Latent drop-out based transitions in linear quantile hidden Markov models for longitudinal responses with attrition. (English) Zbl 1414.62302

Summary: Longitudinal data are characterized by the dependence between observations from the same individual. In a regression perspective, such a dependence can be usefully ascribed to unobserved features (covariates) specific to each individual. On these grounds, random parameter models with time-constant or time-varying structure are now well established in the generalized linear model context. In the quantile regression framework, specifications based on random parameters have only recently known a flowering interest. We start from the recent proposal by A. Farcomeni [Stat. Comput. 22, No. 1, 141–152 (2012; Zbl 1322.62206)] on longitudinal quantile hidden Markov models, and extend it to handle potentially informative missing data mechanisms. In particular, we focus on monotone missingness which may lead to selection bias and, therefore, to unreliable inferences on model parameters. We detail the proposed approach by re-analyzing a well known dataset on the dynamics of CD4 cell counts in HIV seroconverters and by means of a simulation study reported in the supplementary material.


62J02 General nonlinear regression


Zbl 1322.62206
Full Text: DOI


[1] Agresti A (2010) Analysis of ordinal categorical data. Wiley, New York · Zbl 1263.62007
[2] Altman, R., Mixed hidden Markov models: an extension of the hidden Markov model to the longitudinal data setting, J Am Stat Assoc, 102, 201-210, (2007) · Zbl 1284.62803
[3] Bartolucci, F.; Farcomeni, A., A discrete time event-history approach to informative drop-out in mixed latent Markov models with covariates, Biometrics, 71, 80-89, (2015) · Zbl 1419.62308
[4] Bartolucci F, Farcomeni A, Pennoni F (2013) Latent Markov models for longitudinal data. CRC Press, Boca Raton · Zbl 1341.62002
[5] Baum, L.; Petrie, T.; Soules, G.; Weiss, N., A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains, Ann Math Stat, 41, 164-171, (1970) · Zbl 0188.49603
[6] Buchinsky, M., Estimating the asymptotic covariance matrix for quantile regression models. A Monte Carlo study, J Econom, 68, 303-338, (1995) · Zbl 0825.62437
[7] Dempster, A.; Laird, NM; Rubin, DB, Maximum likelihood from incomplete data via the EM algorithm, J R Stat Soc Ser B (Methodol), 39, 1-38, (1977) · Zbl 0364.62022
[8] Farcomeni, A., Quantile regression for longitudinal data based on latent Markov subject-specific parameters, Stat Comput, 22, 141-152, (2012) · Zbl 1322.62206
[9] Farcomeni, A.; Viviani, S., Longitudinal quantile regression in the presence of informative dropout through longitudinal survival joint modeling, Stat Med, 34, 1199-1213, (2015)
[10] Geraci, M.; Bottai, M., Quantile regression for longitudinal data using the asymmetric Laplace distribution, Biostatistics, 8, 140-54, (2007) · Zbl 1170.62380
[11] Geraci, M.; Bottai, M., Linear quantile mixed models, Stat Comput, 24, 461-479, (2014) · Zbl 1325.62010
[12] Kaslow, RA; Ostrow, D.; Detels, R.; Phair, JP; Polk, BF; Rinaldo, C.; etal., The multicenter aids cohort study: rationale, organization, and selected characteristics of the participants, Am J Epidemiol, 126, 310-318, (1987)
[13] Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46:33-50 · Zbl 0373.62038
[14] Laird, NM; Ware, JH, Random-effects models for longitudinal data, Biometrics, 38, 963-974, (1982) · Zbl 0512.62107
[15] Liang, KY; Zeger, SL, Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22, (1986) · Zbl 0595.62110
[16] Lipsitz, SR; Fitzmaurice, GM; Molenberghs, G.; Zhao, LP, Quantile regression methods for longitudinal data with drop-outs: application to CD4 cell counts of patients infected with the human immunodeficiency virus, J R Stat Soc Ser C (Appl Stat), 46, 463-476, (1997) · Zbl 0908.62114
[17] Little RJ, Rubin DB (2002) Statistical analysis with missing data. Wiley, New York · Zbl 1011.62004
[18] Little, R.; Wang, Y., Pattern-mixture models for multivariate incomplete data, J Am Stat Assoc, 88, 125-134, (1993) · Zbl 0775.62134
[19] Liu Y, Bottai M (2009) Mixed-effects models for conditional quantiles with longitudinal data. Int J Biostat 5:1-24
[20] Marino, MF; Farcomeni, A., Linear quantile regression models for longitudinal experiments: an overview, METRON, 73, 229-247, (2015) · Zbl 1329.62317
[21] Marino M, Tzavidis N, Alfó M (2015) Quantile regression for longitudinal data: unobserved heterogeneity and informative missingness (e-prints). arXiv:1501.02157v2
[22] Maruotti, A., Mixed hidden Markov models for longitudinal data: an overview, Int Stat Rev, 79, 427-454, (2011) · Zbl 1238.62094
[23] Maruotti, A., Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure, TEST, 24, 84-109, (2015) · Zbl 1315.62065
[24] Maruotti, A.; Rocci, R., A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption, Stat Med, 31, 871-886, (2012)
[25] Molenberghs, G.; Beunckens, C.; Sotto, C.; Kenward, MG, Every missingness not at random model has a missingness at random counterpart with equal fit, J R Stat Soc Ser B (Methodol), 70, 371-388, (2008) · Zbl 1148.62046
[26] Rizopoulos, D., Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive gaussian quadrature rule, Comput Stat Data Anal, 56, 491-501, (2012) · Zbl 1239.62122
[27] Roy, J., Modeling longitudinal data with nonignorable dropouts using a latent dropout class model, Biometrics, 59, 829-836, (2003) · Zbl 1218.62117
[28] Roy, J.; Daniels, MJ, A general class of pattern mixture models for nonignorable dropout with many possible dropout times, Biometrics, 64, 538-545, (2008) · Zbl 1137.62016
[29] Wiggins LM (1973) Panel analysis: latent probability models for attitude and behavior processes. Jossey-Bass, San Francisco
[30] Yi, GY; He, W., Median regression models for longitudinal data with dropouts, Biometrics, 65, 618-625, (2009) · Zbl 1167.62094
[31] Zeger, SL; Diggle, PJ, Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters, Biometrics, 50, 689-699, (1994) · Zbl 0821.62093
[32] Zucchini W, MacDonald I (2009) Hidden Markov models for time series. In: Monographs on statistics and applied probability, vol 110. CRC Press, Boca Raton · Zbl 1180.62130
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