scholarly journals The partly parametric and partly nonparametric additive risk model

2021 ◽  
Author(s):  
Nils Lid Hjort ◽  
Emil Aas Stoltenberg
Keyword(s):  
Hazard Rate ◽  
Goodness Of Fit ◽  
Risk Model ◽  
Real Data ◽  
Rate Function ◽  
Nonparametric Model ◽  
Additive Risk Model ◽  
Data Application ◽  
Additive Risk ◽  
Hazard Factor

AbstractAalen’s linear hazard rate regression model is a useful and increasingly popular alternative to Cox’ multiplicative hazard rate model. It postulates that an individual has hazard rate function $$h(s)=z_1\alpha _1(s)+\cdots +z_r\alpha _r(s)$$ h ( s ) = z 1 α 1 ( s ) + ⋯ + z r α r ( s ) in terms of his covariate values $$z_1,\ldots ,z_r$$ z 1 , … , z r . These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions $$\alpha _j(s)$$ α j ( s ) are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model’s parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study.

Alpha Power-Kumaraswamy Distribution with An Application on Survival Times of Cancer Patients

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Fatima Ulubekova ◽  
Gamze Ozel
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Alpha Power ◽  
Survival Times ◽  
Kumaraswamy Distribution ◽  
Data Application ◽  
The Right ◽  
Better Than

The aim of the study is to obtain the alpha power Kumaraswamy (APK) distribution. Some main statistical properties of the APK distribution are investigated including survival, hazard rate and quantile functions, skewness, kurtosis, order statistics. The hazard rate function of the proposed distribution could be useful to model data sets with bathtub hazard rates. We provide a real data application and show that the APK distribution is better than the other compared distributions fort the right-skewed data sets.

scholarly journals Modeling Extreme Values Utilizing an Asymmetric Probability Function

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1730
Author(s):  
Mohammed M. A. Almazah ◽  
Muqrin A. Almuqrin ◽  
Mohamed. S. Eliwa ◽  
Mahmoud El-Morshedy ◽  
Haitham M. Yousof
Keyword(s):  
Hazard Rate ◽  
Extreme Values ◽  
Residual Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Rate Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Hazard Rate Function ◽  
Data Application

In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model.

A Partly Parametric Additive Risk Model

1993 ◽  
Author(s):  
Ian W. McKeague ◽  
Peter D. Sasieni
Keyword(s):  
Risk Model ◽  
Additive Risk Model ◽  
Additive Risk

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

scholarly journals A Likelihood Ratio Test for Gene-Environment Interaction Based on the Trend Effect of Genotype Under an Additive Risk Model Using the Gene-Environment Independence Assumption

2020 ◽  
Vol 190 (1) ◽  
pp. 129-141
Author(s):  
Matthieu de Rochemonteix ◽  
Valerio Napolioni ◽  
Nilotpal Sanyal ◽  
Michaël E Belloy ◽  
Neil E Caporaso ◽  
...  
Keyword(s):  
Apolipoprotein E ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Risk Model ◽  
Ratio Test ◽  
Independence Assumption ◽  
Additive Risk Model ◽  
Gene Environment ◽  
Genome Wide ◽  
Additive Risk

Abstract Several statistical methods have been proposed for testing gene-environment (G-E) interactions under additive risk models using data from genome-wide association studies. However, these approaches have strong assumptions from underlying genetic models, such as dominant or recessive effects that are known to be less robust when the true genetic model is unknown. We aimed to develop a robust trend test employing a likelihood ratio test for detecting G-E interaction under an additive risk model, while incorporating the G-E independence assumption to increase power. We used a constrained likelihood to impose 2 sets of constraints for: 1) the linear trend effect of genotype and 2) the additive joint effects of gene and environment. To incorporate the G-E independence assumption, a retrospective likelihood was used versus a standard prospective likelihood. Numerical investigation suggests that the proposed tests are more powerful than tests assuming dominant, recessive, or general models under various parameter settings and under both likelihoods. Incorporation of the independence assumption enhances efficiency by 2.5-fold. We applied the proposed methods to examine the gene-smoking interaction for lung cancer and gene–apolipoprotein E $\varepsilon$4 interaction for Alzheimer disease, which identified 2 interactions between apolipoprotein E $\varepsilon$4 and loci membrane-spanning 4-domains subfamily A (MS4A) and bridging integrator 1 (BIN1) genes at genome-wide significance that were replicated using independent data.

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