Recurrent Event Analysis in the Presence of Real-Time High Frequency Data via Random Subsampling

References

• Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (1993). Statistical Models based on Counting Processes. New York: Springer.
   Google Scholar
• Bai, J., Di, C., Xiao, L., Evenson, K. R., LaCroix, A. Z., Crainiceanu, C. M., and Buchner, D. M. (2016), “An Activity Index for Raw Accelerometry Data and its Comparison with Other Activity Metrics,” PloS One, 11, 1–14. DOI: 10.1371/journal.pone.0160644.
   Web of Science ®Google Scholar
• Baladandayuthapani, V., Mallick, B. K., Young Hong, M., Lupton, J. R., Turner, N. D., and Carroll, R. J. (2008), “Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogensis,” Biometrics, 64, 64–73. DOI: 10.1111/j.1541-0420.2007.00846.x.
   PubMed Web of Science ®Google Scholar
• Bartlett, J. W., and Hughes, R. A. (2020), “Bootstrap Inference for Multiple Imputation Under Uncongeniality and Misspecification,” Statistical Methods in Medical Research, 29, 3533–3546. DOI: 10.1177/0962280220932189.
   PubMed Web of Science ®Google Scholar
• Caffo, B. S., Jank, W., and Jones, G. L. (2005), “Ascent-based Monte Carlo Expectation–Maximization,” Journal of the Royal Statistical Society, Series B, 67, 235–251. DOI: 10.1111/j.1467-9868.2005.00499.x.
   Google Scholar
• Cassel, C., Särndal, C.-E., and Wretman, J. H. (1977), Foundations of Inference in Survey Sampling, New York: Wiley.
   Google Scholar
• Chen, K., and Müller, H.-G. (2012), “Modeling Repeated Functional Observations,” Journal of the American Statistical Association, 107, 1599–1609. DOI: 10.1080/01621459.2012.734196.
   Web of Science ®Google Scholar
• Crainiceanu, C., and Goldsmith, J. (2010), “Bayesian Functional Data Analysis Using Winbugs,” Journal of Statistical Software, 32, 1–33. DOI: 10.18637/jss.v032.i11.
   Web of Science ®Google Scholar
• Crainiceanu, C. M., Staicu, A.-M., and Di, C.-Z. (2009), “Generalized Multilevel Functional Regression,” Journal of the American Statistical Association, 104, 1550–1561. DOI: 10.1198/jasa.2009.tm08564.
   PubMed Web of Science ®Google Scholar
• Cui, E., Crainiceanu, C. M., and Leroux, A. (2021), “Additive Functional Cox Model,” Journal of Computational and Graphical Statistics, 30, 780–793. DOI: 10.1080/10618600.2020.1853550.
   PubMed Web of Science ®Google Scholar
• Di, C. Z., Crainiceanu, C. M., Caffo, B. S., and Punjabi,N. M. (2009), “Multilevel Functional Principal Component Analysis,” Annals of Applied Statistics, 3, 458–488. DOI: 10.1214/08-AOAS206SUPP.
   PubMed Web of Science ®Google Scholar
• Dong, J. (J.), Cao, J., Gill, J., Miles, C., and Plumb, T. (2021). “Functional Joint Models for Chronic Kidney Disease in Kidney Transplant Recipients,” Statistical Methods in Medical Research, 30, 1932–1943. DOI: 10.1177/09622802211009265.
   PubMed Web of Science ®Google Scholar
• Free, C., Phillips, G., Galli, L., Watson, L., Felix, L., Edwards, P., Patel, V., and Haines, A. (2013), “The Effectiveness of Mobile-Health Technology-based Health Behaviour Change or Disease Management Interventions for Health Care Consumers: A Systematic Review,” PLOS Medicine, 10, 1–45. DOI: 10.1371/journal.pmed.1001362.
   Web of Science ®Google Scholar
• Garbarino, M., Lai, M., Bender, D., Picard, R. W., and Tognetti, S. (2014), “Empatica e3—A Wearable Wireless Multi-Sensor Device for Real-Time Computerized Biofeedback and Data Acquisition,” in 2014 4th International Conference on Wireless Mobile Communication and Healthcare - Transforming Healthcare Through Innovations in Mobile and Wireless Technologies (MOBIHEALTH), pp. 39–42.
   Google Scholar
• Goldsmith, J., Bobb, J., Crainiceanu, C., Caffo, B., and Reich, D. (2011), “Penalized Functional Regression,” Jounal of Computational and Graphical Statistics, 20, 830–851. DOI: 10.1198/jcgs.2010.10007.
   PubMed Web of Science ®Google Scholar
• Goldsmith, J., Zipunnikov, V., and Schrck, J. (2015), “Generalized Multilevel Functional-on-Scalar Regression and Principal Component Analysis,” Biometrics, 71, 344–353. DOI: 10.1111/biom.12278.
