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Articles

A latent class based imputation method under Bayesian quantile regression framework using asymmetric Laplace distribution for longitudinal medication usage data with intermittent missing values

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Pages 160-177 | Received 28 Aug 2018, Accepted 16 Aug 2019, Published online: 15 Nov 2019

References

  • Andrews, D. R., and C. L. Nallows. 1974. Scale mixtures of normal distributions. Journal of the Royal Statistical Society: Series B 36:99–102.
  • Ayele, B. T., I. A. Lipkovich, G. Molenberghs, and V. H. Mallinckrodt. 2014. A multiple-imputation-based approach to sensitivity analyses and effectiveness assessments in longitudinal clinical trials. Journal of Biopharmaceutical Statistics 24 (2):211–228. doi:10.1080/10543406.2013.859148.
  • Azur, M. J., E. A. Stuart, C. Frangakis, and P. J. Leaf. 2011. Multiple imputation by chained equations: What is it and how does it work? International Journal of Methods in Psychiatric Research 20 (1):40–49. doi:10.1002/mpr.v20.1.
  • Benoit, D. F., and D. Van den Poel. 2017. bayesQR: A Bayesian approach to quantile regression. Journal of Statistical Software 76. doi:10.18637/jss.v076.i07.
  • Burgette, L. F., and J. P. Reiter. 2012. Nonparametric Bayesian multiple imputation for missing data due to mid-study switching of measurement methods. Journal of the American Statistical Association 498:439–449. doi:10.1080/01621459.2011.643713.
  • Creemers, M. C., M. J. Franssen, M. A. Van’t Hof, F. W. Gribnau, L. B. van de Putte, and P. L. van Riel. 2005. Assessment of outcome in ankylosing spondylitis: An extended radiographic scoring system. Annals of the Rheumatic Diseases 64:127–129. doi:10.1136/ard.2004.020503.
  • Dayton, C. M., and G. B. MacReady. 1988. Concomitant-variable latent class models. Journal of the American Statistical Association 83 (401):173–178. doi:10.1080/01621459.1988.10478584.
  • Dayton, CM, and GB. MacReady. 2002. Use of categorical and continuous covariates in latent class analysis. In Applied latent class analysis, Eds., 213-233. Cambridge, UK: Cambridge University Press.
  • Gebregziabher, M., and S. M. DeSantis. 2010. Latent class based multiple imputation approach for missing categorical data. Journal of Statistical Planning and Inference 140:3252–3262. doi:10.1016/j.jspi.2010.04.020.
  • Gelman, A. 2002. Prior distribution. Encyclopedia of Envioromnentrics 3:1634–1637.
  • Gensler, L. S., M. M. Ward, J. D. Reveille, M. H. Weisman, and J. C. Davis Jr. 2008. Clinical, radiographic and functional differences between juvenile-onset and adult-onset ankylosing spondylitis: Results from the PSOAS cohort. Annals of the Rheumatic Diseases 67 (2):233–237.
  • Green, P. J. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (4):711–732. doi:10.1093/biomet/82.4.711.
  • Harel, O., H. Chung, and D. Miglioretti. 2013. Latent class regression: Inference and estimation with two-stage multiple imputation. Biometrical Journal 55 (4):541–553. doi:10.1002/bimj.v55.4.
  • Haroon, N., T. Kim, and R. D. Inman. 2011. Continuance of non-steroidal anti-inflammatory drugs may reduce radiographic progression in ankylosing spondylitis patients on biological therapy. Arthritis and Rheumatism 63 (10):1593–1595.
  • Hjort, N., C. Holmes, and P. M̈uller, Eds.. 2010. Bayesian nonparametrics: Principles and practice. Cambridge, UK: Cambridge University Press.
  • Ji, Y., N. Lin, and B. Zhang. 2012. Model selection in binary and Tobit quantile regression using the Gibbs sampler. Computational Statistics & Data Analysis 56:827–839. doi:10.1016/j.csda.2011.10.003.
  • Jones, B. L., and D. S. Nagin. 2007. Advances in group-based trajectory modeling and a SAS procedure for estimating them. Sociological Methods & Research 35 (4):542–571. doi:10.1177/0049124106292364.
