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Parameter Estimation in a Hierarchical Random Intercept Model with Censored Response: An Approach using a SEM Algorithm and Gibbs Sampling

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In this paper, we propose an approach, based on the stochastic expectation maximization (SEM) algorithm and Gibbs sampling, to deal with the problem caused by censoring in the response of a hierarchical random intercept models. We compared our approach with the existing methods via real data sets as well as simulations. Results showed that our approach outperformed other approaches in terms of estimation accuracy and computing efficiency.

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  • Briand, V., Hesran, L., Le Watier, J. Y., Garcia, A. and Cot, M. (2005). Coinfection with Plasmodium Falciparum and Schistosoma Haematobium: Protecitive effect of Schistosomiasis on Malaria in Senegalese Children. Am. J. Trop. Med. Hyg., 72, 6, 702–707.

  • Bryk, A. and Raudenbush, S. W. (1992). Hierarchical Linear Models for Social and Behavioral Research: Applications and Data Analysis Methods. Sage, Newbury Park.

  • Casella, G. and George, E. I. (1992). Explaining the Gibbs Sampler. Am. Stat., 46, 167–174.

  • Celeux, G. and Diebolt, J. (1985). The SEM algorithm: a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem. Comput. Stat. Q., 2, 73–82.

  • Chabanet, C. and Pineau, N. (2006). Using linear mixed models to handle variablility of consumer’s liking. Food Qual. Prefer., 17, 658–668.

  • Dempster, A. P., Rubin, D. B. and Tsutakawa, R. K. (1981). Estimation in covariance components models. J. Am. Stat. Assoc., 76, 374, 341–353.

  • Diebolt, J. and Celeux, G. (1993). Asymptotic properties of a stochastic EM algorithm for estimating mixing proportions. Stochast. Model., 9, 599–613.

  • Elston, R. C. and Grizzle, J. E. (1962). Estimation of time response curves and their confidence bands. Biometrics, 18, 148–159.

  • Fitzgerald, A. P., DeGruttola, V. G. and Vaida, F. (2002). Modeling HIV viral rebound using non-linear mixed effects models. Stat. Med., 21, 2093–2108.

  • Goldstein, H. (1995). Multilevel Statistical Models. Edward Arnold, London.

  • Hughes, J. P. (1999). Mixed effects models with censored data with application to HIV RNA Levels. Biometrics, 55, 625–629.

  • Jacqmin-Gadda, H., Chene, G., Thiebaut, R. and Commenges, D. (2000). Analysis of left-censored longitudinal data with application to viral load in HIV infection. Biostatistics, 1, 4, 355–368.

  • Kendall, M. (1938). A new measure of rank correlation. Biometrika 30, 81–89.

  • Kendall, M. (1948). Rank Correlation Methods. Charles Griffin and Company Limited. Biometrika.

  • Kruskal, W. H. (1958). Ordinal measures of association. J. Am. Stat. Assoc., 53, 284, 814–861.

  • Laird, N. M. and Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963–974.

  • Lindstrom, M. J. and Bates, D. M. (1988). Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. J. Am. Stat. Assoc., 83, 404, 1014–1021.

  • McLean, R. A., Sanders, W. L. and Stroup, W. W. (1991). A unified approach to mixed linear models. J. Am. Stat. Assoc., 45, 1, 54–64.

  • Migot-Nabias, F., Pelleau, S., Watier, L., Guitard, J., Toly, C., De Araujo, C., Ngom, M. I., Chevillard, C., Gaye, O. and Garcia, A. (2006). Red blood cell polymorphisms in relation to Plasmodium Falciparum asymptomatic parasite densities and morbidity in Senegal Microbes and Infections 8, 2352–2358.

  • Milet, J., Nuel, G., Watier, L., Courtin, D., Slaoui, Y., Senghor, P., Migot-Nabias, F., Gaye, O. and Garcia, A. (2010). Genome wide linkage study, using a 250K SNP Map, of plasmodium falciparum infection and mild Malaria attack in a senegalese population. PLoS ONE 5, 7, e11616.

  • Nielsen, S. F. (2000). The stochastic EM algorithm: estimation and asymptotic results. Bernoulli 6, 3, 457–489.

  • Robert, C. (1995). Simulation of truncated normal variables. Stat. Comput., 5, 121–125.

  • Robinson, G. K. (1991). That BLUP is a good thing: the estimation of random effects. Stat. Sci., 6, 1, 15–32.

  • Rubin, D. B. (1996). Multiple imputation after 18+ years (with discussion). J. Am. Stat. Assoc., 91, 473–520.

  • Saitoh, A., Foca, M., Viani, R., Heffernan-Vacca, S., Vaida, F., Lujan-Zilbermann, J., Emmanuel, P., Deville, J. and Spector, S. (2008). Clinical outcome in perinatally acquired HIV-infected children and adolescents after unstructured treatment interruption. Pediatrics 121, 513–521.

  • Samson, A., Lavielle, M. and Mentré, F. (2006). Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: application to HIV dynamics model. Comput. Stat. Data Anal., 51, 3, 1562–1574.

  • Snijders, T. and Bosker, R. (1999). Multilevel analysis: an introduction to basic and advanced multilevel modeling. Sage.

  • Thiébault, R., Morlat, P., Jacqmin-Gadda, H., Neau, D., Mercié, P., Dabis, F., Chêne, G., for the GECSA (2000). Clinical progression of HIV-1 infected patients according to the viral response during the first year of anti-retroviral treatment. AIDS 14, 971–978.

  • Vaida, F., Fitzgerald, A. P., Deruttola (2007). Efficient hybrid EM for linear and nonlinear mixed effects models with censored response. Comput. Stat. Data Anal., 51, 12, 5718–5730.

  • Vaida, F. and Liu, L. (2009). Fast implementation for normal mixed effects models with censored response. J. Comput. Graph. Stat. 18, 4, 797–817.

  • Wu, H. and Wu, L. (2000). A multiple imputation method for missing covariates in non-linear mixed-effects models with application to hiv dynamics. Stat. Med. 20, 12, 1755–1769.

  • Wu, L. (2002). A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with application to aids studies. J. Am. Stat. Assoc. 97, 460, 955–964.

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Correspondence to Y. Slaoui.

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Slaoui, Y., Nuel, G. Parameter Estimation in a Hierarchical Random Intercept Model with Censored Response: An Approach using a SEM Algorithm and Gibbs Sampling. Sankhya B 76, 210–233 (2014).

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AMS (2000) subject classification