Is it even rainier in North Vancouver? A non-parametric rank-based test for semicontinuous longitudinal data

References

• A. Arabmazar and P. Schmidt, An investigation of the robustness of the tobit estimator to non-normality, Econometrica 50 (1982), pp. 1055–1063. doi: 10.2307/1912776
   Web of Science ®Google Scholar
• M. Backer, P. Keyser, C. Vroey, and E. Lesaffre, A 12–week treatment for dermatophyte toe onychomycosis terbinafine 250 mg/day vs. itraconazole 200 mg/day - a double-blind comparative trial, Brit. J. Dermatol. 134 (1996), pp. 16–17. doi: 10.1111/j.1365-2133.1996.tb15653.x
   PubMed Web of Science ®Google Scholar
• M. Barros, M. Galea, V. Leiva, and M. Santos-Neto, Generalized tobit models: Diagnostics and application in econometrics, J. Appl. Stat. 45 (2018), pp. 145–167. doi: 10.1080/02664763.2016.1268572
   Web of Science ®Google Scholar
• B. Brown and Y.G. Wang, Standard errors and covariance matrices for smoothed rank estimators, Biometrika 92 (2005), pp. 149–158. doi: 10.1093/biomet/92.1.149
   Web of Science ®Google Scholar
• H. Campbell, Is it even rainier in North Vancouver? A non-parametric rank-based test for semicontinuous longitudinal data, preprint (2017). Available at arXiv:1711.08876.
   Google Scholar
• X. Chen and X. Yin, Nlcoptim: Solve nonlinear optimization with nonlinear constraints (2017).
   Google Scholar
• S. Datta and G.A. Satten, A signed-rank test for clustered data, Biometrics 64 (2008), pp. 501–507. doi: 10.1111/j.1541-0420.2007.00923.x
   PubMed Web of Science ®Google Scholar
• E. Dreassi and E. Rocco, A Bayesian semiparametric model for non negative semicontinuous data, Comm. Statist. Theory Methods 46 (2017), pp. 5133–5146. doi: 10.1080/03610926.2015.1096389
   Web of Science ®Google Scholar
• M.P. Epstein, X. Lin, and M. Boehnke, A tobit variance-component method for linkage analysis of censored trait data, Am. J. Hum. Genet. 72 (2003), pp. 611–620. doi: 10.1086/367924
   PubMed Web of Science ®Google Scholar
• Y. Fan, F. Han, W. Li, and X.H. Zhou, On rank estimators in increasing dimensions (2017).
   Google Scholar
• C. Fan, W. Lu, R. Song, and Y. Zhou, Concordance-assisted learning for estimating optimal individualized treatment regimes, J. R. Stat. Soc. Ser. B 79 (2017), pp. 1565–1582. doi: 10.1111/rssb.12216
   Google Scholar
• C.A. Field and A.H. Welsh, Bootstrapping clustered data, J. R. Stat. Soc. Ser. B 69 (2007), pp. 369–390. doi: 10.1111/j.1467-9868.2007.00593.x
   Google Scholar
• D.M. Finkelstein and D.A. Schoenfeld, Combining mortality and longitudinal measures in clinical trials, Stat. Med. 18 (1999), pp. 1341–1354. doi: 10.1002/(SICI)1097-0258(19990615)18:11<1341::AID-SIM129>3.0.CO;2-7
   PubMed Web of Science ®Google Scholar
• S.W. Fleming, Climatic influences on Markovian transition matrices for Vancouver daily rainfall occurrence, Atmos. Ocean 45 (2007), pp. 163–171. doi: 10.3137/ao.450304
   Web of Science ®Google Scholar
• N. Freemantle, M. Calvert, J. Wood, J. Eastaugh, and C. Griffin, Composite outcomes in randomized trials: Greater precision but with greater uncertainty?, JAMA 289 (2003), pp. 2554–2559. doi: 10.1001/jama.289.19.2554
   PubMed Web of Science ®Google Scholar
• J. George, J. Letha, and P. Jairaj, Daily rainfall prediction using generalized linear bivariate model–a case study, Procedia Technol. 24 (2016), pp. 31–38. doi: 10.1016/j.protcy.2016.05.006
   Google Scholar
• A.K. Han, Non-parametric analysis of a generalized regression model: The maximum rank correlation estimator, J. Econom. 35 (1987), pp. 303–316. doi: 10.1016/0304-4076(87)90030-3
   Web of Science ®Google Scholar
• A. Han, Large sample properties of the maximum rank correlation estimator in generalized regression models, Preprint, Department of Economics, Harvard University, Cambridge, MA, 1988.