   PubMed Web of Science ®Google Scholar
• Greven, S., Crainiceanu, C., Caffo, B., and Reich, D. (2010), “Longitudinal Functional Principal Component Analysis,” Electronic Journal of Statistics, 4, 1022–1054. DOI: 10.1214/10-EJS575.
   PubMed Web of Science ®Google Scholar
• Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning. Springer Series in Statistics, New York: Springer.
   Google Scholar
• Henderson, R., Diggle, P., and Dobson, A. (2000), “Joint Modeling of Longitudinal Measurements and Event Time Data,” Biostatistics, 1, 465–480. DOI: 10.1093/biostatistics/1.4.465.
   PubMedGoogle Scholar
• James, G. (2002), “Generalized Linear Models with Functional Predictors,” Journal of the Royal Statistical Society, Series B, 64411–432. DOI: 10.1111/1467-9868.00342.
   Google Scholar
• James, G., and Silverman, B. (2005), Functional Adaptive Model Estimation,” Journal of the American Statistical Association, 100, 565–576. DOI: 10.1198/016214504000001556.
   Web of Science ®Google Scholar
• Kim, K., Şentürk, D., and Li, R. (2011), “Recent History Functional Linear Models for Sparse Longitudinal Data,” Journal of Statistical Planning and Inference, 141, 1554–1566. https://www.sciencedirect.com/science/article/pii/S0378375810005033. DOI: 10.1016/j.jspi.2010.11.003.
   PubMed Web of Science ®Google Scholar
• Klasnja, P., Smith, S., Seewald, N., Lee, A., Hall, K., Luers, B., Hekler, E., and Murphy, S. A. (2019), “Efficacy of Contextually Tailored Suggestions for Physical Activity: A Micro-Randomized Optimization Trial of Heartsteps,” Annals of Behavioral Medicine, 53, 573–582. DOI: 10.1093/abm/kay067.
   PubMed Web of Science ®Google Scholar
• Kleiman, E. M., Turner, B. J., Fedor, S., Beale, E. E., Picard, R. W., Huffman, J. C., and Nock, M. K. (2018), “Digital Phenotyping of Suicidal Thoughts,” Depression and Anxiety, 35, 601–608. DOI: 10.1002/da.22730.
   PubMed Web of Science ®Google Scholar
• Kokoszka, P., and Reimherr, M. (2017), Introduction to Functional Data Analysis (1st ed.), London: Chapman and Hall/CRC. DOI: 10.1201/9781315117416.
   Google Scholar
• Kong, D., Ibrahim, J. G., Lee, E., and Zhu, H. (2018), “Flcrm: Functional Linear Cox Regression Model,” Biometrics, 74, 109–117. DOI: 10.1111/biom.12748.
   PubMed Web of Science ®Google Scholar
• Li, C., Xiao, L., and Luo, S. (2022), “Joint Model for Survival and Multivariate Sparse Functional Data with Application to a Study of Alzheimer’s Disease,” Biometrics, 78, 435–447. DOI: 10.1111/biom.13427.
   PubMed Web of Science ®Google Scholar
• Li, Y., and Guan, Y. (2014), “Functional Principal Component Analysis of Spatio-Temporal Point Processes with Applications in Disease Surveillance,” Journal of the American Statistical Association, 109, 1205–1215. DOI: 10.1080/01621459.2014.885434.
   PubMed Web of Science ®Google Scholar
• Little, R. J. A., and Rubin, D. B. (2002), Statistical Analysis with Missing Data (2nd ed.), Hoboken, NJ: Wiley.
   Google Scholar
• Liu, H., You, J., and Cao, J. (2021), “Functional l-Optimality Subsampling for Massive Data,” available at https://arxiv.org/abs/2104.03446.
   Google Scholar
• Marx, B. D., and Eilers, P. H. (2006), “Low-Rank Scale-Invariant Tensor Product Smooths for Generalized Additive Mixed Models,” Biometrics, 62, 1025–1036.
   PubMed Web of Science ®Google Scholar
• McCulloch, C. E., and Searle, S. R. (2001), Generalized, Linear and Mixed Models, New York: Wiley.
   Google Scholar
• Meng, X. L. (1994), “Multiple-Imputation Inferences with Uncongenial Sources of Input,” (with Discussion), Statistical Science, 10, 538–573. DOI: 10.1214/ss/1177010269.
   Google Scholar
• Morris, J. S., and Carroll, R. J. (2006), “Wavelet-based Functional Mixed Models,” Journal of the Royal Statistical Society, Series B, 68, 179–199. DOI: 10.1111/j.1467-9868.2006.00539.x.
