scholarly journals Application of Survival Analysis of TB Patients Using Parametric Model: A Case Study of General Hospital Bayara

2020 ◽  
pp. 54-65
Author(s):  
Samson Daniel ◽  
K. E. Lasisi ◽  
Jerry Banister
Keyword(s):  
Goodness Of Fit ◽  
Smoking Habit ◽  
Secondary Data ◽  
Frailty Model ◽  
Hazard Model ◽  
Parametric Models ◽  
Distribution Model ◽  
Weight Category ◽  
Gamma Frailty ◽  
Cox Hazard Model

Aim: We evaluate the performance of parametric models, mixture of generalized gamma frailty model with Gompertz distribution and compare it with Cox proportional hazard model that is commonly used in the analysis of TB patients and also by [1]. Place and the Duration of the Study: The study was carried out in Bauchi State, Nigeria from January, 2017 to January, 2020. Methodology: In this study secondary data was used and gotten from the patients’ treatment card and TB registers from January 2015 to December 2017. The covariates used were, drug, age, marital status, smoking habit, educational level, weight, category, and risk factor. We used AIC and BIC selection tool to select the model with the lowest value and then compare it with Cox hazard model. Data analysis was done in Stata version 14. Results: The result of the analysis shows that mixture of frailty model with Gompertz baseline distribution has the lowest AIC and BIC value when compared to Cox Proportional model therefore shows a better goodness of fit for our dataset. Conclusion: We therefore conclude that mixture of frailty model with Gompertz baseline distribution model can serve as an alternative to Cox Proportional Model.

Comparison of Parametric and Nonparametric Hazard Models for Stop Durations on Urban Tours with Commercial Vehicles

2012 ◽  
Vol 2269 (1) ◽  
pp. 117-126 ◽  
Author(s):  
Bryce W. Sharman ◽  
Matthew J. Roorda ◽  
Khandker M. Nurul Habib
Keyword(s):  
Urban Areas ◽  
Goodness Of Fit ◽  
Failure Time ◽  
Hazard Model ◽  
Time Of Day ◽  
Parametric Models ◽  
Duration Models ◽  
Gps Data ◽  
Commercial Vehicles ◽  
Explanatory Variables

Hazard-based stop duration models for the stop duration of commercial vehicles in urban areas are presented. Passively collected GPS data were used to estimate two hazard-survival models to predict the stop duration of commercial vehicles undertaking urban pickup and delivery tours. The first was an accelerated failure-time parametric hazard model, and the second was a proportional nonparametric hazard model. Explanatory variables included time of day, population or employment density, number of stops, distance of inbound and outbound trips, and attributes of destination establishments, such as sales volume and industry classification. Models were estimated with and without establishment data because these data may not always be available for model application. Results showed that passively collected GPS data could be used to estimate stop duration models when linked with other data sources that provided appropriate explanatory variables. The parametric models were shown to outperform the nonparametric models and had higher measures of goodness of fit and better hazard distributions for stop duration.

scholarly journals Asymptotic theory for the correlated gamma-frailty model

1998 ◽  
Vol 26 (1) ◽  
pp. 183-214 ◽  
Author(s):  
Erik Parner
Keyword(s):  
Asymptotic Theory ◽  
Frailty Model ◽  
Gamma Frailty

scholarly journals Mathematical pattern of Kessler psychological distress distribution in the general population of the U.S. and Japan

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Shinichiro Tomitaka ◽  
Toshiaki A. Furukawa
Keyword(s):  
United States ◽  
General Population ◽  
National Survey ◽  
Goodness Of Fit ◽  
Quadratic Function ◽  
The United States ◽  
Depression Screening ◽  
Distribution Model ◽  
Epidemiological Surveys ◽  
Screening Scale

Abstract Background Although the 6-item Kessler psychological scale (K6) is a useful depression screening scale in clinical settings and epidemiological surveys, little is known about the distribution model of the K6 score in the general population. Using four major national survey datasets from the United States and Japan, we explored the mathematical pattern of the K6 distributions in the general population. Methods We analyzed four datasets from the National Health Interview Survey, the National Survey on Drug Use and Health, and the Behavioral Risk Factor Surveillance System in the United States, and the Comprehensive Survey of Living Conditions in Japan. We compared the goodness of fit between three models: exponential, power law, and quadratic function models. Graphical and regression analyses were employed to investigate the mathematical patterns of the K6 distributions. Results The exponential function had the best fit among the three models. The K6 distributions exhibited an exponential pattern, except for the lower end of the distribution across the four surveys. The rate parameter of the K6 distributions was similar across all surveys. Conclusions Our results suggest that, regardless of different sample populations and methodologies, the K6 scores exhibit a common mathematical distribution in the general population. Our findings will contribute to the development of the distribution model for such a depression screening scale.

scholarly journals Gamma frailty model for linkage analysis with application to interval-censored migraine data

