Bayesian functional joint models for multivariate longitudinal and time-to-event data. (English) Zbl 1469.62103
Summary: A multivariate functional joint model framework is proposed which enables the repeatedly measured functional outcomes, scalar outcomes, and survival process to be modeled simultaneously while accounting for association among the multiple (functional and scalar) longitudinal and survival processes. This data structure is increasingly common across medical studies of neurodegenerative diseases and is exemplified by the motivating Alzheimer’s Disease Neuroimaging Initiative (ADNI) study, in which serial brain imaging, clinical and neuropsychological assessments are collected to measure the progression of Alzheimer’s disease (AD). The proposed functional joint model consists of a longitudinal function-on-scalar submodel, a regular longitudinal submodel, and a survival submodel which allows time-dependent functional and scalar covariates. A Bayesian approach is adopted for parameter estimation and a dynamic prediction framework is introduced for predicting the subjects’ future health outcomes and risk of AD conversion. The proposed model is evaluated by a simulation study and is applied to the motivating ADNI study.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
References:
| [1] | Apostolova, L. G.; Mosconi, L.; Thompson, P. M.; Green, A. E.; Hwang, K. S.; Ramirez, A.; Mistur, R.; Tsui, W. H.; de Leon, M. J., Subregional hippocampal atrophy predicts alzheimer’s dementia in the cognitively normal, Neurobiol. Aging, 31, 7, 1077-1088, (2010) |
| [2] | Brumback, B. A.; Rice, J. A., Smoothing spline models for the analysis of nested and crossed samples of curves, J. Amer. Statist. Assoc., 93, 443, 961-976, (1998) · Zbl 1064.62515 |
| [3] | Chen, K. H.M.; Chuah, L. Y.M.; Sim, S. K.Y.; Chee, M. W.L., Hippocampal region-specific contributions to memory performance in normal elderly, Brain Cogn., 72, 3, 400-407, (2010) |
| [4] | Corder, E.; Saunders, A.; Strittmatter, W.; Schmechel, D.; Gaskell, P.; Small, G.; Roses, A. D.; Haines, J.; Pericak-Vance, M. A., Gene dose of apolipoprotein E type 4 allele and the risk of alzheimer’s disease in late onset families, Science, 261, 5123, 921-923, (1993) |
| [5] | Crainiceanu, C. M.; Goldsmith, A. J., Bayesian functional data analysis using winbugs, J. Stat. Softw., 32, 11, (2010) |
| [6] | Crainiceanu, C. M.; Staicu, A.-M.; Di, C.-Z., Generalized multilevel functional regression, J. Amer. Statist. Assoc., 104, 488, 1550-1561, (2009) · Zbl 1205.62099 |
| [7] | Cui, Y.; Liu, B.; Luo, S.; Zhen, X.; Fan, M.; Liu, T.; Zhu, W.; Park, M.; Jiang, T.; Jin, J. S., Identification of conversion from mild cognitive impairment to alzheimer’s disease using multivariate predictors, PLoS One, 6, 7, (2011) |
| [8] | Di, C.-Z.; Crainiceanu, C. M.; Caffo, B. S.; Punjabi, N. M., Multilevel functional principal component analysis, Ann. Appl. Stat., 3, 1, 458-488, (2009) · Zbl 1160.62061 |
| [9] | Du, A. T., Magnetic resonance imaging of the entorhinal cortex and hippocampus in mild cognitive impairment and alzheimer’s disease, J. Neurol. Neurosurg. Psychiatry, 71, 4, 441-447, (2001) |
| [10] | Dunson, D. B., Dynamic latent trait models for multidimensional longitudinal data, J. Amer. Statist. Assoc., 98, 463, 555-563, (2003) · Zbl 1040.62100 |
| [11] | Faucett, C. L.; Thomas, D. C., Simultaneously modelling censored survival data and repeatedly measured covariates: A Gibbs sampling approach, Stat. Med., 15, 15, 1663-1685, (1996) |
