotherapy of the localized prostatic adenocarcinoma: the reliability of PSA slope changes as a response surrogate endpoint

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e7172
Author(s):  
Reza Ali Mohammadpour ◽  
Jamshid Yazdani- Charati ◽  
SZahra Faghani ◽  
Ahad Alizadeh ◽  
Mohammadreza Barzegartahamtan
Keyword(s):  
Radiation Dose ◽  
Dose Response ◽  
Specific Antigen ◽  
Surrogate Endpoint ◽  
Assessment System ◽  
T Stage ◽  
Kaplan Meier ◽  
Total Radiation Dose ◽  
Product Limit ◽  
The Relationship

Purpose One of the characteristics of Prostate-Specific Antigen (PSA) is PSA slope. It is the rate of diminishing PSA marker over time after radiotherapy (RT) in prostate cancer (PC) patients. The purpose of this study was to evaluate the relationship between increasing RT doses and PSA slope as a potential surrogate for PC recurrence. Patients and Methods This retrospective study was conducted on PC patients who were treated by radiotherapy in the Cancer Institute of Iran during 2007–2012. By reviewing the records of these patients, the baseline PSA measurement before treatment (iPSA), Gleason score (GS), clinical T stage (T. stage), and periodic PSA measurements after RT and the total radiation dose received were extracted for each patient separately. We used a Bayesian dose-response model, analysis of variance, Kruskal–Wallis test, Kaplan–Meier product-limit method for analysis. Probability values less 0.05 were considered statistically significant. Results Based on the D’Amico risk assessment system, 13.34% of patients were classified as “Low Risk”, 51.79% were “Intermediate Risk”, and 34.87% were “High Risk”. In terms of radiation doses, 12.31% of the patients received fewer than 50 Gy, 15.38% received 50 to 69 Gy, 61.03% received 70 Gy, and 11.28% received more than 70 Gy. The PSA values decreased after RT for all dose levels. The slope of PSA changes was negative for 176 of 195 patients. By increasing the dosage of radiation, the PSA decreased but these changes were not statistically significant (p = 0.701) and PSA slope as a surrogate end point cannot met the Prentice’s criteria for PC recurrence. Conclusion Significant changes in the dose-response relationship were not observed when the PSA slope was considered as the response criterion. Therefore, although the absolute value of the PSA decreased with increasing doses of RT, the relationship between PSA slope changes and increasing doses was not clear and cannot be used as a reliable response surrogate endpoint.

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