scholarly journals A scalable discrete-time survival model for neural networks

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e6257 ◽  
Author(s):  
Michael F. Gensheimer ◽  
Balasubramanian Narasimhan
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Survival Data ◽  
Real Data ◽  
Survival Model ◽  
Stochastic Gradient Descent ◽  
Likelihood Method ◽  
Learning Framework ◽  
Censoring Indicator

There is currently great interest in applying neural networks to prediction tasks in medicine. It is important for predictive models to be able to use survival data, where each patient has a known follow-up time and event/censoring indicator. This avoids information loss when training the model and enables generation of predicted survival curves. In this paper, we describe a discrete-time survival model that is designed to be used with neural networks, which we refer to as Nnet-survival. The model is trained with the maximum likelihood method using mini-batch stochastic gradient descent (SGD). The use of SGD enables rapid convergence and application to large datasets that do not fit in memory. The model is flexible, so that the baseline hazard rate and the effect of the input data on hazard probability can vary with follow-up time. It has been implemented in the Keras deep learning framework, and source code for the model and several examples is available online. We demonstrate the performance of the model on both simulated and real data and compare it to existing models Cox-nnet and Deepsurv.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

scholarly journals The One-Parameter Odd Lindley Exponential Model: Mathematical Properties and Applications

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Mustafa Ç. Korkmaz ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Residual Life ◽  
Real Data ◽  
Exponential Model ◽  
Likelihood Method ◽  
Mean Squared Errors ◽  
Mathematical Properties ◽  
Data Application ◽  
The One

AbstractIn this article, an exponential model with only one shape parameter, which can be used in modeling survival data, reliability problems and fatigue life studies, is studied. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. The model parameter is estimated by using the maximum likelihood method. A real data application is given to illustrate the flexibility of the model. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.

Extended exponentiated Nadarajah-Haghighi model: Mathematical properties, characterizations and applications

2018 ◽  
Vol 55 (4) ◽  
pp. 498-522
Author(s):  
Morad Alizadeh ◽  
Mahdi Rasekhi ◽  
Haitham M. Yousof ◽  
Thiago G. Ramires ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Failure Rate Function ◽  
Data Set ◽  
Mathematical Properties

In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.

scholarly journals On the Gumbel-Burr XII Distribution: Regression and Application

2021 ◽  
Vol 10 (6) ◽  
pp. 31
Author(s):  
Raid Al-Aqtash ◽  
Avishek Mallick ◽  
G.G. Hamedani ◽  
Mahmoud Aldeni
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Burr Xii Distribution ◽  
Distribution Parameters ◽  
Different Shapes

In this article, additional properties of the Gumbel-Burr XII distribution, denoted by (GBXII(L)), defined in (Osatohanmwen et al., 2017), are studied. We consider some useful characterizations for the GBXII(L) distribution and some of its properties. A simulation study is conducted to assess the performance of the MLEs and the usefulness of the GBXII(L) distribution is illustrated by means of three real data sets. The simulation study suggests that the maximum likelihood method can be used to estimate the distribution parameters, and the three examples show that the GBXII(L) is very flexible in fitting different shapes of data. A log-GBXII(L) regression model is proposed and a survival data is used in an application of the proposed regression model. The log-GBXII(L) regression model is adequate and can be used in comparison to other models.

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

Gamma Knife surgery combined with resection for treatment of a single brain metastasis: preliminary results

2010 ◽  
Vol 113 (Special_Supplement) ◽  
pp. 90-96 ◽  
Author(s):  
M. Yashar S. Kalani ◽  
Aristotelis S. Filippidis ◽  
Maziyar A. Kalani ◽  
Nader Sanai ◽  
David Brachman ◽  
...  
Keyword(s):  
Survival Data ◽  
Initial Treatment ◽  
Median Survival Time ◽  
Local Tumor Control ◽  
Survival Duration ◽  
Tumor Control ◽  
Local Tumor ◽  
Systemic Control ◽  
Cranial Metastasis

Object Resection and whole-brain radiation therapy (WBRT) have classically been the standard treatment for a single metastasis to the brain. The objective of this study was to evaluate the use of Gamma Knife surgery (GKS) as an alternative to WBRT in patients who had undergone resection and to evaluate patient survival and local tumor control. Methods The authors retrospectively reviewed the charts of 150 patients treated with a combination of stereotactic radiosurgery and resection of a cranial metastasis at their institution between April 1997 and September 2009. Patients who had multiple lesions or underwent both WBRT and GKS were excluded, as were patients for whom survival data beyond the initial treatment were not available. Clinical and imaging follow-up was assessed using notes from clinic visits and MR imaging studies when available. Follow-up data beyond the initial treatment and survival data were available for 68 patients. Results The study included 37 women (54.4%) and 31 men (45.6%) (mean age 60 years, range 28–89 years). In 45 patients (66.2%) there was systemic control of the primary tumor when the cranial metastasis was identified. The median duration between resection and radiosurgery was 15.5 days. The median volume of the treated cavity was 10.35 cm3 (range 0.9–45.4 cm3), and the median dose to the cavity margin was 15 Gy (range 14–30 Gy), delivered to the 50% isodose line (range 50%–76% isodose line). The patients' median preradiosurgery Karnofsky Performance Scale (KPS) score was 90 (range 40–100). During the follow-up period we identified 27 patients (39.7%) with recurrent tumor located either local or distant to the site of treatment. The median time from primary treatment of metastasis to recurrence was 10.6 months. The patients' median length of survival (interval between first treatment of cerebral metastasis and last follow-up) was 13.2 months. For the patient who died during follow-up, the median time from diagnosis of cerebral metastasis to death was 11.5 months. The median duration of survival from diagnosis of the primary cancer to last follow-up was 30.2 months. Patients with a pretreatment KPS score ≥ 90 had a median survival time of 23.2 months, and patients with a pretreatment KPS score < 90 had a median survival time of 10 months (p < 0.008). Systemic control of disease at the time of metastasis was not predictive of increased survival duration, although it did tend to improve survival. Conclusions Although the debate about the ideal form of radiation treatment after resection continues, these findings indicate that GKS combined with surgery offers comparable survival duration and local tumor control to WBRT for patients with a diagnosis of a single metastasis.

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