   Google Scholar
• F. Han, H. Ji, Z. Ji, and H. Wang, A provable smoothing approach for high dimensional generalized regression with applications in genomics, Electron. J. Stat. 11 (2017), pp. 4347–4403. doi: 10.1214/17-EJS1352
   Web of Science ®Google Scholar
• D. Holden, Testing for heteroskedasticity in the tobit and probit models, J. Appl. Stat. 38 (2011), pp. 735–744. doi: 10.1080/02664760903563684
   Web of Science ®Google Scholar
• J.L. Horowitz, Bootstrap critical values for tests based on the smoothed maximum score estimator, J. Econom. 111 (2002), pp. 141–167. doi: 10.1016/S0304-4076(02)00102-1
   Web of Science ®Google Scholar
• Y. Jiang, X. He, M.L.T. Lee, B. Rosner, and J. Yan, Wilcoxon rank-based tests for clustered data with r package clusrank, preprint (2017). Available at arXiv:1706.03409.
   Google Scholar
• Z. Jin, D. Lin, L. Wei, and Z. Ying, Rank-based inference for the accelerated failure time model, Biometrika 90 (2003), pp. 341–353. doi: 10.1093/biomet/90.2.341
   Web of Science ®Google Scholar
• Z. Jin, Z. Ying, and L.J. Wei, A simple resampling method by perturbing the minimand, Biometrika 88 (2001), pp. 381–390. doi: 10.1093/biomet/88.2.381
   Web of Science ®Google Scholar
• Y. Kim and B.O. Muthén, Two-part factor mixture modeling: Application to an aggressive behavior measurement instrument, Struct. Equ. Modeling. 16 (2009), pp. 602–624. doi: 10.1080/10705510903203516
   PubMed Web of Science ®Google Scholar
• B.F. Kurland, L.L. Johnson, B.L. Egleston, and P.H. Diehr, Longitudinal data with follow-up truncated by death: Match the analysis method to research aims, Stat. Sci. 24 (2009), p. 211. doi: 10.1214/09-STS293
   PubMed Web of Science ®Google Scholar
• N.M. Laird and J.H. Ware, Random-effects models for longitudinal data, Biometrics 38 (1982), pp. 963–974. doi: 10.2307/2529876
   PubMed Web of Science ®Google Scholar
• H. Lin, Y. Li, and M.T. Tan, Estimating a unitary effect summary based on combined survival and quantitative outcomes, Comput. Stat. Data. Anal. 66 (2013), pp. 129–139. doi: 10.1016/j.csda.2013.03.028
   Web of Science ®Google Scholar
• H. Lin and H. Peng, Smoothed rank correlation of the linear transformation regression model, Comput. Stat. Data. Anal. 57 (2013), pp. 615–630. doi: 10.1016/j.csda.2012.07.012
   Web of Science ®Google Scholar
• H. Lin, L. Zhou, H. Peng, and X.H. Zhou, Selection and combination of biomarkers using roc method for disease classification and prediction, Canad. J. Statist. 39 (2011), pp. 324–343. doi: 10.1002/cjs.10107
   Web of Science ®Google Scholar
• L. Liu, R.L. Strawderman, M.E. Cowen, and Y.C.T. Shih, A flexible two-part random effects model for correlated medical costs, J. Health. Econ. 29 (2010), pp. 110–123. doi: 10.1016/j.jhealeco.2009.11.010
   PubMed Web of Science ®Google Scholar
• L. Liu, R.L. Strawderman, B.A. Johnson, and J.M. O'Quigley, Analyzing repeated measures semi-continuous data, with application to an alcohol dependence study, Stat. Methods. Med. Res. 25 (2012), pp. 133–152. doi: 10.1177/0962280212443324
   PubMedGoogle Scholar
• Y. Lo, Assessing effects of an intervention on bottle-weaning and reducing daily milk intake from bottles in toddlers using two-part random effects models, J. Data. Sci. 13 (2015), pp. 1–20.
