Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation
Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework...
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MDPI AG
2021-01-01
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| Online Access: | https://www.mdpi.com/2227-7390/9/3/248 |
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| author | Reem Aljarallah Samer A Kharroubi |
| author_facet | Reem Aljarallah Samer A Kharroubi |
| author_sort | Reem Aljarallah |
| collection | DOAJ |
| description | Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework using Gibbs sampling Markov chain Monte Carlo simulation methods in WinBUGS. We focus on the modeling and prediction of Down syndrome (DS) and Mental retardation (MR) data from an observational study at Kuwait Medical Genetic Center over a 30-year time period between 1979 and 2009. Modeling algorithms were used in two distinct ways; firstly, using three different methods at the disease level, including logistic, probit and cloglog models, and, secondly, using bivariate logistic regression to study the association between the two diseases in question. The models are compared in terms of their predictive ability via <i>R<sup>2</sup></i>, adjusted <i>R<sup>2</sup></i>, root mean square error (RMSE) and Bayesian Deviance Information Criterion (DIC). In the univariate analysis, the logistic model performed best, with <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.1145), adjusted <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.114), RMSE (0.3074) and DIC (7435.98) for DS, and <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.0626), adjusted <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.0621), RMSE (0.4676) and DIC (23120) for MR. In the bivariate case, results revealed that 7 and 8 out of the 10 selected covariates were significantly associated with DS and MR respectively, whilst none were associated with the interaction between the two outcomes. Bayesian methods are more flexible in handling complex non-standard models as well as they allow model fit and complexity to be assessed straightforwardly for non-nested hierarchical models. |
| first_indexed | 2024-03-09T03:33:26Z |
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| id | doaj.art-5b0b57296e564211b9a7576668a04764 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T03:33:26Z |
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| spelling | doaj.art-5b0b57296e564211b9a7576668a047642023-12-03T14:51:30ZengMDPI AGMathematics2227-73902021-01-019324810.3390/math9030248Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental RetardationReem Aljarallah0Samer A Kharroubi1Department of Statistics and Operations Research, Kuwait University, Kuwait, P.O. Box 5969, Safat 13060, KuwaitDepartment of Nutrition and Food Sciences, Faculty of Agricultural and Food Sciences, American University of Beirut, P.O. Box 11-0236, Riad El Solh 1107-2020, Beirut, LebanonLogit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework using Gibbs sampling Markov chain Monte Carlo simulation methods in WinBUGS. We focus on the modeling and prediction of Down syndrome (DS) and Mental retardation (MR) data from an observational study at Kuwait Medical Genetic Center over a 30-year time period between 1979 and 2009. Modeling algorithms were used in two distinct ways; firstly, using three different methods at the disease level, including logistic, probit and cloglog models, and, secondly, using bivariate logistic regression to study the association between the two diseases in question. The models are compared in terms of their predictive ability via <i>R<sup>2</sup></i>, adjusted <i>R<sup>2</sup></i>, root mean square error (RMSE) and Bayesian Deviance Information Criterion (DIC). In the univariate analysis, the logistic model performed best, with <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.1145), adjusted <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.114), RMSE (0.3074) and DIC (7435.98) for DS, and <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.0626), adjusted <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> (0.0621), RMSE (0.4676) and DIC (23120) for MR. In the bivariate case, results revealed that 7 and 8 out of the 10 selected covariates were significantly associated with DS and MR respectively, whilst none were associated with the interaction between the two outcomes. Bayesian methods are more flexible in handling complex non-standard models as well as they allow model fit and complexity to be assessed straightforwardly for non-nested hierarchical models.https://www.mdpi.com/2227-7390/9/3/248Bayesian methodsKuwait Medical Genetic Centerregression modelingbivariate logistic regressionMarkov chain Monte Carlo |
| spellingShingle | Reem Aljarallah Samer A Kharroubi Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation Mathematics Bayesian methods Kuwait Medical Genetic Center regression modeling bivariate logistic regression Markov chain Monte Carlo |
| title | Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation |
| title_full | Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation |
| title_fullStr | Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation |
| title_full_unstemmed | Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation |
| title_short | Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation |
| title_sort | use of bayesian markov chain monte carlo methods to model kuwait medical genetic center data an application to down syndrome and mental retardation |
| topic | Bayesian methods Kuwait Medical Genetic Center regression modeling bivariate logistic regression Markov chain Monte Carlo |
| url | https://www.mdpi.com/2227-7390/9/3/248 |
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