Multiple imputation for ordinal longitudinal data with monotone missing data patterns

References

• P.D. Allison, Multiple imputation for missing data: A cautionary tale, Sociol. Methods Res. 28 (2000), pp. 301–309. doi: 10.1177/0049124100028003003
   Web of Science ®Google Scholar
• P.D. Allison, Missing Data, SAGE, Thousand Oaks, CA, 2001.
   Google Scholar
• P.D. Allison, Imputation of categorical variables with PROC MI, in SAS Users Group International, 30th Meeting (SUGI 30), 2005, April.
   Google Scholar
• C.V. Ananth and D.G. Kleinbaum, Regression models for ordinal responses: A review of methods and applications, Int. J. Epidemiol. 26 (1997), pp. 1323–1333. doi: 10.1093/ije/26.6.1323
   PubMed Web of Science ®Google Scholar
• B.G. Armstrong and M. Sloan, Ordinal regression models for epidemiologic data, Am. J. Epidemiol. 129 (1989), pp. 191–204.
   PubMed Web of Science ®Google Scholar
• D.J. Bauer and S.K. Sterba, Fitting multilevel models with ordinal outcomes: Performance of alternative specifications and methods of estimation, Psychol. Methods 16 (2011), pp. 373–390. doi: 10.1037/a0025813
   PubMed Web of Science ®Google Scholar
• R. Bender and U. Grouven, Using binary logistic regression models for ordinal data with non-proportional odds, J. Clin. Epidemiol. 51 (1998), pp. 809–816. doi: 10.1016/S0895-4356(98)00066-3
   PubMed Web of Science ®Google Scholar
• C. Beunckens, G. Molenberghs, and M.G. Kenward, Direct likelihood analysis versus simple forms of imputation for missing data in randomized clinical trials, Clin. Trials 2 (2005), pp. 379–386. doi: 10.1191/1740774505cn119oa
   PubMed Web of Science ®Google Scholar
• S. Buuren and K. Groothuis-Oudshoorn, MICE: Multivariate imputation by chained equations in R, J. Stat. Softw. 45 (2011). doi: 10.18637/jss.v045.i03
   PubMed Web of Science ®Google Scholar
• J.R. Carpenter and M.G. Kenward, Multiple Imputation and its Application, Wiley, Chichester, 2013.
   Google Scholar
• L. Chen, M. Toma-Drane, R.F. Valois, and J.W. Drane, Multiple imputation for missing ordinal data, J. Mod. Appl. Stat. Methods 4 (2005), p. 26.
   Google Scholar
• K. -H. Choi, C. Hoff, S.E. Gregorich, O. Grinstead, C. Gomez, and W. Hussey, The efficacy of female condom skills training in HIV risk reduction among women: A randomized controlled trial, Am. J. Public Health 98 (2008), pp. 1841–1848. doi: 10.2105/AJPH.2007.113050
   PubMed Web of Science ®Google Scholar
• L.M. Collins, J.L. Schafer, and C. -M. Kam, A comparison of inclusive and restrictive strategies in modern missing data procedures, Psychol. Methods 6 (2001), pp. 330–351. doi: 10.1037/1082-989X.6.4.330
   PubMed Web of Science ®Google Scholar
• C. Cox, Location-scale cumulative odds models for ordinal data: A generalized non-linear model approach, Stat. Med. 14 (1995), pp. 1191–1203. doi: 10.1002/sim.4780141105
   PubMed Web of Science ®Google Scholar
• R.M. Daniel and M.G. Kenward, A method for increasing the robustness of multiple imputation, Comput. Stat. Data Anal. 56 (2012), pp. 1624–1643. doi: 10.1016/j.csda.2011.10.006
   Web of Science ®Google Scholar
• S. Das and R.M. Rahman, Application of ordinal logistic regression analysis in determining risk factors of child malnutrition in Bangladesh, Nutr. J. 10 (2011), p. 124. doi: 10.1186/1475-2891-10-124
   PubMed Web of Science ®Google Scholar
• H. Demirtas and D. Hedeker, An imputation strategy for incomplete longitudinal ordinal data, Stat. Med. 27 (2008), pp. 4086–4093. doi: 10.1002/sim.3239
   PubMed Web of Science ®Google Scholar
• H. Demirtas, S.A. Freels, and R.M. Yucel, Plausibility of multivariate normality assumption when multiply imputing non-Gaussian continuous outcomes: a simulation assessment, J. Stat. Comput. Simul. 78 (2008), pp. 69–84. doi: 10.1080/10629360600903866
   Web of Science ®Google Scholar
• A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B (1977), pp. 1–38.
   Google Scholar
• P.J. Diggle, P. Heagerty, K.Y. Liang, and S.L. Zeger, Analysis of Longitudinal Data, Oxford, Oxford University Press, 2002.
   Google Scholar
• P. Diggle and M.G. Kenward, Informative drop-out in longitudinal data analysis, Appl. Stat. (1994), pp. 49–93. doi: 10.2307/2986113
   Web of Science ®Google Scholar
• M.J. Gameroff, Using the proportional odds model for health-related outcomes: Why, when, and how with various SAS procedures. In SUGI 30 (2005, April), pp. 205–230.
