zbMATH — the first resource for mathematics

Integrative analysis using coupled latent variable models for individualizing prognoses. (English) Zbl 1404.68117
Summary: Complex chronic diseases (e.g., autism, lupus, and Parkinson’s) are remarkably heterogeneous across individuals. This heterogeneity makes treatment difficult for caregivers because they cannot accurately predict the way in which the disease will progress in order to guide treatment decisions. Therefore, tools that help to predict the trajectory of these complex chronic diseases can help to improve the quality of health care. To build such tools, we can leverage clinical markers that are collected at baseline when a patient first presents and longitudinally over time during follow-up visits. Because complex chronic diseases are typically systemic, the longitudinal markers often track disease progression in multiple organ systems. In this paper, our goal is to predict a function of time that models the future trajectory of a single target clinical marker tracking a disease process of interest. We want to make these predictions using the histories of many related clinical markers as input. Our proposed solution tackles several key challenges. First, we can easily handle irregularly and sparsely sampled markers, which are standard in clinical data. Second, the number of parameters and the computational complexity of learning our model grows linearly in the number of marker types included in the model. This makes our approach applicable to diseases where many different markers are recorded over time. Finally, our model accounts for latent factors influencing disease expression, whereas standard regression models rely on observed features alone to explain variability. Moreover, our approach can be applied dynamically in continous-time and updates its predictions as soon as any new data is available. We apply our approach to the problem of predicting lung disease trajectories in scleroderma, a complex autoimmune disease. We show that our model improves over state-of-the-art baselines in predictive accuracy and we provide a qualitative analysis of our model’s output. Finally, the variability of disease presentation in scleroderma makes clinical trial recruitment challenging. We show that a prognostic tool that integrates multiple types of routinely collected longitudinal data can be used to identify individuals at greatest risk of rapid progression and to target trial recruitment.

68T05 Learning and adaptive systems in artificial intelligence
62M40 Random fields; image analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
PDF BibTeX Cite
Full Text: Link
[1] Y. Allanore, R. Simms, O. Distler, M. Trojanowska, J. Pope, C.P. Denton, and J. Varga. Systemic sclerosis. Nature Reviews Disease Primers, 2015.
[2] G. Andrew and J. Gao. Scalable training of l1-regularized log-linear models. In International Conference on Machine Learning (ICML), 2007.
[3] K.H. Brodersen, F. Gallusser, J. Koehler, N. Remy, and S.L. Scott. Inferring causal impact using bayesian structural time-series models.The Annals of Applied Statistics, 9(1): 247–274, 2015. · Zbl 1454.62473
[4] S. Chib and B.H. Hamilton. Semiparametric bayes analysis of longitudinal data treatment models. Journal of Econometrics, 110(1):67–89, 2002. · Zbl 1030.62017
[5] R.Y. Coley, A.J. Fisher, M. Mamawala, H.B. Carter, K.J. Pienta, and S.L. Zeger. A bayesian hierarchical model for prediction of latent health states from multiple data sources with application to active surveillance of prostate cancer. Biometrics, 2016. · Zbl 1372.62063
[6] F.S. Collins and H. Varmus. A new initiative on precision medicine. New England Journal of Medicine, 372(9):793–795, 2015. 32
[7] J. Craig. Complex diseases: Research and applications. Nature Education, 1(1):184, 2008.
[8] A.P. Dempster, N.M. Laird, and D.B. Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B (methodological), pages 1–38, 1977. · Zbl 0364.62022
[9] F. Doshi-Velez, Y. Ge, and I. Kohane. Comorbidity clusters in autism spectrum disorders: an electronic health record time-series analysis. Pediatrics, 133(1):e54–e63, 2014.
[10] R. D”urichen, M.A.F. Pimentel, L. Clifton, A. Schweikard, and D.A. Clifton. Multitask gaussian processes for multivariate physiological time-series analysis. Biomedical Engineering, IEEE Transactions on, 62(1):314–322, 2015.
