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Influence diagnostics in linear and nonlinear mixed-effects models with censored data

Author

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  • Matos, Larissa A.
  • Lachos, Victor H.
  • Balakrishnan, N.
  • Labra, Filidor V.

Abstract

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays, and consequently the responses are either left or right censored. Linear and nonlinear mixed-effects models, with modifications to accommodate censoring (LMEC and NLMEC), are routinely used to analyze this type of data. Recently, Vaida and Liu (2009) proposed an exact EM-type algorithm for LMEC/NLMEC, called the SAGE algorithm (Meng and Van Dyk, 1997), that uses closed-form expressions at the E-step, as opposed to Monte Carlo simulations. Motivated by this algorithm, we propose here an exact ECM algorithm (Meng and Rubin, 1993) for LMEC/NLMEC, which enables us to develop local influence analysis for mixed-effects models on the basis of conditional expectation of the complete-data log-likelihood function. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex which makes it difficult to directly apply the approach of Cook (1977, 1986). Some useful perturbation schemes are also discussed. Finally, the results obtained from the analyses of two HIV AIDS studies on viral loads are presented to illustrate the newly developed methodology.

Suggested Citation

  • Matos, Larissa A. & Lachos, Victor H. & Balakrishnan, N. & Labra, Filidor V., 2013. "Influence diagnostics in linear and nonlinear mixed-effects models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 450-464.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:450-464
    DOI: 10.1016/j.csda.2012.06.021
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    References listed on IDEAS

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    1. Vaida, Florin & Fitzgerald, Anthony P. & DeGruttola, Victor, 2007. "Efficient hybrid EM for linear and nonlinear mixed effects models with censored response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5718-5730, August.
    2. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    3. Hong-Tu Zhu & Sik-Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    4. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
    5. W.-Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    6. Feng-Chang Xie & Bo-Cheng Wei & Jin-Guan Lin, 2007. "Case-deletion Influence Measures for the Data from Multivariate t Distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(8), pages 907-921.
    7. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    8. Víctor Lachos & Filidor Vilca & Manuel Galea, 2007. "Influence diagnostics for the Grubbs's model," Statistical Papers, Springer, vol. 48(3), pages 419-436, September.
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    Cited by:

    1. repec:eee:jmvana:v:159:y:2017:i:c:p:151-167 is not listed on IDEAS
    2. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    3. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.

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