   Google Scholar
• J.J. Heckman, The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models, in Annals of Economic and Social Measurement, Vol. 5, NBER, Cambridge, 1976, pp. 475–492.
   Google Scholar
• D.T. Kadengye, W. Cools, E. Ceulemans, and W. Van den Noortgate, Simple imputation methods versus direct likelihood analysis for missing item scores in multilevel educational data, Behav. Res. Methods 44 (2012), pp. 516–531. doi: 10.3758/s13428-011-0157-x
   PubMed Web of Science ®Google Scholar
• M.G. Kenward, Selection models for repeated measurements with non-random dropout: An illustration of sensitivity, Stat. Med. 17 (1998), pp. 2723–2732. doi: 10.1002/(SICI)1097-0258(19981215)17:23<2723::AID-SIM38>3.0.CO;2-5
   PubMed Web of Science ®Google Scholar
• M.G. Kenward and J. Carpenter, Multiple imputation: Current perspectives, Statist. Methods Med. Res. 16 (2007), pp. 199–218. doi: 10.1177/0962280206075304
   PubMed Web of Science ®Google Scholar
• K.J. Lee and J.B. Carlin, Multiple imputation for missing data: fully conditional specification versus multivariate normal imputation, J. Epidemiol. 171 (2010), pp. 624–632. doi: 10.1093/aje/kwp425
   Web of Science ®Google Scholar
• K.J. Lee, J.C. Galati, J.A. Simpson, and J.B. Carlin, Comparison of methods for imputing ordinal data using multivariate normal imputation: A case study of non-linear effects in a large cohort study, Stat. Med. 31 (2012), pp. 4164–4174. doi: 10.1002/sim.5445
   PubMed Web of Science ®Google Scholar
• K. -Y. Liang and S.L. Zeger, Longitudinal data analysis using generalized linear models, Biometrika 73 (1986), pp. 13–22. doi: 10.1093/biomet/73.1.13
   Web of Science ®Google Scholar
• I. Liu and A. Agresti, The analysis of ordered categorical data: An overview and a survey of recent developments, Test 14 (2005), pp. 1–73. doi: 10.1007/BF02595397
   Web of Science ®Google Scholar
• C.H. Mallinckrodt, S.W.S. Clark, R.J. Carroll, and G. Molenberghs, Assessing response profiles from incomplete longitudinal clinical trial data under regulatory considerations, J. Biopharm. Stat. 13 (2003), pp. 179–190. doi: 10.1081/BIP-120019265
   PubMedGoogle Scholar
• P. McCullagh, Regression models for ordinal data, J. Royal Stat. Soc. Ser. B (1980), pp. 109–142.
   Google Scholar
• X.L. Meng, Multiple-imputation inferences with uncongenial sources of input, Statist. Sci. 9 (1994), pp. 538–558.
   Web of Science ®Google Scholar
• G. Molenberghs, C. Beunckens, C. Sotto, and M.G. Kenward, Every missingness not at random model has a missingness at random counterpart with equal fit, J. R. Statist. Soc. Ser. B 70 (2008), pp. 371–388. doi: 10.1111/j.1467-9868.2007.00640.x
   Google Scholar
• G. Molenberghs and M. Kenward, Missing Data in Clinical Studies, Vol. 61, Chichester, Wiley, 2007.
   Google Scholar
• G. Molenberghs and G. Verbeke, Models for Discrete Longitudinal Data, Springer, New York, 2005.
   Google Scholar
• J. Newsom, R.N. Jones, and S.M. Hofer (Eds.), Longitudinal Data Analysis: A Practical Guide for Researchers in Aging, Health, and Social Sciences, New York, Routledge, 2012.
   Google Scholar
• Y. Pawitan, In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford, Oxford University Press, 2001.
   Google Scholar
• B. Ratitch, I. Lipkovich, and M. O'kelly, Combining analysis results from multiply imputed categorical data, PharmaSUG 2013-PaperSP03, pp. 1–10.
   Google Scholar
• C.H. Rhoads, Problems with tests of the missingness mechanism in quantitative policy studies, Stat. Politics Policy 3 (2012). doi: 10.1515/2151-7509.1012
   Google Scholar
• J.M. Robins and R.D. Gill, Non-response models for the analysis of non-monotone ignorable missing data, Stat. Med. 16 (1997), pp. 39–56. doi: 10.1002/(SICI)1097-0258(19970115)16:1<39::AID-SIM535>3.0.CO;2-D
   PubMed Web of Science ®Google Scholar
• J.M. Robins, A. Rotnitzky, and L.P. Zhao, Analysis of semiparametric regression models for repeated outcomes in the presence of missing data, J. Am. Stat. Assoc. 90 (1995), pp. 106–121. doi: 10.1080/01621459.1995.10476493
   Web of Science ®Google Scholar
• P. Royston, Multiple imputation of missing values, Stata J. 4 (2004), pp. 227–241.