[11] P.H.C Eilers and B.D. Marx. Flexible smoothing with b-splines and penalties. Statistical Science, pages 89–102, 1996. · Zbl 0955.62562
[12] J. Friedman, T. Hastie, and R. Tibshirani. The Elements of Statistical Learning. Springer, 2001. · Zbl 0973.62007
[13] A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin. Bayesian Data Analysis. Taylor & Francis, 2014. · Zbl 1279.62004
[14] M.R Hassan and B. Nath. Stock market forecasting using hidden markov model: a new approach. In Intelligent Systems Design and Applications, 5th International Conference on, pages 192–196. IEEE, 2005.
[15] G.M. James and C.A. Sugar. Clustering for sparsely sampled functional data. Journal of the American Statistical Association, 98(462):397–408, 2003. · Zbl 1041.62052
[16] D. Khanna, C.H Tseng, N. Farmani, V. Steen, D.E. Furst, P.J. Clements, M.D. Roth, J. Goldin, R. Elashoff, J.R. Seibold, R. Saggar, and D.P. Tashkin. Clinical course of lung physiology in patients with scleroderma and interstitial lung disease: analysis of the scleroderma lung study placebo group. Arthritis & Rheumatism, 63(10):3078–3085, 2011.
[17] S. Kleinberg and G. Hripcsak. A review of causal inference for biomedical informatics. Journal of Biomedical Informatics, 44(6):1102–1112, 2011.
[18] J.M. Lange, R.A. Hubbard, L.Y.T Inoue, and V.N. Minin. A joint model for multistate disease processes and random informative observation times, with applications to electronic medical records data. Biometrics, 71(1):90–101, 2015. · Zbl 1419.62384
[19] M. L’azaro-Gredilla, S. Van Vaerenbergh, and N.D. Lawrence. Overlapping mixtures of gaussian processes for the data association problem. Pattern Recognition, 45(4):1386– 1395, 2012. · Zbl 1231.62179
[20] D.S. Lee, P.C. Austin, J.L. Rouleau, P.P. Liu, D. Naimark, and J.V. Tu. Predicting mortality among patients hospitalized for heart failure: derivation and validation of a clinical model. Journal of the American Medical Association, 290(19):2581–2587, 2003. 33
[21] S.J.G. Lewis, T. Foltynie, A.D. Blackwell, T.W. Robbins, A.M. Owen, and R.A. Barker. Heterogeneity of parkinsons disease in the early clinical stages using a data driven approach. Journal of Neurology, Neurosurgery & Psychiatry, 76(3):343–348, 2005.
[22] R.J.A. Little and D.B. Rubin. Statistical Analysis with Missing Data. John Wiley & Sons, 2014. · Zbl 0665.62004
[23] Z. Liu and M. Hauskrecht. Clinical time series prediction: Toward a hierarchical dynamical system framework. Artificial Intelligence in Medicine, 2014.
[24] J. L”otvall, C.A. Akdis, L.B. Bacharier, L. Bjermer, T.B. Casale, A. Custovic, R.F. Lemanske, A.J. Wardlaw, S.E. Wenzel, and P.A. Greenberger. Asthma endotypes: a new approach to classification of disease entities within the asthma syndrome. Journal of Allergy and Clinical Immunology, 127(2):355–360, 2011.
[25] K.P. Murphy. Dynamic bayesian networks: representation, inference and learning. PhD thesis, University of California, Berkeley, 2002.
[26] K.P. Murphy. Machine Learning: A Probabilistic Perspective. MIT press, 2012. · Zbl 1295.68003
[27] J.B. Oliva, W. Neiswanger, B. P’oczos, E.P. Xing, H. Trac, S. Ho, and J.G. Schneider. Fast function to function regression. In Conference on Artificial Intelligence and Statistics (AISTATS), 2015.
[28] C. Proust-Lima, M. S’ene, J.M.G Taylor, and H. Jacqmin-Gadda. Joint latent class models for longitudinal and time-to-event data: A review. Statistical Methods in Medical Research, 23(1):74–90, 2014.
