Skip to main content
Top

2015 | OriginalPaper | Chapter

A Mixed-Effects Model with Time Reparametrization for Longitudinal Univariate Manifold-Valued Data

Authors : J.-B. Schiratti, S. Allassonnière, A. Routier, O. Colliot, S. Durrleman, the Alzheimers Disease Neuroimaging Initiative

Published in: Information Processing in Medical Imaging

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Mixed-effects models provide a rich theoretical framework for the analysis of longitudinal data. However, when used to analyze or predict the progression of a neurodegenerative disease such as Alzheimer’s disease, these models usually do not take into account the fact that subjects may be at different stages of disease progression and the interpretation of the model may depend on some implicit reference time. In this paper, we propose a generative statistical model for longitudinal data, described in a univariate Riemannian manifold setting, which estimates an average disease progression model, subject-specific time shifts and acceleration factors. The time shifts account for variability in age at disease-onset time. The acceleration factors account for variability in speed of disease progression. For a given individual, the estimated time shift and acceleration factor define an affine reparametrization of the average disease progression model. This statistical model has been used to analyze neuropsychological assessments scores and cortical thickness measurements from the Alzheimer’s Disease Neuroimaging Initiative database. The numerical results showed that we can distinguish between slow versus fast progressing and early versus late-onset individuals.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Jack Jr., C.R., Knopman, D.S., Jagust, W.J., Shaw, L.M., Aisen, P.S., Weiner, M.W.: Hypothetical model of dynamic biomarkers of the Alzheimer’s pathological cascade. Lancet Neurol. 9(1), 119–128 (2010)CrossRef Jack Jr., C.R., Knopman, D.S., Jagust, W.J., Shaw, L.M., Aisen, P.S., Weiner, M.W.: Hypothetical model of dynamic biomarkers of the Alzheimer’s pathological cascade. Lancet Neurol. 9(1), 119–128 (2010)CrossRef
2.
go back to reference Samtani, M.N., Raghavan, N., Shi, Y., Novak, G., Farnum, M., Lobanov, V.: Disease progression model in subjects with mild cognitive impairment from the Alzheimer’s disease neuroimaging initiative: CSF biomarkers predict population subtypes. Brit. J. Clin. Pharmacol. 75(1), 146–161 (2013)CrossRef Samtani, M.N., Raghavan, N., Shi, Y., Novak, G., Farnum, M., Lobanov, V.: Disease progression model in subjects with mild cognitive impairment from the Alzheimer’s disease neuroimaging initiative: CSF biomarkers predict population subtypes. Brit. J. Clin. Pharmacol. 75(1), 146–161 (2013)CrossRef
3.
go back to reference Delor, I., Charoin, J.E., Gieschke, R., Retout, S., Jacqmin, P.: Modeling Alzheimers disease progression using disease onset time and disease trajectory concepts applied to cdr-sob scores from ADNI. CPT Pharmacometrics Syst. Pharmacol. 2(10), e78 (2013)CrossRef Delor, I., Charoin, J.E., Gieschke, R., Retout, S., Jacqmin, P.: Modeling Alzheimers disease progression using disease onset time and disease trajectory concepts applied to cdr-sob scores from ADNI. CPT Pharmacometrics Syst. Pharmacol. 2(10), e78 (2013)CrossRef
4.
go back to reference Yang, E., Farnum, M., Lobanov, V., Schultz, T., Raghavan, N., Samtani, M.N.: Quantifying the pathophysiological timeline of Alzheimer’s disease. J. Alzheimer’s Dis. 26(4), 745–753 (2011) Yang, E., Farnum, M., Lobanov, V., Schultz, T., Raghavan, N., Samtani, M.N.: Quantifying the pathophysiological timeline of Alzheimer’s disease. J. Alzheimer’s Dis. 26(4), 745–753 (2011)
5.
go back to reference Laird, N.M., Ware, J.H.: Random-effects models for longitudinal data. Biometrics 38, 963–974 (1982)MATHCrossRef Laird, N.M., Ware, J.H.: Random-effects models for longitudinal data. Biometrics 38, 963–974 (1982)MATHCrossRef
6.
go back to reference DoCarmo, M.P.: Riemannian Geometry. Springer, Hiedelberg (1992) DoCarmo, M.P.: Riemannian Geometry. Springer, Hiedelberg (1992)
7.
go back to reference Datar, M., Muralidharan, P., Kumar, A., Gouttard, S., Piven, J., Gerig, G., Whitaker, R., Fletcher, P.T.: Mixed-effects shape models for estimating longitudinal changes in anatomy. In: Durrleman, S., Fletcher, T., Gerig, G., Niethammer, M. (eds.) STIA 2012. LNCS, vol. 7570, pp. 76–87. Springer, Heidelberg (2012) CrossRef Datar, M., Muralidharan, P., Kumar, A., Gouttard, S., Piven, J., Gerig, G., Whitaker, R., Fletcher, P.T.: Mixed-effects shape models for estimating longitudinal changes in anatomy. In: Durrleman, S., Fletcher, T., Gerig, G., Niethammer, M. (eds.) STIA 2012. LNCS, vol. 7570, pp. 76–87. Springer, Heidelberg (2012) CrossRef