   Web of Science ®Google Scholar
• D.B. Rubin, Inference and missing data, Biometrika 63 (1976), pp. 581–592. doi: 10.1093/biomet/63.3.581
   Web of Science ®Google Scholar
• D.B. Rubin, Formalizing subjective notions about the effect of nonrespondents in sample surveys, J. Am. Statist. Assoc. 72 (1977), pp. 538–543. doi: 10.1080/01621459.1977.10480610
   Web of Science ®Google Scholar
• D.B. Rubin, Multiple Imputation for Nonresponse in Surveys, Wiley, New York, 1987.
   Google Scholar
• D.B. Rubin and J.L. Schafer, Efficiently creating multiple imputations for incomplete multivariate normal data, in Proceedings of the Statistical Computing Section of the American Statistical Association 83, American Statistical Association, Alexandria, VA, 1990, p. 88.
   Google Scholar
• J.L. Schafer, Analysis of Incomplete Multivariate Data, Chapman and Hall, New York, 1997.
   Google Scholar
• J.L. Schafer, Multiple imputation in multivariate problems when the imputation and analysis models differ, Statist. Neerlandica 57 (2003), pp. 19–35. doi: 10.1111/1467-9574.00218
   Web of Science ®Google Scholar
• J.L. Schafer and R.M Yucel, Computational strategies for multivariate linear mixed-effects models with missing values, J. Comput. Graph. Stat. 11 (2002), pp. 437–457. doi: 10.1198/106186002760180608
   Web of Science ®Google Scholar
• S.R. Seaman, J.W. Bartlett, and I.R. White, Multiple imputation of missing covariates with non-linear effects and interactions: An evaluation of statistical methods, BMC Med. Res. Methodol. 12 (2012), p. 46. doi: 10.1186/1471-2288-12-46
   PubMed Web of Science ®Google Scholar
• R.L. Seitzman, V.B. Mahajan, C. Mangione, J.A. Cauley, K.E. Ensrud, K.L. Stone, S.R. Cummings, M.C. Hochberg, T.A. Hillier, J.S. Sinsheimer, F. Yu, and A.L. Coleman, Estrogen receptor alpha and matrix metalloproteinase 2 polymorphisms and age-related maculopathy in older women, Am. J. Epidemiol. 167 (2008), pp. 1217–1225. doi: 10.1093/aje/kwn024
   PubMed Web of Science ®Google Scholar
• M.A. Tanner and W.H. Wong, The calculation of posterior distributions by data augmentation, J. Am. Statist. Assoc. 82 (1987), pp. 528–540. doi: 10.1080/01621459.1987.10478458
   Web of Science ®Google Scholar
• UCLA: Statistical Consulting Group, Statistical computing seminars. Multiple imputation in STATA, Part1, from http://www.ats.ucl.edu/stat/stata/seminars/missing_data/mi_in_stat_pt1.htm (accessed on November 12, 2015).
   Google Scholar
• S. Van Buuren, Multiple imputation of discrete and continuous data by fully conditional specification, Statist. Methods Med. Res. 16 (2007), pp. 219–242. doi: 10.1177/0962280206074463
   PubMed Web of Science ®Google Scholar
• S. Van Buuren, Flexible Imputation of Missing Data, Boca Raton, FL, CRC Press, 2012.
   Google Scholar
• S. Van Buuren, H.C. Boshuizen, and D.L. Knook, Multiple imputation of missing blood pressure covariates in survival analysis, Stat. Med. 18 (1999), pp. 681–694. doi: 10.1002/(SICI)1097-0258(19990330)18:6<681::AID-SIM71>3.0.CO;2-R
   PubMed Web of Science ®Google Scholar
• S. Van Buuren, J.P.L. Brand, C.G.M. Groothuis-Oudshoorn, and D.B. Rubin, Fully conditional specification in multivariate imputation, J. Statist. Comput. Simul. 76 (2006), pp. 1049–1064. doi: 10.1080/10629360600810434
   Web of Science ®Google Scholar
• I.R. White, P. Royston, and A.M. Wood, Multiple imputation using chained equations: Issues and guidance for practice, Stat. Med. 30 (2011), pp. 377–399. doi: 10.1002/sim.4067
   PubMed Web of Science ®Google Scholar
• A.M. Wood, I.R. White, M. Hillsdon, and J. Carpenter, Comparison of imputation and modelling methods in the analysis of a physical activity trial with missing outcomes, Int. J. Epidemiol. 34 (2005), pp. 89–99. doi: 10.1093/ije/dyh297
   PubMed Web of Science ®Google Scholar
• L. -M. Yu, A. Burton, and O. Rivero-Arias, Evaluation of software for multiple imputation of semi-continuous data, Statist. Methods Med. Res. 16 (2007), pp. 243–258. doi: 10.1177/0962280206074464
   PubMed Web of Science ®Google Scholar
• A. Agresti, Tutorial on modeling ordered categorical response data, Psychol. Bull. 105 (1989), pp. 290–301. doi: 10.1037/0033-2909.105.2.290
   PubMed Web of Science ®Google Scholar