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Validation Data-Located Modification for the Multilevel Analysis of Miscategorized Nominal Response with Covariates Subject to Measurement Error

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Abstract

In many longitudinal and hierarchical epidemiological frameworks, observations regarding to each individual are recorded repeatedly over time. In these follow-ups, accurate measurements of time-dependent covariates might be invalid or expensive to be obtained. In addition, in the recording process, or as a result of other undetected reasons, miscategorization of the response variable might occur, that does not demonstrate the true condition of the response process. In contrast with binary outcome by which classification error occurs between two categories, disorderliness in categorical outcome has more intricate impacts, as a result of the increased number of categories and asymmetric miscategorization matrix. When no modification is made, insensitivity of errors in either covariate or response variable, results in potentially incorrect conclusion, tends to bias the statistical inference and eventually degrades the efficiency of the decision-making procedure. In this article, we provide an approach to simultaneously adjust for misclassification in the correlated nominal response and measurement error in the covariates, incorporating validation data in the estimation of misclassification probabilities, using the multivariate Gauss–Hermite quadrature technique for the approximation of the likelihood function. Simulation results demonstrate the effects of modifying covariate measurement error and response misclassification on the estimation procedure.

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REFERENCES

  1. C. E. McCullach, S. R. Searle, and J. M. Neuhaus, Generalized, Linear, and Mixed Models (John Wiley & Sons, London, 2008).

    Google Scholar 

  2. C. E. McCullach, ‘‘Maximum likelihood variance components estimation for binary data,’’ Journal of the American Statistical Association 89, 330–335 (1994).

    Article  Google Scholar 

  3. L. Wu, Mixed Effects Models for Complex Data (CRC Press, Boca Raton, 2009).

    Book  Google Scholar 

  4. W. W. Stroup, Generalized Linear Mixed Models: Modern Concepts, Methods, and Applications (CRC Press,Boca Raton, 2012).

    Google Scholar 

  5. P. J. Diggle, K. Y. Liang, and S. L. Zeger, Analysis of Longitudinal Data (Oxford University Press, Oxford, 1994).

    Google Scholar 

  6. M. A. Tanner, Tools for Statistical Inference: Observed Data and Data Augmentation (Springer, New York, 1993).

    Book  Google Scholar 

  7. N. Wang, X. Lin, and R. G. Guttierrez, ‘‘A bias correction regression calibration approach in generalized linear mixed measurement error models,’’ Communications in Statistics 28, 217–232 (1999).

    Article  Google Scholar 

  8. N. Wang, X. Lin, R. G. Guttierrez, and R. J. Carroll, ‘‘ Bias analysis and SIMEX approach in generalized linear mixed measurement error models,’’ Journal of American Statistical Association 93, 249–261 (1998).

    Article  MathSciNet  Google Scholar 

  9. J. P. Buonaccorsi, G. Romeo, and M. Thoresen, ‘‘Model-based bootstapping when correcting for measurement error with application to logistic regression,’’ Biometrics 74, 135–144 (2018).

    Article  MathSciNet  Google Scholar 

  10. R. J. Carroll, D. Ruppert, L. A. Stefanski, and C. M. Crainiceanu, Measurement Error in Nonlinear Models: A Modern Perspective (CRC Press, Boca Raton, 2006).

    Book  Google Scholar 

  11. M. Torabi, ‘‘Likelihood inference in generalized linear mixed measurement error models,’’ Computational Statistics and Data Analysis 57, 549–557 (2013).

    Article  MathSciNet  Google Scholar 

  12. X. Xie, X. Xue, and H. D. Strickler, ‘‘Generalized linear mixed model for binary outcomes when covariates are subject to measurement errors and detection limits,’’ Statistics in Medicine 37, 119–136 (2017).

    Article  MathSciNet  Google Scholar 

  13. G. Y. Yi, Statistical Analysis with Measurement Error or Misclassification (Springer, New York, 2017).

    Book  Google Scholar 

  14. L. S. Magder and J. P. Hughes, ‘‘Logistic regression when the outcome is measured with uncertainty,’’ American Journal of Epidemiology 146 (2), 195–203 (1997).

    Article  Google Scholar 

  15. J. M. Neuhaus, ‘‘Bias and efficiency loss due to misclassified responses in binary regression,’’ Biometrika 86(4), 843–855 (1999).

    Article  MathSciNet  Google Scholar 

  16. J. M. Neuhaus, ‘‘Analysis of clustered and longitudinal binary data subject to response misclassification,’’ Biometrics 58(3), 675–683 (2002).

