scholarly journals A Reliability Growth Process Model with Time-Varying Covariates and Its Application

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 905
Author(s):  
Xin-Yu Tian ◽  
Xincheng Shi ◽  
Cheng Peng ◽  
Xiao-Jian Yi
Keyword(s):  
Poisson Process ◽  
Process Model ◽  
Growth Process ◽  
Nonhomogeneous Poisson Process ◽  
Reliability Growth ◽  
Time Varying ◽  
Repairable Systems ◽  
Martingale Theory ◽  
Amsaa Model ◽  
Time Varying Covariates

The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models.

scholarly journals Bayesian modeling and prediction of accrual in multi-regional clinical trials

2014 ◽  
Vol 26 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Yi Deng ◽  
Xiaoxi Zhang ◽  
Qi Long
Keyword(s):  
Clinical Trials ◽  
Poisson Process ◽  
Process Model ◽  
Nonhomogeneous Poisson Process ◽  
Modeling And Prediction ◽  
Accuracy And Precision ◽  
Start Up ◽  
Accrual Rate ◽  
Model Region ◽  
Over Time

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the nonhomogeneous Poisson process model that does not model region-specific accrual.

scholarly journals A Spatial Nonhomogeneous Poisson Process Model Using Bayesian Approach on a Space-Time Geostatistical Data

2021 ◽  
Vol 4 (3) ◽  
pp. 186-198
Author(s):  
Anggun Y.Q. ◽  
Subanar .
Keyword(s):  
Poisson Process ◽  
Bayesian Approach ◽  
Process Model ◽  
Goodness Of Fit ◽  
Nonhomogeneous Poisson Process ◽  
Mcmc Method ◽  
Good Convergence ◽  
Time Component ◽  
Study Case ◽  
Special Region

In this research, we propose the nonhomogeneous Poisson process on geostatistical data by adding a time component to be applied in the study case of air pollution in the Special Region of Yogyakarta. We use the Bayesian approach to inference the model using the MCMC method. And to generate samples of the posterior distribution, we wield the Metropolis-Hastings algorithm, and we obtained it has good convergence for this case. And to show the goodness of fit of this model, we had the value of DIC.

scholarly journals Nonhomogeneous Poisson Process Model of Summer High Temperature Extremes Over China

2021 ◽  
Author(s):  
Meng Gao ◽  
Han Zhang ◽  
Aidi Zhang ◽  
Yueqi Wang
Keyword(s):  
High Temperature ◽  
Poisson Process ◽  
Poisson Regression ◽  
Process Model ◽  
Value Theory ◽  
Nonhomogeneous Poisson Process ◽  
Occurrence Rate ◽  
Temperature Extremes ◽  
Teleconnection Patterns ◽  
High Temperature Extremes

Abstract In this study, nonhomogeneous Poisson process (NHPP) models arising from the extreme value theory have been fitted to summer high temperature extremes (HTEs) at 359 meteorological stations over China. The seasonality and six prominent atmospheric teleconnection patterns in Northern Hemisphere are incorporated in the NHPP models reflecting the non-stationarity in occurrence rate in Poisson process of HTEs. In addition, Poisson regression model has also been applied to link HTEs and teleconnection patterns. The linkages of HTEs and teleconnection patterns have been identified in both NHPP modeling and Poisson regression. Composite maps of differences of 500-hPa geopotential height and wind fields in the positive and negative phases of teleconnection patterns are constructed to show the impacts of atmospheric circulation patterns on extreme heat events. The spatial pattern of the associated anticyclonic or cyclonic circulations with teleconnection patterns partly explains the spatial variability of the occurrences of summer HTEs over China.

scholarly journals A competing risks model with binary time varying covariates for estimation of breast cancer risks in BRCA1 families

2021 ◽  
pp. 096228022110089
Author(s):  
Yun-Hee Choi ◽  
Hae Jung ◽  
Saundra Buys ◽  
Mary Daly ◽  
Esther M John ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Ovarian Cancer ◽  
Competing Risks ◽  
Brca1 Mutation ◽  
Prophylactic Surgery ◽  
Time Varying ◽  
Cancer Risks ◽  
Competing Risks Model ◽  
Time Varying Covariates ◽  
Risk Reducing

Mammographic screening and prophylactic surgery such as risk-reducing salpingo oophorectomy can potentially reduce breast cancer risks among mutation carriers of BRCA families. The evaluation of these interventions is usually complicated by the fact that their effects on breast cancer may change over time and by the presence of competing risks. We introduce a correlated competing risks model to model breast and ovarian cancer risks within BRCA1 families that accounts for time-varying covariates. Different parametric forms for the effects of time-varying covariates are proposed for more flexibility and a correlated gamma frailty model is specified to account for the correlated competing events.We also introduce a new ascertainment correction approach that accounts for the selection of families through probands affected with either breast or ovarian cancer, or unaffected. Our simulation studies demonstrate the good performances of our proposed approach in terms of bias and precision of the estimators of model parameters and cause-specific penetrances over different levels of familial correlations. We applied our new approach to 498 BRCA1 mutation carrier families recruited through the Breast Cancer Family Registry. Our results demonstrate the importance of the functional form of the time-varying covariate effect when assessing the role of risk-reducing salpingo oophorectomy on breast cancer. In particular, under the best fitting time-varying covariate model, the overall effect of risk-reducing salpingo oophorectomy on breast cancer risk was statistically significant in women with BRCA1 mutation.

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