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A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. (English) Zbl 1210.62132
Summary: Joint models for a time-to-event (e.g., survival) and a longitudinal response have generated considerable recent interest. The longitudinal data are assumed to follow a mixed effects model, and a proportional hazards model depending on the longitudinal random effects and other covariates is assumed for the survival endpoint. Interest may focus on inference on the longitudinal data process, which is informatively censored, or on the hazard relationship. Several methods for fitting such models have been proposed, most requiring a parametric distributional assumption (normality) on the random effects. A natural concern is sensitivity to violation of this assumption; moreover, a restrictive distributional assumption may obscure key features in the data. We investigate these issues through our proposal of a likelihood-based approach that requires only the assumption that the random effects have a smooth density. Implementation via the EM algorithm is described, and performance and the benefits for uncovering noteworthy features are illustrated by application to data from an HIV clinical trial and by simulation.

MSC:
62N02 Estimation in survival analysis and censored data
62N01 Censored data models
65C60 Computational problems in statistics (MSC2010)
62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Abramowitz, Handbook of Mathematical Functions (1970)
[2] Andersen, Statistical Models Based on Counting Processes (1993) · Zbl 0769.62061 · doi:10.1007/978-1-4612-4348-9
[3] Breslow, Contribution to the discussion on the paper by D. R. Cox, Journal of the Royal Statistical Society, Series B 34 pp 216– (1972)
[4] Davidian, Smooth nonparametric maximum likelihood for population pharmacokinetics, with application to quinidine, Journal of Pharmacokinetics and Biopharmaceutics 20 pp 529– (1992) · doi:10.1007/BF01061470
[5] Davidian, The nonlinear mixed effects model with a smooth random effects density, Biometrika 80 pp 475– (1993) · Zbl 0788.62028 · doi:10.1093/biomet/80.3.475
[6] DeGruttola, Modeling progression of CD-4 lymphocyte count and its relationship to survival time, Biometrics 50 pp 1003– (1994) · Zbl 0825.62792 · doi:10.2307/2533439
[7] Eastwood, Adaptive truncation rules for seminonparametric estimators that achieve asymptotic normality, Econometric Theory 7 pp 307– (1991) · Zbl 04505240 · doi:10.1017/S0266466600004497
[8] Faucett, Simultaneously modeling censored survival data and repeatedly measured covariates: A Gibbs sampling approach, Statistics in Medicine 15 pp 1663– (1996) · doi:10.1002/(SICI)1097-0258(19960815)15:15<1663::AID-SIM294>3.0.CO;2-1
[9] Gallant, Seminonparametric maximum likelihood estimation, Econometrica 55 pp 363– (1987) · Zbl 0631.62110 · doi:10.2307/1913241
[10] Hammer, A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter, New England Journal of Medicine 335 pp 1081– (1996) · doi:10.1056/NEJM199610103351501
[11] Heagerty, Misspecified maximum likelihood estimates and generalised linear mixed models, Biometrika 88 pp 973– (2001) · Zbl 0986.62060 · doi:10.1093/biomet/88.4.973
[12] Henderson, Joint modeling of longitudinal measurements and event time data, Biostatistics 4 pp 465– (2000) · Zbl 1089.62519 · doi:10.1093/biostatistics/1.4.465
[13] Hogan, Model-based approaches to analysing incomplete longitudinal and failure time data, Statistics in Medicine 16 pp 259– (1997) · doi:10.1002/(SICI)1097-0258(19970215)16:3<259::AID-SIM484>3.0.CO;2-S
[14] Johansen, An extension of Cox’s regression model, International Statistical Review 51 pp 165– (1983) · Zbl 0526.62081 · doi:10.2307/1402746
[15] Johnson, Continuous Univariate Distributions 1 (1994)
[16] Pawitan, Modeling disease marker processes in AIDS, Journal of the American Statistical Association 83 pp 719– (1993) · Zbl 0800.62728 · doi:10.2307/2290756
[17] Schluchter, Methods for the analysis of informatively censored longitudinal data, Statistics in Medicine 11 pp 1861– (1992) · doi:10.1002/sim.4780111408
[18] Song , X. 2002 Topics in joint modeling of survival and longitudinal data Ph.D. thesis, North Carolina State University, Raleigh, North Carolina
[19] Tao, An estimation method for the semiparametric mixed effects model, Biometrics 55 pp 102– (1999) · Zbl 1059.62572 · doi:10.1111/j.0006-341X.1999.00102.x
[20] Tsiatis, A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error, Biometrika 88 pp 447– (2001) · Zbl 0984.62078 · doi:10.1093/biomet/88.2.447
[21] Tsiatis, 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 pp 27– (1995) · Zbl 0818.62102 · doi:10.2307/2291126
[22] Verbeke, The effect of misspeeifying the random effects distribution in linear mixed effects models for longitudinal data, Computational Statistics and Data Analysis 23 pp 541– (1997) · Zbl 0900.62374 · doi:10.1016/S0167-9473(96)00047-3
[23] Wu, Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process, Biometrics 44 pp 175– (1988) · Zbl 0707.62210 · doi:10.2307/2531905
[24] Wulfsohn, A joint model for survival and longitudinal data measured with error, Biometrics 53 pp 330– (1997) · Zbl 0874.62140 · doi:10.2307/2533118
[25] Xu, Joint analysis of longitudinal data comprising repeated measures and times to events, Applied Statistics 50 pp 375– (2001) · Zbl 1112.62312
[26] Zhang, Linear mixed models with flexible distributions of random effects for longitudinal data, Biometrics 57 pp 795– (2001) · Zbl 1209.62087 · doi:10.1111/j.0006-341X.2001.00795.x
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