  • Jørgensen, A. W., L. H. Lundstrøm, J. Wetterslev, A. Astrup, and P. C. Gøtzsche. 2014. Comparison of results from different imputation techniques for missing data from an anti-obesity drug trial. PLoS One 9 (11):e111964. doi:10.1371/journal.pone.0111964.
  • Koenker, R., and B. Park. 1996. An interior point algorithm for nonlinear quantile regression. Journal of Econometrics 71 (1–2):265–283. doi:10.1016/0304-4076(96)84507-6.
  • Komunjer, I. 2005. Quasi-maximum likelihood estimation for conditional quantiles. Journal of Econometrics 128 (1):137–164. doi:10.1016/j.jeconom.2004.08.010.
  • Kozumi, H., and G. Kobayashi. 2011. Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation 81 (11):1565–1578. doi:10.1080/00949655.2010.496117.
  • Lee, M., L. Kong, and L. Weissfeld. 2012. Multiple imputation for left-censored biomarker data based on Gibbs sampling method. Statistics in Medicine 31 (17):1838–1848. doi:10.1002/sim.v31.17.
  • Lee, M., M. H. Rahbar, M. A. Brown, L. S. Gensler, M. H. Weisman, L. Diekman, and J. D. Reveille. 2018. Multiple imputation method based on weighted quantile regression models for longitudinal censored biomarker data with missing early visits. BMC Medical Research Methodology 18 (1):8. doi:10.1186/s12874-017-0463-9.
  • Li, K. H. 1988. Imputation using markov chains. Journal of Statistical Computation and Simulation 30::57–79. doi:10.1080/00949658808811085.
  • Li, Q., R. Xi, and N. Lin. 2010. Bayesian regularized quantile regression. Bayesian Analysis 5:533–556. doi:10.1214/10-BA521.
  • Little, R. J. A., and D. B. Rubin. 2002. Statistical analysis with missing data. 2nd ed. New York: John Wiley & Sons.
  • Liu, M., L. Wei, and J. Zhang. 2006. Review of guidelines and literature for handling missing data in longitudinal clinical trials with a case study. Pharmaceutical Statistics 5:7–18. doi:10.1002/pst.189.
  • Liu, M., M. J. Daniewls, and M. G. Perri. 2016. Quantile regression in the presence of monotone missingness with sensitivity analysis. Biostatistics 17 (1):108–121. doi:10.1093/biostatistics/kxv023.
  • Luo, Y., H. Lian, and M. Tian. 2012. Bayesian quantile regression for longitudinal data models. Journal of Statistical Computation and Simulation 82 (11):1635–1649. doi:10.1080/00949655.2011.590488.
  • Mackay, K., C. Mack, S. Brophy, and A. Calin. 1998. The Bath Ankylosing Spondylitis Radiology Index (BASRI): A new, validated approach to disease assessment. Arthritis and Rheumatism 41:2263–2270. doi:10.1002/1529-0131(199812)41:12<2263::AID-ART23>3.0.CO;2-I.
  • Mackinnon, A. 2010. The use and reporting of multiple imputation in medical research – A review. Journal of Internal Medicine 268 (6):586–593. doi:10.1111/j.1365-2796.2010.02274.x.
  • Manrique-Vallier, D., and J. P. Reiter. 2014. Bayesian multiple imputation for large-scale categorical data with structural zeros. Survey Methodology 40 (1):125–134.
  • Meng, X. 1994. Multiple-imputation inferences with uncongenial sources of input. Statistical Science 9 (4):538–573. doi:10.1214/ss/1177010269.
  • Miceli-Richard, C., and M. Dougados. 2002. NSAIDs in ankylosing spondylitis. Clinical and Experimental Rheumatology 20 (6 Suppl 28):S65–S66.
  • Nagin, D. S. 2005. Group-based modeling of development.  Cambridge, UK: Cambridge University Press.
  • Nagin, D. S., and C. L. Odgers. 2010. Group-based trajectory modeling in clinical research. Annual Review of Clinical Psychology 6:109–138. doi:10.1146/annurev.clinpsy.121208.131413.
  • Neelon, B., A. J. O’Malley, and S. T. Normand. 2011. A Bayesian two-part latent class model for longitudinal medical expenditure data: Assessing the impact of mental health and substance abuse parity. Biometrics 67 (1):280–289. doi:10.1111/j.1541-0420.2010.01439.x.