Biostatistics ◽  
2008 ◽  
Vol 10 (1) ◽  
pp. 187-200 ◽  
Author(s):  
M. A. Jonker ◽  
S. Bhulai ◽  
D. I. Boomsma ◽  
R. S. L. Ligthart ◽  
D. Posthuma ◽  
...  
Keyword(s):  
Linkage Analysis ◽  
Frailty Model ◽  
Gamma Frailty ◽  
Interval Censored

scholarly journals On the Connection between the GEP Performances and the Time Series Properties

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1853
Author(s):  
Alina Bărbulescu ◽  
Cristian Ștefan Dumitriu
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Functional Form ◽  
Financial Time Series ◽  
Gene Expression Programming ◽  
Parametric Models ◽  
Statistical Characteristics ◽  
Data Series ◽  
Financial Time ◽  
Data Generating Process

Artificial intelligence (AI) methods are interesting alternatives to classical approaches for modeling financial time series since they relax the assumptions imposed on the data generating process by the parametric models and do not impose any constraint on the model’s functional form. Even if many studies employed these techniques for modeling financial time series, the connection of the models’ performances with the statistical characteristics of the data series has not yet been investigated. Therefore, this research aims to study the performances of Gene Expression Programming (GEP) for modeling monthly and weekly financial series that present trend and/or seasonality and after the removal of each component. It is shown that series normality and homoskedasticity do not influence the models’ quality. The trend removal increases the models’ performance, whereas the seasonality elimination results in diminishing the goodness of fit. Comparisons with ARIMA models built are also provided.

Political parties in Canada: What determines entry, exit and the duration of their lives?

2018 ◽  
Vol 26 (5) ◽  
pp. 543-554 ◽  
Author(s):  
J Stephen Ferris ◽  
Marcel-Cristian Voia
Keyword(s):  
Political Parties ◽  
Political Party ◽  
Public Funding ◽  
Hazard Model ◽  
Parametric Models ◽  
Extensive Margin ◽  
Finite Mixtures ◽  
Entry And Exit ◽  
Intensive Margin ◽  
Economic Circumstance

Two margins of political party life in Canada since Confederation (1867) are analyzed—the extensive margin involving entry and exit (together with party turnover or churning) and the intensive margin determining survival length. The results confirm many hypotheses advanced to explain entry and exit—the importance of social and religious cleavage, election institutions, and economic circumstance. More novel are the findings that public election funding and periods with larger immigration flows have reinforced established parties at the expense of entrants and smaller sized parties. The intensive margin uses a discrete hazard model with discrete finite mixtures to confirm the Duverger-type presence of two distinct long-lived political parties surrounded by a fringe of smaller parties. Both parametric and semi-parametric models concur in finding that public funding and higher immigration flows are as successful in extending the life of established parties as in discouraging entry and exit.

Remaining Useful Life Estimation Based on a Segmental Hidden Markov Model With Continuous Observations

2017 ◽  
Author(s):  
Zhen Chen ◽  
Tangbin Xia ◽  
Ershun Pan
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Goodness Of Fit ◽  
Hidden Markov ◽  
Remaining Useful Life ◽  
Likelihood Method ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Useful Life ◽  
Hidden States

In this paper, a segmental hidden Markov model (SHMM) with continuous observations, is developed to tackle the problem of remaining useful life (RUL) estimation. The proposed approach has the advantage of predicting the RUL and detecting the degradation states simultaneously. As the observation space is discretized into N segments corresponding to N hidden states, the explicit relationship between actual degradation paths and the hidden states can be depicted. The continuous observations are fitted by Gaussian, Gamma and Lognormal distribution, respectively. To select a more suitable distribution, model validation metrics are employed for evaluating the goodness-of-fit of the available models to the observed data. The unknown parameters of the SHMM can be estimated by the maximum likelihood method with the complete data. Then a recursive method is used for RUL estimation. Finally, an illustrate case is analyzed to demonstrate the accuracy and efficiency of the proposed method. The result also suggests that SHMM with observation probability distribution which is closer to the real data behavior may be more suitable for the prediction of RUL.

scholarly journals Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1963
Author(s):  
Jingting Yao ◽  
Muhammad Ali Raza Anjum ◽  
Anshuman Swain ◽  
David A. Reiter
Keyword(s):  
Skeletal Muscle ◽  
Goodness Of Fit ◽  
Numerical Models ◽  
Tissue Perfusion ◽  
Parametric Models ◽  
Intravoxel Incoherent Motion ◽  
Fickian Diffusion ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Stretched Exponential

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

Small Sample Bias in the Gamma Frailty Model for Univariate Survival

2005 ◽  
Vol 11 (2) ◽  
pp. 265-284 ◽  
Author(s):  
Peter Barker ◽  
Robin Henderson
Keyword(s):  
Frailty Model ◽  
Small Sample ◽  
Sample Bias ◽  
Gamma Frailty
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