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A Flexible Joint Longitudinal-Survival Model for Analyzing Longitudinally Sampled Biomarkers
Facebook, Menlo Park, USA
Department of Computer Science, University of California, Irvine, USA
Department of Statistics, University of California, Irvine, USA
Department of Statistics, University of California, Irvine, USA
- 1 Facebook, Menlo Park, USA
- 2 Department of Computer Science, University of California, Irvine, USA
- 3 Department of Statistics, University of California, Irvine, USA
- 4 Department of Statistics, University of California, Irvine, USA
Open Journal of Statistics·Volume 11 (2021)·Pages 778–805·Published 27 September 2021·DOI10.4236/ojs.2021.115046
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Abstract
We propose a flexible joint longitudinal-survival framework to examine the association between longitudinally collected biomarkers and a time-to-event endpoint. More specifically, we use our method for analyzing the survival outcome of end-stage renal disease patients with time-varying serum albumin measurements. Our proposed method is robust to common parametric assumptions in that it avoids explicit specification of the distribution of longitudinal responses and allows for a subject-specific baseline hazard in the survival component. Fully joint estimation is performed to account for uncertainty in the estimated longitudinal biomarkers that are included in the survival model.
KeywordsJoint Longitudinal-SurvivalBayesian NonparametericsGaussian Processes
- Fung, F., Sherrard, D.J., Gillen, D.L., Wong, C., Kestenbaum, B., Seliger, S., Ball, A. and Stehman-Breen, C. (2002) Increased Risk for Cardiovascular Mortality among Malnourished End-Stage Renal Disease Patients. American Journal of Kidney Diseases, 40, 307-314. https://doi.org/10.1053/ajkd.2002.34509
- Wong, C.S., Hingorani, S., Gillen, D.L., Sherrard, D.J., Watkins, S.L., Brandt, J.R., Ball, A. and Stehman-Breen, C.O. (2002) Hypoalbuminemia and Risk of Death in Pediatric Patients with End-Stage Renal Disease. Kidney International, 61, 630-637. https://doi.org/10.1046/j.1523-1755.2002.00169.x
- Prentice, R.L. (1982) Covariate Measurement Errors and Parameter Estimation in a Failure Time Regression Model. Biometrika, 69, 331-342. https://doi.org/10.1093/biomet/69.2.331
- Dafni, U.G. and Tsiatis, A.A. (1998) Evaluating Surrogate Markers of Clinical Outcome When Measured with Error. Biometrics, 54, 1445-1462. https://doi.org/10.2307/2533670
- Tsiatis, A.A., Degruttola, V. and Wulfsohn, M.S. (1995) Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and cd4 Counts in Patients with Aids. Journal of the American Statistical Association, 90, 27-37. https://doi.org/10.1080/01621459.1995.10476485
- Verbeke, G. and Molenberghs, G. (2000) Linear Mixed Models for Longitudinal Data. Springer, New York. https://doi.org/10.1007/978-1-4419-0300-6
- Pinheiro, J.C. and Bates, D.M. (2000) Mixed Effects Models in S and S-Plus. Springer, New York. https://doi.org/10.1007/b98882
- Christensen, R., Johnson, W., Branscum, A. and Hanson, T.E. (2010) Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. CRC Texts in Statistical Science, CRC Press, Boca Raton.
- Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (2003) Bayesian Data Analysis. Chapman and Hall, London. https://doi.org/10.1201/9780429258480
- Shi, J.Q., Wang, B., Murray-Smith, R. and Titterington, D.M. (2007) Gaussian Process Functional Regression Modeling for Batch Data. Biometrics, 63, 714-723. https://doi.org/10.1111/j.1541-0420.2007.00758.x
- Liu, Q., Lin, K.K., Andersen, B., Smyth, P. and Ihler, A. (2010) Estimating Replicate Time Shifts Using Gaussian Process Regression. Bioinformatics, 26, 770-776. https://doi.org/10.1093/bioinformatics/btq022
- Bycott, P. and Taylor, J. (1998) A Comparison of Smoothing Techniques for cd4 Data Measured with Error in a Time-Dependent Cox Proportional Hazards Model. Statistics in Medicine, 17, 2061-2077. https://doi.org/10.1002/(SICI)1097-0258(19980930)17:18%3C2061::AID-SIM896%3E3.0.CO;2-O