[29] J.A. Quinn, C.K. Williams, and N. McIntosh. Factorial switching linear dynamical systems applied to physiological condition monitoring. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 31(9):1537–1551, 2009.
[30] R. Raina, Y. Shen, A. Mccallum, and A.Y. Ng.Classification with hybrid generative/discriminative models.In Advances in Neural Information Processing Systems (NIPS), 2003.
[31] J.O. Ramsay. Functional Data Analysis. Wiley Online Library, 2006.
[32] C.E. Rasmussen and C.K. Williams. Gaussian Processes for Machine Learning. The MIT Press, 2006. · Zbl 1177.68165
[33] D. Rizopoulos. Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics, 67(3):819–829, 2011. · Zbl 1226.62124
[34] D. Rizopoulos and P. Ghosh. A bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event. Statistics in Medicine, 30(12):1366–1380, 2011.
[35] S. Roberts, M. Osborne, M. Ebden, S. Reece, N. Gibson, and S. Aigrain. Gaussian processes for time-series modelling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1984):20110550, 2013. 34 · Zbl 1353.62103
[36] K.R. Rosenbloom, C.A. Sloan, V.S. Malladi, T.R. Dreszer, K. Learned, V.M. Kirkup, M.C. Wong, M. Maddren, R. Fang, S.G. Heitner, B.T. Lee, G.P. Barber, R.A. Harte, M. Diekhans, J.C. Long, S.P. Wilder, A.S. Zweig, D. Karolchik, R.M. Kuhn, D. Haussler, and W.J. Kent. Encode data in the UCSC genome browser: year 5 update. Nucleic acids research, 41(D1):D56–D63, 2013.
[37] D.B. Rubin. Inference and missing data. Biometrika, 63(3):581–592, 1976. · Zbl 0344.62034
[38] S. Saria and A. Goldenberg. Subtyping: What Is It and Its Role in Precision Medicine. IEEE Intelligent Systems, 30, 2015.
[39] P.F. Schulam and S. Saria. A framework for individualizing predictions of disease trajectories by exploiting multi-resolution structure. In Advances in Neural Information Processing Systems (NIPS), pages 748–756, 2015.
[40] P.F. Schulam, F. Wigley, and S. Saria. Clustering longitudinal clinical marker trajectories from electronic health data: Applications to phenotyping and endotype discovery. In Conference on Artificial Intelligence (AAAI), 2015.
[41] J.Q. Shi, R. Murray-Smith, and D.M. Titterington. Hierarchical gaussian process mixtures for regression. Statistics and Computing, 15(1):31–41, 2005.
[42] J.Q. Shi, B. Wang, E.J. Will, and R.M. West.Mixed-effects gaussian process functional regression models with application to dose–response curve prediction. Statistics in Medicine, 31(26):3165–3177, 2012.
[43] D.P. Tashkin et al. Cyclophosphamide versus placebo in scleroderma lung disease. New England Journal of Medicine, 354(25):2655–2666, 2006.
[44] J. Varga, C.P. Denton, and F.M. Wigley. Scleroderma: From Pathogenesis to Comprehensive Management. Springer Science & Business Media, 2012.
[45] H. Wang, F. Nie, H. Huang, J. Yan, S. Kim, S. Risacher, A. Saykin, and L. Shen. High-order multi-task feature learning to identify longitudinal phenotypic markers for alzheimer’s disease progression prediction. In Advances in Neural Information Processing Systems (NIPS), pages 1277–1285, 2012.
[46] Y. Xu, Y. Xu, and S. Saria. A bayesian nonparametic approach for estimating individualized treatment-response curves. arXiv preprint arXiv:1608.05182, 2016.
[47] J. Zhou, L. Yuan, J. Liu, and J. Ye. A multi-task learning formulation for predicting disease progression. In International Conference on Knowledge Discovery and Data Mining (KDD), pages 814–822, 2011. 35
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.