Small sample confidence intervals for survival functions under the proportional hazards model

2017 ◽  
Vol 47 (24) ◽  
pp. 6108-6124
Author(s):  
Robert L. Paige ◽  
Emad Abdurasul
Keyword(s):  
Confidence Intervals ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Small Sample ◽  
Survival Functions ◽  
Hazards Model

scholarly journals An Inference-based Prognostic Framework for Health Management of Automotive Systems

2020 ◽  
Vol 7 (2) ◽  
Author(s):  
Chaitanya Sankavaram ◽  
Anuradha Kodali ◽  
Krishna Pattipati ◽  
Satnam Singh ◽  
Yilu Zhang ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Failure Time ◽  
Remaining Useful Life ◽  
Survival Functions ◽  
Time Data ◽  
Automotive Systems ◽  
Multiple Fault Diagnosis ◽  
Hazards Model ◽  
Useful Life

This paper presents a unified data-driven prognostic framework that combines failure time data, static parameter data and dynamic time-series data. The framework employs proportional hazards model and a soft dynamic multiple fault diagnosis algorithm for inferring the degraded state trajectories of components and to estimate their remaining useful life times. The framework takes into account the cross-subsystem fault propagation, a case prevalent in any networked and embedded system. The key idea is to use Cox proportional hazards model to estimate the survival functions of error codes and symptoms (probabilistic test outcomes/prognostic indicators) from failure time data and static parameter data, and use them to infer the survival functions of components via soft dynamic multiple fault diagnosis algorithm. The average remaining useful life and its higher-order central moments (e.g., variance, skewness, kurtosis) can be estimated from these component survival functions. The framework is demonstrated on datasets derived from two automotive systems, namely hybrid electric vehicle regenerative braking system, and an electronic throttle control subsystem simulator. Although the proposed framework is validated on automotive systems, it has the potential to be applicable to a wide variety of systems, ranging from aerospace systems to buildings to power grids.

scholarly journals Integrating multi-omics data with deep learning for predicting cancer prognosis

2019 ◽  
Author(s):  
Hua Chai ◽  
Xiang Zhou ◽  
Zifeng Cui ◽  
Jiahua Rao ◽  
Zheng Hu ◽  
...  
Keyword(s):  
Deep Learning ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Small Sample ◽  
The Cancer Genome Atlas ◽  
Cancer Prognosis ◽  
Omics Data ◽  
Hazards Model ◽  
Small Sample Sizes ◽  
The Impact

AbstractMotivationAccurately predicting cancer prognosis is necessary to choose precise strategies of treatment for patients. One of effective approaches in the prediction is the integration of multi-omics data, which reduces the impact of noise within single omics data. However, integrating multi-omics data brings large number of redundant variables and relative small sample sizes. In this study, we employed Autoencoder networks to extract important features that were then input to the proportional hazards model to predict the cancer prognosis.ResultsThe method was applied to 12 common cancers from the Cancer Genome Atlas. The results show that the multi-omics averagely improves 4.1% C-index for prognosis prediction over single mRNA data, and our method outperforms previous approaches by at least 7.4%. A comparison of the contribution of single omics data show that mRNA contributes the most, followed by the DNA methylation, miRNA, and the copy number variation. In the case study for differential gene expression analysis, we identified 161 differentially expressed genes in the cervical cancer, among which 77 genes (65.8%) have been proven to be associated with cancer. In addition, we performed the cross-cancer test where the model trained on one cancer was used to predict the prognosis of another cancer, and found 23 pairs of cancers have a C-index larger than 0.5, with the largest value of 0.68. Thus, this study has provided a deep learning framework to effectively integrate multiple omics data to predict cancer prognosis.

scholarly journals Improvement of the accuracy in testing the effect in the cox proportional hazards model using higher order approximations

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5591-5601
Author(s):  
Silvie Bělasková ◽  
Eva Fiserová
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Higher Order ◽  
Cox Proportional Hazards ◽  
Small Sample ◽  
Cox Proportional Hazards Model ◽  
Ratio Test ◽  
Truncated Data ◽  
Hazards Model ◽  
Left Truncated Data

Small-sample properties of the likelihood ratio test, the Wald test and the score test about significance of the effect in the Cox proportional hazards model for the right-censored and left-truncated data are investigated. These are large-sample tests, and, therefore, these are only approximate tests and they do not necessary maintain chosen significance level. Consequently, the p-value can be inaccurate as well. Higher order approximations of the likelihood function based on the Barndorff-Nielsen formula and the Lugannani-Rice formula are used in order to improve the accuracy of statistical inferences. The accuracy of these tests together with proposed approximations are compared by means of simulations under conditions of decreasing the sample size, and increasing proportion of right-censored and left-truncated data in the Cox model with the exponential and the Weibull distribution of the baseline hazard function. The results show that higher order approximations based on the Lugannani-Rice and the Barndorff-Nielsen formulas in combination with the Wald statistic improve the accuracy.

A Note on Standard Errors for Survival Curves in Discrete-Time Survival Analysis

2005 ◽  
Vol 30 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Rebecca Zwick ◽  
Jeffrey C. Sklar
Keyword(s):  
Logistic Regression ◽  
Discrete Time ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Standard Errors ◽  
Survival Functions ◽  
Hazards Model ◽  
Time Period ◽  
Flexible Form ◽  
Ordinary Logistic Regression

Cox (1972) proposed a discrete-time survival model that is somewhat analogous to the proportional hazards model for continuous time. Efron (1988) showed that this model can be estimated using ordinary logistic regression software, and Singer and Willett (1993) provided a detailed illustration of a particularly flexible form of the model that includes one parameter per time period. This work has been expanded to show how logistic regression output can also be used to estimate the standard errors of the survival functions. This is particularly simple under the model described by Singer and Willett, when there are no predictors other than time.

HRA Model for Hypercholesterolemia Based on a Longitudinal Health Database

1998 ◽  
Vol 37 (02) ◽  
pp. 130-133
Author(s):  
T. Kishimoto ◽  
Y. Iida ◽  
K. Yoshida ◽  
M. Miyakawa ◽  
H. Sugimori ◽  
...  
Keyword(s):  
Total Cholesterol ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Model Analysis ◽  
Serum Total Cholesterol ◽  
Hazards Model ◽  
The Mean ◽  
Health Database ◽  
Observation Period

AbstractTo evaluate the risk factors for hypercholesterolemia, we examined 4,371 subjects (3,207 males and 1,164 females) who received medical checkups more than twice at an AMHTS in Tokyo during the period from 1976 through 1991; and whose serum total cholesterol was under 250 mg/dl. The mean follow-up duration was 6.6 years. A self-registering questionnaire was administered at the time of the health checkup. The endpoint of this study was the onset of hypercholesterolemia when the level of serum total cholesterol was 250 mg/dl and over. We compared two prognosis groups (normal and hypercholesterol) in terms of age, examination findings and lifestyle. After assessing each variable, we employed Cox's proportional hazards model analysis to determine the factors related to the occurrence of hypercholesterolemia. According to proportional hazards model analysis, total cholesterol, triglyceride and smoking at the beginning, and hypertension during the observation period were selected in males; and total cholesterol at the beginning and age were selected in females to determine the factors related to the occurrence of hypercholesterolemia.

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