   Google Scholar
• Morris, J. S., Vannucci, M., Brown, P. J., and Carroll, R. J. (2003), “Wavelet-based Nonparametric Modeling of Hierarchical Functions in Colon Carginogenesis,” Journal of the American Statistical Association, 98, 573–583. DOI: 10.1198/016214503000000422.
   Web of Science ®Google Scholar
• Muller, H. (2005), “Functional Modelling and Classification of Longitudinal Data,” Scandinavian Journal of Statistics, 32, 223–240. DOI: 10.1111/j.1467-9469.2005.00429.x.
   Web of Science ®Google Scholar
• Park, S. Y., and Staicu, A. M. (2015), “Longitudinal Functional Data Analysis,” Stat, 4, 212–226. DOI: 10.1002/sta4.89.
   PubMed Web of Science ®Google Scholar
• Petrovich, J., Reimherr, M., and Daymont, C. (2019), “Highly Irregular Functional Generalized Linear Regression with Electronic Health Records.” arXiv 1805.08518.
   Google Scholar
• Ramsay, J., and Silverman, B. (2005a), Functional Data Analysis, New York: Springer.
   Google Scholar
• Ramsay, J. O., and Silverman, B. W. (2005b), Functional Data Analysis, New York: Springer.
   Google Scholar
• Rathbun, S. (2012), “Optimal Estimation of Poisson Intensity with Partially Observed Covariates,” Biometrika, 100, 277–281. DOI: 10.1093/biomet/ass069.
   Web of Science ®Google Scholar
• Rathbun, S., and Shiffman, S. (2016), “Mixed Effects Models for Recurrent Events Data with Partially Oserved Time-Varying Covariates: Ecological Momentary Assessment of Smoking,” Biometrics, 72, 46–55. DOI: 10.1111/biom.12416.
   PubMed Web of Science ®Google Scholar
• Reiss, P. T., and Todd Ogden, R. (2007). “Functional Principal Component Regression and Functional Partial Least Squares,” Journal of the American Statistical Association, 102, 984–996. DOI: 10.1198/016214507000000527.
   Web of Science ®Google Scholar
• Rizopoulos, D. (2010), “Jm: An r Package for the Joint Modeling of Longitudinal and Time-to-Event Data,” Journal of Statistical Software, 35, 1–33. DOI: 10.18637/jss.v035.i09.
   PubMed Web of Science ®Google Scholar
• Ruppert, D. (2002), “Selecting the Number of Knots for Penalized Splines,” Journal of Computational and Graphical Statistics, 11, 735–757. DOI: 10.1198/106186002853.
   Web of Science ®Google Scholar
• Ruppert, D., Wand, M., and Carroll, R. (2003), Semiparametric Regression, Cambridge: Cambridge University Press.
   Google Scholar
• Shao, J., and Sitter, R. R. (1996), “Bootstrap for Imputed Survey Data,” Journal of the American Statistical Association, 91, 1278–1288. DOI: 10.1080/01621459.1996.10476997.
   Web of Science ®Google Scholar
• Spring, B. (2019), “Sense2stop: Mobile Sensor Data to Knowledge,” available at https://clinicaltrials.gov/ct2/show/NCT03184389.
   Google Scholar
• Staicu, A.-M., Crainiceanu, C. M., and Carroll, R. J. (2010), “Fast Methods for Spatially Correlated Multilevel Functional Data,” Biostatistics, 11, 177–194. DOI: 10.1093/biostatistics/kxp058.
   PubMed Web of Science ®Google Scholar
• Tsiatis, A. A., and Davidian, M. (2004), “Joint Modeling of Longitudinal and Time-to-Event Data: An Overview,” Statistica Sinica, 14, 809–834.
   Web of Science ®Google Scholar
• Waagepetersen, R. (2008), “Estimating Functions for Inhomogeneous Spatial Point Processes with Incomplete Covariate Data,” Biometrika, 95, 351–363. DOI: 10.1093/biomet/asn020.
   Web of Science ®Google Scholar
• Wood, S. (2003), Generalized Additive Models: An Introduction with R, London: Chapman & Hall.
   Google Scholar
• Wood, S. N. (2003), “Low-Rank Scale-Invariant Tensor Product Smooths for Generalized Additive Mixed Models,” Biometrics, 62, 1025–1036. DOI: 10.1111/j.1541-0420.2006.00574.x.
   Google Scholar
• Xiao, L., Li, Y., and Ruppert, D. (2013), “Fast Bivariate p-splines: The Sandwich Smoother,” Journal of the Royal Statistical Society, Series B, 75, 5770–599. DOI: 10.1111/rssb.12007.
   Google Scholar
• Yao, F., Müller, H.-G., and Wang, J.-L. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590. DOI: 10.1198/016214504000001745.
   Web of Science ®Google Scholar