   Google Scholar
• E. Lorenz, C. Jenkner, W. Sauerbrei, and H. Becher, Modeling variables with a spike at zero: Examples and practical recommendations, Am. J. Epidemiol. 185 (2017), pp. 650–660. doi: 10.1093/aje/kww122
   PubMed Web of Science ®Google Scholar
• S. Ma and J. Huang, Regularized ROC method for disease classification and biomarker selection with microarray data, Bioinformatics 21 (2005), pp. 4356–4362. doi: 10.1093/bioinformatics/bti724
   PubMed Web of Science ®Google Scholar
• S.E. Mahabadi, A bayesian shared parameter model for incomplete semicontinuous longitudinal data: An application to toenail dermatophyte onychomycosis study, J. Stat. Theory Appl. 13 (2014), pp. 317–332.
   Google Scholar
• R.I. Mian and M.T. Hasan, Two-part pattern-mixture model for longitudinal incomplete semi-continuous toenail data, Int. J. Stat. Med. Res. 1 (2012), pp. 120–127.
   Google Scholar
• L.A. Moyé, B.R. Davis, and C.M. Hawkins, Analysis of a clinical trial involving a combined mortality and adherence dependent interval censored endpoint, Stat. Med. 11 (1992), pp. 1705–1717. doi: 10.1002/sim.4780111305
   PubMed Web of Science ®Google Scholar
• B. Neelon, A.J. O'Malley, and V.A. Smith, Modeling zero-modified count and semicontinuous data in health services research part 1: Background and overview, Stat. Med. 35 (2016), pp. 5070–5093. doi: 10.1002/sim.7050
   PubMed Web of Science ®Google Scholar
• J. Nolan, Sphericalcubature: Numerical integration over spheres and balls in n-dimensions; multivariate polar coordinates, R package version 1 (2015).
   Google Scholar
• M.K. Olsen and J.L. Schafer, A class of models for semicontinuous longitudinal data, American statistical association proceedings on survey research methods, 1998, pp. 721–726.
   Google Scholar
• M.K. Olsen and J.L. Schafer, A two-part random-effects model for semicontinuous longitudinal data, J. Am. Stat. Assoc. 96 (2001), pp. 730–745. doi: 10.1198/016214501753168389
   Web of Science ®Google Scholar
• M. Parzen and S.R. Lipsitz, Perturbing the minimand resampling with gamma(1,1) random variables as an extension of the Bayesian bootstrap, Stat. Probab. Lett. 77 (2007), pp. 654–657. doi: 10.1016/j.spl.2006.09.017
   Web of Science ®Google Scholar
• L. Peng and Y. Huang, Survival analysis with quantile regression models, J. Am. Stat. Assoc. 103 (2008), pp. 637–649. doi: 10.1198/016214508000000355
   Web of Science ®Google Scholar
• D.B. Rubin, The Bayesian bootstrap, Ann. Statist. 9 (1981), pp. 130–134. doi: 10.1214/aos/1176345338
   Web of Science ®Google Scholar
• J.L. Schafer and M.K. Olsen, Modeling and imputation of semicontinuous survey variables, Proceedings of the federal committee on statistical methodology research conference, Citeseer, 1999, pp. 565–74.
   Google Scholar
• R.P. Sherman, The limiting distribution of the maximum rank correlation estimator, Econometrica 61 (1993), pp. 123–137. doi: 10.2307/2951780
   Web of Science ®Google Scholar
• X. Su and S. Luo, Analysis of censored longitudinal data with skewness and a terminal event, Comm. Statist. Simul. Comput. 46 (2017), pp. 5378–5391. doi: 10.1080/03610918.2016.1157181
   PubMed Web of Science ®Google Scholar
• L. Su, B.D. Tom, and V.T. Farewell, Bias in 2-part mixed models for longitudinal semicontinuous data, Biostatistics 10 (2009), pp. 374–389. doi: 10.1093/biostatistics/kxn044
   PubMed Web of Science ®Google Scholar
• V. Subbotin, Asymptotic and bootstrap properties of rank regressions, Working paper, Northwestern University, 2007.