8.
go back to reference Singh, N., Hinkle, J., Joshi, S., Fletcher, P.T.: A hierarchical geodesic model for diffeomorphic longitudinal shape analysis. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 560–571. Springer, Heidelberg (2013) CrossRef Singh, N., Hinkle, J., Joshi, S., Fletcher, P.T.: A hierarchical geodesic model for diffeomorphic longitudinal shape analysis. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 560–571. Springer, Heidelberg (2013) CrossRef
9.
go back to reference Lorenzi, M., Pennec, X., Frisoni, G.B., Ayache, N.: Alzheimer’s disease neuroimaging initiative: disentangling normal aging from alzheimer’s disease in structural magnetic resonance images. Neurobiol Aging 31(8), 1443–1451 (2015)CrossRef Lorenzi, M., Pennec, X., Frisoni, G.B., Ayache, N.: Alzheimer’s disease neuroimaging initiative: disentangling normal aging from alzheimer’s disease in structural magnetic resonance images. Neurobiol Aging 31(8), 1443–1451 (2015)CrossRef
10.
go back to reference Durrleman, S., Pennec, X., Trouvé, A., Braga, J., Gerig, G., Ayache, N.: Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data. IJCV 103(1), 22–59 (2013)MATHCrossRef Durrleman, S., Pennec, X., Trouvé, A., Braga, J., Gerig, G., Ayache, N.: Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data. IJCV 103(1), 22–59 (2013)MATHCrossRef
11.
go back to reference Durrleman, S., Pennec, X., Trouvé, A., Gerig, G., Ayache, N.: Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets. In: Yang, G.Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, pp. 297–304. Springer, Heidelberg (2009) CrossRef Durrleman, S., Pennec, X., Trouvé, A., Gerig, G., Ayache, N.: Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets. In: Yang, G.Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, pp. 297–304. Springer, Heidelberg (2009) CrossRef
12.
13.
go back to reference Lindstrom, M.J., Bates, D.M.: Nonlinear mixed effects models for repeated measures data. Biometrics 46, 673–687 (1990)MathSciNetCrossRef Lindstrom, M.J., Bates, D.M.: Nonlinear mixed effects models for repeated measures data. Biometrics 46, 673–687 (1990)MathSciNetCrossRef
14.
go back to reference Fonteijn, H.M., Modat, M., Clarkson, M.J., Barnes, J., Lehmann, M., Hobbs, N.Z., Alexander, D.C.: An event-based model for disease progression and its application in familial Alzheimer’s disease and Huntington’s disease. NeuroImage 60(3), 1880–1889 (2012)CrossRef Fonteijn, H.M., Modat, M., Clarkson, M.J., Barnes, J., Lehmann, M., Hobbs, N.Z., Alexander, D.C.: An event-based model for disease progression and its application in familial Alzheimer’s disease and Huntington’s disease. NeuroImage 60(3), 1880–1889 (2012)CrossRef
16.
go back to reference Braak, H., Braak, E.: Staging of Alzheimer’s disease-related neurofibrillary changes. Neurobiol Aging 16(3), 271–278 (1995)CrossRef Braak, H., Braak, E.: Staging of Alzheimer’s disease-related neurofibrillary changes. Neurobiol Aging 16(3), 271–278 (1995)CrossRef
17.
go back to reference Delacourte, A., David, J.P., Sergeant, N., Buee, L., Wattez, A., Vermersch, P., Di Menza, C.: The biochemical pathway of neurofibrillary degeneration in aging and Alzheimer’s disease. Neurology 52(6), 1158–1165 (1999)CrossRef Delacourte, A., David, J.P., Sergeant, N., Buee, L., Wattez, A., Vermersch, P., Di Menza, C.: The biochemical pathway of neurofibrillary degeneration in aging and Alzheimer’s disease. Neurology 52(6), 1158–1165 (1999)CrossRef
18.
go back to reference Benzinger, T.L., Blazey, T., Jack, C.R., Koeppe, R.A., Su, Y., Xiong, C., Morris, J.C.: Regional variability of imaging biomarkers in autosomal dominant Alzheimer’s disease. Proc. Natl. Acad. Sci. USA 110(47), 18982–18987 (2013)CrossRef Benzinger, T.L., Blazey, T., Jack, C.R., Koeppe, R.A., Su, Y., Xiong, C., Morris, J.C.: Regional variability of imaging biomarkers in autosomal dominant Alzheimer’s disease. Proc. Natl. Acad. Sci. USA 110(47), 18982–18987 (2013)CrossRef
19.
go back to reference Desikan, R.S., Ségonne, F., Fischl, B., Quinn, B.T., Dickerson, B.C., Blacker, D., Killiany, R.J.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage 31(3), 968–980 (2006)CrossRef Desikan, R.S., Ségonne, F., Fischl, B., Quinn, B.T., Dickerson, B.C., Blacker, D., Killiany, R.J.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage 31(3), 968–980 (2006)CrossRef
Metadata
Title
A Mixed-Effects Model with Time Reparametrization for Longitudinal Univariate Manifold-Valued Data
Authors
J.-B. Schiratti
S. Allassonnière
A. Routier
O. Colliot
S. Durrleman
the Alzheimers Disease Neuroimaging Initiative
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-19992-4_44

Premium Partner