| [12] | Frisoni, G. B.; Fox, N. C.; Jack, C. R.; Scheltens, P.; Thompson, P. M., The clinical use of structural mri in alzheimer disease, Nature Reviews Neurology, 6, 2, 67-77, (2010) |
| [13] | Gelman, A., Prior distributions for variance parameters in hierarchical models (comment on article by browne and draper), Bayesian Anal., 1, 3, 515-534, (2006) · Zbl 1331.62139 |
| [14] | Gelman, A.; Carlin, J. B.; Stern, H. S.; Rubin, D. B., Bayesian data analysis, (2013), CRC Press |
| [15] | Gilks, W. R.; Best, N. G.; Tan, K. K.C., Adaptive rejection metropolis sampling within Gibbs sampling, J. R. Stat. Soc. Ser. C. Appl. Stat., 44, 4, 455-472, (1995) · Zbl 0893.62110 |
| [16] | Goldsmith, J.; Kitago, T., Assessing systematic effects of stroke on motor control by using hierarchical function-on-scalar regression, J. R. Stat. Soc. Ser. C. Appl. Stat., 65, 2, 215-236, (2016) |
| [17] | Goldsmith, J.; Zipunnikov, V.; Schrack, J., Generalized multilevel function-on-scalar regression and principal component analysis, Biometrics, 71, 2, 344-353, (2015) · Zbl 1390.62259 |
| [18] | Gomar, J. J.; Bobes-Bascaran, M. T.; Conejero-Goldberg, C.; Davies, P.; Goldberg, T. E., Utility of combinations of biomarkers, cognitive markers, and risk factors to predict conversion from mild cognitive impairment to alzheimer disease in patients in the alzheimer’s disease neuroimaging initiative, Arch. Gen. Psychiatry, 68, 9, 961-969, (2011) |
| [19] | Greven, S.; Crainiceanu, C.; Caffo, B.; Reich, D., Longitudinal functional principal component analysis, Electron. J. Stat., 4, 1022-1054, (2010) · Zbl 1329.62334 |
| [20] | Guo, W., Functional mixed effects models, Biometrics, 58, 1, 121-128, (2002) · Zbl 1209.62072 |
| [21] | Henderson, R.; Diggle, P.; Dobson, A., Joint modelling of longitudinal measurements and event time data, Biostatistics, 1, 4, 465-480, (2000) · Zbl 1089.62519 |
| [22] | Hickey, G. L.; Philipson, P.; Jorgensen, A.; Kolamunnage-Dona, R., Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues, BMC Med. Res. Methodol., 16, 117, (2016) |
| [23] | Hoffman, M. D.; Gelman, A., The no-u-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo, J. Mach. Learn. Res., 15, 1, 1593-1623, (2014) · Zbl 1319.60150 |
| [24] | Huang, M.; Yang, W.; Feng, Q.; Chen, W.; Initiative, A. D.N., Longitudinal measurement and hierarchical classification framework for the prediction of alzheimers disease, Sci. Rep., 7, (2017) |
| [25] | Jack Jr., C. R.; Knopman, D. S.; Jagust, W. J.; Shaw, L. M.; Aisen, P. S.; Weiner, M. W.; Petersen, R. C.; Trojanowski, J. Q., Hypothetical model of dynamic biomarkers of the alzheimer’s pathological cascade, Lancet Neurol., 9, 1, 119-128, (2010) |
| [26] | Jenkinson, M.; Beckmann, C. F.; Behrens, T. E.; Woolrich, M. W.; Smith, S. M., Fsl, NeuroImage, 62, 2, 782-790, (2012) |
| [27] | Lang, S.; Brezger, A., Bayesian P-splines, J. Comput. Graph. Statist., 13, 1, 183-212, (2004) |
| [28] | Li, K.; Chan, W.; Doody, R. S.; Quinn, J.; Luo, S., Prediction of conversion to alzheimers disease with longitudinal measures and time-to-event data, J. Alzheimer’s Dis., 58, 2, 361-371, (2017) |
| [29] | Li, L.; Greene, T.; Hu, B., A simple method to estimate the time-dependent receiver operating characteristic curve and the area under the curve with right censored data, Stat. Methods Med. Res., OnlineFirst, (2016) |
| [30] | Li, K.; Luo, S., Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: an application to alzheimers disease, Stat. Methods Med. Res., OnlineFirst, (2017) |
