Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors
For subject <i>i</i>, we monitor an event that can occur multiple times over a random observation window [0, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>i<...
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MDPI AG
2024-12-01
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| author | Ravinath Alahakoon Gideon K. D. Zamba Xuerong Meggie Wen Akim Adekpedjou |
| author_facet | Ravinath Alahakoon Gideon K. D. Zamba Xuerong Meggie Wen Akim Adekpedjou |
| author_sort | Ravinath Alahakoon |
| collection | DOAJ |
| description | For subject <i>i</i>, we monitor an event that can occur multiple times over a random observation window [0, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>i</mi></msub></semantics></math></inline-formula>). At each recurrence, <i>p</i> concomitant variables, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="bold">x</mi><mi>i</mi></msub></semantics></math></inline-formula>, associated to the event recurrence are recorded—a subset (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>≤</mo><mi>p</mi></mrow></semantics></math></inline-formula>) of which is measured with errors. To circumvent the problem of bias and consistency associated with parameter estimation in the presence of measurement errors, we propose inference for corrected estimating equations with well-behaved roots under an additive measurement errors model. We show that estimation is essentially unbiased under the corrected profile likelihood for recurrent events, in comparison to biased estimations under a likelihood function that ignores correction. We propose methods for obtaining estimators of error variance and discuss the properties of the estimators. We further investigate the case of misspecified error models and show that the resulting estimators under misspecification converge to a value different from that of the true parameter—thereby providing a basis for bias assessment. We demonstrate the foregoing correction methods on an open-source rhDNase dataset gathered in a clinical setting. |
| format | Article |
| id | doaj-art-5d2d06c9892f4fb5804e442f874dbf65 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5d2d06c9892f4fb5804e442f874dbf652025-01-10T13:18:17ZengMDPI AGMathematics2227-73902024-12-0113111310.3390/math13010113Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement ErrorsRavinath Alahakoon0Gideon K. D. Zamba1Xuerong Meggie Wen2Akim Adekpedjou3Gary W. Rollins College of Business, The University of Tennessee-Chattanooga, Chattanooga, TN 37403, USADepartment of Biostatistics, The University of Iowa, Iowa City, IA 52242, USADepartment of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USADepartment of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USAFor subject <i>i</i>, we monitor an event that can occur multiple times over a random observation window [0, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>i</mi></msub></semantics></math></inline-formula>). At each recurrence, <i>p</i> concomitant variables, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="bold">x</mi><mi>i</mi></msub></semantics></math></inline-formula>, associated to the event recurrence are recorded—a subset (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>≤</mo><mi>p</mi></mrow></semantics></math></inline-formula>) of which is measured with errors. To circumvent the problem of bias and consistency associated with parameter estimation in the presence of measurement errors, we propose inference for corrected estimating equations with well-behaved roots under an additive measurement errors model. We show that estimation is essentially unbiased under the corrected profile likelihood for recurrent events, in comparison to biased estimations under a likelihood function that ignores correction. We propose methods for obtaining estimators of error variance and discuss the properties of the estimators. We further investigate the case of misspecified error models and show that the resulting estimators under misspecification converge to a value different from that of the true parameter—thereby providing a basis for bias assessment. We demonstrate the foregoing correction methods on an open-source rhDNase dataset gathered in a clinical setting.https://www.mdpi.com/2227-7390/13/1/113recurrent eventscovariate measurement errorsmodel misspecificationKullback–Leibler divergencecorrected score |
| spellingShingle | Ravinath Alahakoon Gideon K. D. Zamba Xuerong Meggie Wen Akim Adekpedjou Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors Mathematics recurrent events covariate measurement errors model misspecification Kullback–Leibler divergence corrected score |
| title | Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors |
| title_full | Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors |
| title_fullStr | Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors |
| title_full_unstemmed | Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors |
| title_short | Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors |
| title_sort | estimation and model misspecification for recurrent event data with covariates under measurement errors |
| topic | recurrent events covariate measurement errors model misspecification Kullback–Leibler divergence corrected score |
| url | https://www.mdpi.com/2227-7390/13/1/113 |
| work_keys_str_mv | AT ravinathalahakoon estimationandmodelmisspecificationforrecurrenteventdatawithcovariatesundermeasurementerrors AT gideonkdzamba estimationandmodelmisspecificationforrecurrenteventdatawithcovariatesundermeasurementerrors AT xuerongmeggiewen estimationandmodelmisspecificationforrecurrenteventdatawithcovariatesundermeasurementerrors AT akimadekpedjou estimationandmodelmisspecificationforrecurrenteventdatawithcovariatesundermeasurementerrors |