  • Rahbar, M. H., M. Lee, M. Hessabi, A. Tahanan, M. A. Brown, T. J. Learch, L. A. Diekman, M. H. Weisman, and J. D. Reveille. 2018. Harmonization, data management, and statistical issues related to prospective multicenter studies in Ankylosing spondylitis (AS): Experience from The Prospective Study of Ankylosing Spondylitis (PSOAS) cohort. Contemporary Clinical Trials Communications 11 (2018):127–135. doi:10.1016/j.conctc.2018.07.004.
  • Rezvan, R. H., K. J. Lee, and J. A. Simpson. 2015. The rise of multiple imputation: A review of the reporting and implementation of the method in medical research. BMC Medical Research Methodology 15:30. doi:10.1186/s12874-015-0022-1.
  • Rubin, D. B. 1987. Multiple imputation for nonresponse in surveys. New York: John Wiley & Sons.
  • Rubin, D. B. 1996. Multiple imputation after 18+ years. Journal of the American Statistical Association 91 (434):473–489. doi:10.1080/01621459.1996.10476908.
  • Si, Y., and J. P. Reiter. 2013. Nonparametric Bayesian multiple imputation for incomplete categorical variables in large-scale assessment surveys. Journal of Educational and Behavioral Statistics 38 (5):499–521. doi:10.3102/1076998613480394.
  • Spiegelhalter, D. J., N. G. Best, B. P. Carlin, and A. van der Linde. 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B 64 (4):583–639. doi:10.1111/1467-9868.00353.
  • Sriram K, Ramamoorthi RV, Ghosh P. Simultaneous Bayesian estimation of multiple quantiles with an extension to hierarchical models. SSRN Electronic Journal  2012; Indian Institute of Management (IIM) Bangalore Research Paper No. 359, 41 Pages. DOI: 10.2139/ssrn.2117722.
  • Sriram, K., R. V. Ramamoorthi, and P. Ghosh. 2013. Posterior consistency of bayesian quantile regression based on the misspecified asymmetric laplace density. Bayesian Analysis 8 (2):479–504. doi:10.1214/13-BA817.
  • Taddy, M. A., and A. Kottas. 2010. A Bayesian nonparametric approach to inference for quantile regression. Journal of Business & Economic Statistics 28:357–369. doi:10.1198/jbes.2009.07331.
  • van Buuren, S., and K. Groothuis-Oudshoorn. 2013. mice: Multivariate imputation by chained equations in R. Journal of Statistical Software 8 (2):479–504.
  • van der Linden, S., H. Valkenburg, and A. Cats. 1984. Evaluation of diagnostic criteria for ankylosing spondylitis. A proposal for modification of the New York criteria. Arthritis and Rheumatism 27:361–368. doi:10.1002/art.1780270401.
  • Vidotto, D., J. K. Vermunt, and M. C. Kaptein. 2015. Multiple imputation of missing categorical data using latent class models: State of the art. Psychological Test and Assessment Modeling 57 (4):542–576.
  • Wang, J. H., and X. Feng. 2012. Multiple imputation for M-regression with censored covariates. Journal of the American Statistical Association 107 (497):194–204. doi:10.1080/01621459.2011.643198.
  • Wei, Y., Y. Ma, and R. J. Carroll. 2012. Multiple imputation in quantile regression. Biometrika 99 (2):423–438. doi:10.1093/biomet/ass007.
  • West, M. 1984. Outlier models and prior distributions in Bayesian linear regression. Journal of the Royal Statistical Society: Series B 46:431–439.
  • Yang, Y., H. J. Wang, and X. He. 2016. Posterior inference in Bayesian quantile regression with asymmetric laplace likelihood. International Statisitcal Review 84 (3):327–344. doi:10.1111/insr.12114.
  • Yu, K., and R. A. Moyeed. 2001. Bayesian quantile regression. Statistics & Probability Letters 54:437–447. doi:10.1016/S0167-7152(01)00124-9.
  • Yuan, Y., and G. Yin. 2012. Bayesian quantile regression for longitudinal studies with nonignorable missing data. Biometrics 66 (1):4105–4114.

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