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Case Studies of Autoregressive Linear Mixed Effects Models: Missing Data and Time-Dependent Covariates

  • Ikuko FunatogawaEmail author
  • Takashi Funatogawa
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

In the previous chapter, we introduced autoregressive linear mixed effects models for analysis of longitudinal data. In this chapter, we provide examples of actual data analysis using these models. We also discuss two topics from the medical field: response-dependent dropouts and response-dependent dose modifications. When the missing mechanism depends on the observed, but not on the unobserved, responses, it is termed missing at random (MAR). The missing process does not need to be simultaneously modeled for the likelihood because the likelihood can be factorized into two parts: one for the measurement process and the other for the missing process. Maximum likelihood estimators are consistent under MAR if the joint distribution of the response vector is correctly specified. For the problem of dose modification, similar concepts are applied. When the dose modification depends on the observed, but not on the unobserved, responses, the dose process does not need to be simultaneously modeled for the likelihood. Here, we analyze schizophrenia data and multiple sclerosis data using autoregressive linear mixed effects models as examples of response-dependent dropouts and response-dependent dose modifications, respectively.

Keywords

Autoregressive linear mixed effects model Dose modification Longitudinal Missing Time-dependent covariate 

References

  1. Diggle PJ, Heagerty P, Liang K-Y, Zeger SL (2002) Analysis of longitudinal data (2nd edn). Oxford University PressGoogle Scholar
  2. Ellison GW, Myers LW, Mickey MR, Graves MC, Tourtellotte WW, Syndulko K, Holevoet-Howson MI, Lerner CD, Frane MV, Pettler-Jennings P (1989) A placebo-controlled, randomized, double-masked, variable dosage, clinical trial of azathioprine with and without methylprednisolone in multiple sclerosis. Neurology 39:1018–1026CrossRefGoogle Scholar
  3. Funatogawa I, Funatogawa T (2012a) An autoregressive linear mixed effects model for the analysis of unequally spaced longitudinal data with dose-modification. Stat Med 31:589–599MathSciNetCrossRefGoogle Scholar
  4. Funatogawa I, Funatogawa T (2012b) Dose-response relationship from longitudinal data with response-dependent dose-modification using likelihood methods. Biometrical J 54:494–506MathSciNetCrossRefGoogle Scholar
  5. Funatogawa I, Funatogawa T, Ohashi Y (2007) An autoregressive linear mixed effects model for the analysis of longitudinal data which show profiles approaching asymptotes. Stat Med 26:2113–2130MathSciNetCrossRefGoogle Scholar
  6. Funatogawa I, Funatogawa T, Ohashi Y (2008a) A bivariate autoregressive linear mixed effects model for the analysis of longitudinal data. Stat Med 27:6367–6378MathSciNetCrossRefGoogle Scholar
  7. Funatogawa T, Funatogawa I, Takeuchi M (2008b) An autoregressive linear mixed effects model for the analysis of longitudinal data which include dropouts and show profiles approaching asymptotes. Stat Med 27:6351–6366MathSciNetCrossRefGoogle Scholar
  8. Heitjan DF (1991) Nonlinear modeling of serial immunologic data: a case study. J Am Stat Assoc 86:891–898CrossRefGoogle Scholar
  9. Henderson R, Diggle P, Dobson A (2000) Joint modelling of longitudinal measurements and event time data. Biostatistics 1:465–480CrossRefGoogle Scholar
  10. KDOQI (2007) KDOQI clinical practice guideline and clinical practice recommendations for anemia in chronic kidney disease: 2007 update of hemoglobin target. Am J Kidney Dis 50:471–530CrossRefGoogle Scholar
  11. Laird NM (1988) Missing data in longitudinal studies. Stat Med 7:305–315CrossRefGoogle Scholar
  12. Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974CrossRefGoogle Scholar
  13. Lindsey JK (1993) Models for repeated measurements. Oxford University PressGoogle Scholar
  14. Lipkovich I, Adams DH, Mallinckrodt C, Faries D, Baron D, Houston JP (2008) Evaluating dose response from flexible dose clinical trials. BMC Psychiatry 8:3CrossRefGoogle Scholar
  15. Little RJA, Rubin DB (1987) Statistical analysis with missing data. WileyGoogle Scholar
  16. Marder SR, Meibach RC (1994) Risperidone in the treatment of schizophrenia. Am J Psychiatry 151:825–835CrossRefGoogle Scholar
  17. Misumi T, Konishi S (2016) Mixed effects historical varying-coefficient model for evaluating dose-response in flexible dose trials. J R Stat Soc Ser C 65:331–344MathSciNetCrossRefGoogle Scholar
  18. Nasserinejad K, Rosmalen J, Kort W, Rizopoulos D, Lesaffre E (2016) Prediction of hemoglobin in blood donors using a latent class mixed-effects transition model. Stat Med 35:581–594MathSciNetCrossRefGoogle Scholar
  19. National Kidney Foundation (2003) K/DOQI clinical practice guidelines for bone metabolism and disease in chronic kidney disease. Am J Kidney Dis 42(4 Suppl 3):S1–S201Google Scholar
  20. Xu J, Zeger SL (2001) Joint analysis of longitudinal data comprising repeated measures and times to events. Appl Stat 50:375–387MathSciNetzbMATHGoogle Scholar
  21. Xu XS, Yuan M, Nandy P (2012) Analysis of dose-response in flexible dose titration clinical studies. Pharm Stat 11:280–286CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Statistical Data ScienceThe Institute of Statistical MathematicsTachikawaJapan
  2. 2.Clinical Science and Strategy DepartmentChugai Pharmaceutical Co. Ltd.ChūōJapan

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