| [31] | Li, K.; Luo, S., Functional joint model for longitudinal and time-to-event data: an application to alzheimer’s disease, Stat. Med., 36, 22, 3560-3572, (2017) |
| [32] | Li, S.; Okonkwo, O.; Albert, M.; Wang, M. C., Variation in variables that predict progression from mci to ad dementia over duration of follow-up, Amer. J. Alzheimer’s Dis., 2, 1, 12-28, (2013) |
| [33] | Liu, F.; Li, Q., A Bayesian model for joint analysis of multivariate repeated measures and time to event data in crossover trials, Stat. Methods Med. Res., 25, 5, 2180-2192, (2016) |
| [34] | Morris, J. S., Functional regression, Annu. Rev. Statist. Appl., 2, 1, 321-359, (2015) |
| [35] | Morris, J. S.; Carroll, R. J., Wavelet-based functional mixed models, J. R. Stat. Soc. Ser. B Stat. Methodol., 68, 2, 179-199, (2006) · Zbl 1110.62053 |
| [36] | Neal, R. M., Mcmc using Hamiltonian dynamics, Handb. Markov Chain Monte Carlo, 2, 113-162, (2011) · Zbl 1229.65018 |
| [37] | Park, S. Y.; Staicu, A.-M., Longitudinal functional data analysis, Stat, 4, 1, 212-226, (2015) · Zbl 07847944 |
| [38] | Patenaude, B.; Smith, S. M.; Kennedy, D. N.; Jenkinson, M., A Bayesian model of shape and appearance for subcortical brain segmentation, NeuroImage, 56, 3, 907-922, (2011) |
| [39] | Perrin, R. J.; Fagan, A. M.; Holtzman, D. M., Multi-modal techniques for diagnosis and prognosis of alzheimers disease, Nature, 461, 7266, 916-922, (2009) |
| [40] | Petersen, R. C.; Smith, G. E.; Waring, S. C.; Ivnik, R. J.; Tangalos, E. G.; Kokmen, E., Mild cognitive impairment: clinical characterization and outcome, Arch. Neurol., 56, 3, 303-308, (1999) |
| [41] | Qiu, A.; Fennema-Notestine, C.; Dale, A. M.; Miller, M. I.; Initiative, A. D.N., Regional shape abnormalities in mild cognitive impairment and alzheimer’s disease, NeuroImage, 45, 3, 656-661, (2009) |
| [42] | Risacher, S. L.; Saykin, A. J.; Wes, J. D.; Shen, L.; Firpi, H. A.; McDonald, B. C., Baseline mri predictors of conversion from mci to probable ad in the adni cohort, Curr. Alzheimer Res., 6, 4, 347-361, (2009) |
| [43] | Rizopoulos, D., Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data, Biometrics, 67, 3, 819-829, (2011) · Zbl 1226.62124 |
| [44] | Rizopoulos, D.; Hatfield, L. A.; Carlin, B. P.; Takkenberg, J. J., Combining dynamic predictions from joint models for longitudinal and time-to-event data using Bayesian model averaging, J. Amer. Statist. Assoc., 109, 508, 1385-1397, (2014) |
| [45] | Ruppert, D., Selecting the number of knots for penalized splines, J. Comput. Graph. Statist., 11, 4, 735-757, (2002) |
| [46] | Ruppert, D.; Wand, M. P.; Carroll, R. J., Semiparametric regression, no. 12, (2003), Cambridge University Press · Zbl 1038.62042 |
| [47] | Schmand, B.; Huizenga, H. M.; Gool, W. A.v., Meta-analysis of CSF and MRI biomarkers for detecting preclinical alzheimer’s disease, Psychol. Med., 40, 1, 135-145, (2010) |
| [48] | Tsiatis, A. A.; Davidian, M., Joint modeling of longitudinal and time-to-event data: an overview, Statist. Sinica, 14, 3, 809-834, (2004) · Zbl 1073.62087 |
| [49] | Wang, J.; Luo, S.; Li, L., Dynamic prediction for multiple repeated measures and event time data: an application to parkinsons disease, Ann. Appl. Stat., 11, 3, 1787, (2017) · Zbl 1380.62260 |
| [50] | Weiner, M. W.; Veitch, D. P.; Aisen, P. S.; Beckett, L. A.; Cairns, N. J.; Green, R. C.; Harvey, D.; Jack, C. R.; Jagust, W.; Liu, E., The alzheimer’s disease neuroimaging initiative: a review of papers published Since its inception, Alzheimer’s Dement., 9, 5, e111-e194, (2013) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
