Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees
Alzheimer’s disease (AD) affects about a tenth of the population aged over 65 and nearly half of those over 85, and the number of AD patients continues to grow. Several studies have shown that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inlin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/3019 |
| _version_ | 1797591227418279936 |
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| author | Yifan Xia Baosheng Liang |
| author_facet | Yifan Xia Baosheng Liang |
| author_sort | Yifan Xia |
| collection | DOAJ |
| description | Alzheimer’s disease (AD) affects about a tenth of the population aged over 65 and nearly half of those over 85, and the number of AD patients continues to grow. Several studies have shown that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> variant of the apolipoprotein E (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>) gene is potentially associated with an increased risk of AD. In this study, we aimed to investigate the causal effect of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> on Alzheimer’s disease under the potential outcome framework and evaluate the individualized risk of disease onset for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carriers. A total of 1705 Hispanic individuals from the Washington Heights-Inwood Columbia Aging Project (WHICAP) were included in this study, comprising 453 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carriers and 1252 non-carriers. Among them, 265 subjects had developed AD (23.2%). The non-parametric Bayesian additive regression trees (BART) approach was applied to model the individualized causal effects of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> on disease onset in the presence of right-censored outcomes. The heterogeneous risk of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> on AD was examined through the individualized posterior survival probability and posterior causal effects. The results showed that, on average, patients carrying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.968</mn></mrow></semantics></math></inline-formula> years younger at onset than those with non-carrying status, and the disease risk associated with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carrying status was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.9</mn><mo>%</mo></mrow></semantics></math></inline-formula> higher than that for non-carrying status; however, it should be noted that neither result was statistically significant. The posterior causal effects of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> for individualized subjects indicate that 14.41% of carriers presented strong evidence of AD risk and approximately 38.65% presented mild evidence, while around 13.71% of non-carriers presented strong evidence of AD risk and 40.89% presented mild evidence. Furthermore, 79.26% of carriers exhibited a posterior probability of disease risk greater than 0.5. In conclusion, no significant causal effect of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> gene on AD was observed at the population level, but strong evidence of AD risk was identified in a sub-group of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carriers. |
| first_indexed | 2024-03-11T01:34:29Z |
| format | Article |
| id | doaj.art-b1ccdbe296ab44a9b069cdb06612e246 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:34:29Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b1ccdbe296ab44a9b069cdb06612e2462023-11-18T17:04:40ZengMDPI AGMathematics2227-73902023-07-011113301910.3390/math11133019Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression TreesYifan Xia0Baosheng Liang1Institute of Medical Technology, Peking University, Beijing 100191, ChinaDepartment of Biostatistics, School of Public Health, Peking University, Beijing 100191, ChinaAlzheimer’s disease (AD) affects about a tenth of the population aged over 65 and nearly half of those over 85, and the number of AD patients continues to grow. Several studies have shown that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> variant of the apolipoprotein E (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>) gene is potentially associated with an increased risk of AD. In this study, we aimed to investigate the causal effect of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> on Alzheimer’s disease under the potential outcome framework and evaluate the individualized risk of disease onset for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carriers. A total of 1705 Hispanic individuals from the Washington Heights-Inwood Columbia Aging Project (WHICAP) were included in this study, comprising 453 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carriers and 1252 non-carriers. Among them, 265 subjects had developed AD (23.2%). The non-parametric Bayesian additive regression trees (BART) approach was applied to model the individualized causal effects of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> on disease onset in the presence of right-censored outcomes. The heterogeneous risk of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> on AD was examined through the individualized posterior survival probability and posterior causal effects. The results showed that, on average, patients carrying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.968</mn></mrow></semantics></math></inline-formula> years younger at onset than those with non-carrying status, and the disease risk associated with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carrying status was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.9</mn><mo>%</mo></mrow></semantics></math></inline-formula> higher than that for non-carrying status; however, it should be noted that neither result was statistically significant. The posterior causal effects of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> for individualized subjects indicate that 14.41% of carriers presented strong evidence of AD risk and approximately 38.65% presented mild evidence, while around 13.71% of non-carriers presented strong evidence of AD risk and 40.89% presented mild evidence. Furthermore, 79.26% of carriers exhibited a posterior probability of disease risk greater than 0.5. In conclusion, no significant causal effect of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> gene on AD was observed at the population level, but strong evidence of AD risk was identified in a sub-group of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>P</mi><mi>O</mi><mi>E</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mn>4</mn></mrow></semantics></math></inline-formula> carriers.https://www.mdpi.com/2227-7390/11/13/3019Bayesian modelindividualized disease riskright-censored dataAlzheimer’s disease |
| spellingShingle | Yifan Xia Baosheng Liang Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees Mathematics Bayesian model individualized disease risk right-censored data Alzheimer’s disease |
| title | Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees |
| title_full | Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees |
| title_fullStr | Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees |
| title_full_unstemmed | Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees |
| title_short | Assessing the Risk of <i>APOE</i>-<i>ϵ</i>4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees |
| title_sort | assessing the risk of i apoe i i ϵ i 4 on alzheimer s disease using bayesian additive regression trees |
| topic | Bayesian model individualized disease risk right-censored data Alzheimer’s disease |
| url | https://www.mdpi.com/2227-7390/11/13/3019 |
| work_keys_str_mv | AT yifanxia assessingtheriskofiapoeiiei4onalzheimersdiseaseusingbayesianadditiveregressiontrees AT baoshengliang assessingtheriskofiapoeiiei4onalzheimersdiseaseusingbayesianadditiveregressiontrees |