    Article  MathSciNet  Google Scholar 

  17. C. D. Paulino, P. Soares, and J. Neuhaus, ‘‘Binomial regression with misclassification,’’ Biometrics 59 (3), 670–675 (2003).

    Article  MathSciNet  Google Scholar 

  18. R. Gerlach and J. Stamey, ‘‘Bayesian model selection for logistic regression with misclassified outcomes,’’ Statistical Modelling 7 (3), 255–273, (2007).

    Article  MathSciNet  Google Scholar 

  19. L. Tang, R. H. Lyles, C. C. King, J. W. Hogan, and Y. Lo, ‘‘Regression analysis for differentially misclassified correlated binary outcomes,’’ Journal of the Royal Statistical Society. Series C, Applied Statistics 64 (3), 433–449 (2015).

    Article  MathSciNet  Google Scholar 

  20. R. H. Lyles, L. Tang, H. M. Superak, C. C. King, D. D. Celentano, Y. Lo, and J. D. Sobel, ‘‘Validation data-based adjustments for outcome misclassification in logistic regression: An illustration, Epidemiology (Cambridge, Mass.) 22 (4), 589 (2011).

    Article  Google Scholar 

  21. L. Naranjo, C. J. Prez, J. Martn, T. Mutsvari, and E. Lesaffre, ‘‘A Bayesian approach for misclassified ordinal response data,’’ Journal of Applied Statistics 46 (12), 2198-2215, (2019).

    Article  MathSciNet  Google Scholar 

  22. D. Cheng, A. J. Branscum, and J. D. Stamey, ‘‘Accounting for response misclassification and covariate measurement error improves power and reduces bias in epidemiologic studies,’’ Annals of Epidemiology 20(7), 562–567, (2010).

    Article  Google Scholar 

  23. D. Shu and G. Y. Yi, ‘‘Weighted causal inference methods with mismeasured covariates and misclassified outcomes,’’ Statistics in Medicine 38 (10), 1835–1854 (2019).

    Article  MathSciNet  Google Scholar 

  24. S. Roy, ‘‘Accounting for response misclassification and covariate measurement error using a random effect logit model,’’ Communications in Statistics-Simulation and Computation 41(9), 1623–1636 (2012).

    Article  MathSciNet  Google Scholar 

  25. S. Roy, ‘‘Analysis of ordered probit model with surrogate response data and measurement error in covariates,’’ Communications in Statistics-Theory and Methods 45 (9), 2665–2678 (2016).

    Article  MathSciNet  Google Scholar 

  26. J. P. Buonaccorsi, Measurement Error, Models, Methods, and Applications (CRC Press, New York, 2010).

    Book  Google Scholar 

  27. R. H. Keogh, P. A. Shaw, P. Gustafson, R. J. Carroll, V. Deffner, K. W. Dodd, H. Kchenhoff, J. A. Tooze, M. P. Wallace, V. Kipnis, and L. S. Freedman, ‘‘STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1-basic theory and simple methods of adjustment,’’ Statistics in Medicine 39 (16), 2197–2231 (2020).

    Article  MathSciNet  Google Scholar 

  28. P. Jaeckel, A Note on Multivariate Gauss-Hermite Quadrature (ABN-Amro, London, 2005).

    Google Scholar 

  29. A. Agresti, Categorical Data Analysis (John Wiley and Sons, New York, 2002).

    Book  Google Scholar 

  30. A. Skrondal and S. Rabe-Hesketh, Generalized Latent Variable Modeling (CRC Press, Boca Raton, 2004).

    Book  Google Scholar 

  31. G. Molenberghs and G. Verbeke, Models for Discrete Longitudinal Data (Springer, New York, 2006).

    Google Scholar 

  32. J. Pan and R. Thompson, ‘‘Gauss-hermite quadrature approximation estimation in generalized linear mixed models,’’ Computational Statistics 18, 57–78 (2003).

    Article  MathSciNet  Google Scholar 

  33. J. A. Nelder and R. Mead, ‘‘A simplex algorithm for function minimization,’’ Computer Journal 7, 308–313 (1965).

    Article  MathSciNet  Google Scholar 

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ACKNOWLEDGMENTS

Receiving support from the Center of Excellence in Analysis of Spatio-Temporal Correlated Data at Tarbiat Modares University is acknowledged.

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Correspondence to Mousa Golalizadeh.

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Ahangari, M., Golalizadeh, M. & Ghahroodi, Z.R. Validation Data-Located Modification for the Multilevel Analysis of Miscategorized Nominal Response with Covariates Subject to Measurement Error. Math. Meth. Stat. 32, 223–240 (2023). https://doi.org/10.3103/S1066530723040026

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  • DOI: https://doi.org/10.3103/S1066530723040026

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