   Google Scholar
• D.J. Thompson, Survival models for data arising from multiphase hazards, latent subgroups or subject to time-dependent treatment effects, Ph.D. diss., Simon Fraser University, 2011.
   Google Scholar
• B.D. Tom, L. Su, and V.T. Farewell, A corrected formulation for marginal inference derived from two-part mixed models for longitudinal semi-continuous data, Stat. Methods. Med. Res. 25 (2016), pp. 2014–2020. doi: 10.1177/0962280213509798
   PubMed Web of Science ®Google Scholar
• J.A. Tooze, G.K. Grunwald, and R.H. Jones, Analysis of repeated measures data with clumping at zero, Stat. Methods. Med. Res. 11 (2002), pp. 341–355. doi: 10.1191/0962280202sm291ra
   PubMed Web of Science ®Google Scholar
• V. Tran, D. Liu, A.K. Pradhan, K. Li, C.R. Bingham, B.G. Simons-Morton, and P.S. Albert, Assessing risk-taking in a driving simulator study: Modeling longitudinal semi-continuous driving data using a two-part regression model with correlated random effects, Anal. Methods Accident Res. 5 (2015), pp. 17–27. doi: 10.1016/j.amar.2014.12.001
   PubMed Web of Science ®Google Scholar
• W. Tu and X.H. Zhou, A Wald test comparing medical costs based on log-normal distributions with zero valued costs, Stat. Med. 18 (1999), pp. 2749–2761. doi: 10.1002/(SICI)1097-0258(19991030)18:20<2749::AID-SIM195>3.0.CO;2-C
   PubMed Web of Science ®Google Scholar
• J. Twisk and F. Rijmen, Longitudinal tobit regression: A new approach to analyze outcome variables with floor or ceiling effects, J. Clin. Epidemiol. 62 (2009), pp. 953–958. doi: 10.1016/j.jclinepi.2008.10.003
   PubMed Web of Science ®Google Scholar
• F. van Leth and J.M. Lange, Use of composite end points to measure clinical events' reply, J. Am. Med. Assoc. 290 (2003), pp. 1456–1457. doi: 10.1001/jama.290.11.1456-c
   Web of Science ®Google Scholar
• H. Wang, A note on iterative marginal optimization: A simple algorithm for maximum rank correlation estimation, Comput. Stat. Data. Anal. 51 (2007), pp. 2803–2812. doi: 10.1016/j.csda.2006.10.004
   Web of Science ®Google Scholar
• P. Wang and M.L. Puterman, Mixed logistic regression models, J. Agric. Biol. Environ. Stat. 3 (1998), pp. 175–200. doi: 10.2307/1400650
   Google Scholar
• B. Zhang, W. Liu, H. Zhang, Q. Chen, and Z. Zhang, Composite likelihood and maximum likelihood methods for joint latent class modeling of disease prevalence and high-dimensional semicontinuous biomarker data, Comput. Stat. 31 (2016), pp. 425–449. doi: 10.1007/s00180-015-0597-3
   Web of Science ®Google Scholar
• M. Zhou, Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model, Biometrika 92 (2005), pp. 492–498. doi: 10.1093/biomet/92.2.492
   Web of Science ®Google Scholar
• G. Zhou, Multivariate one-sided tests for multivariate normal and mixed effects regression models with missing data, semi-continuous data and censored data, Ph.D. diss., University of British Columbia, 2017.
   Google Scholar
• X.H. Zhou and W. Tu, Comparison of several independent population means when their samples contain log-normal and possibly zero observations, Biometrics 55 (1999), pp. 645–651. doi: 10.1111/j.0006-341X.1999.00645.x
   PubMed Web of Science ®Google Scholar