A Comparison of Joint Models for Longitudinal and Competing Risks Data, with Application to an Epilepsy Drug Randomized Controlled Trial
Tóm tắt
Joint modelling of longitudinal data and competing risks has grown over the past decade. Despite the recent methodological developments, there are still limited options for fitting these models in standard statistical software programs, which prohibits their adoption by applied biostatisticians. We summarize four published models, each of which has software available for model estimation. Each model features a different hazard function, latent association structure between the submodels, estimation approach and software implementation. Of the four models considered here, the model specifications and association structures are substantially different, thus complicating model-to-model comparison. The models are applied to the ‘Standard and new anti-epileptic drugs’ trial of anti-epileptic drugs to investigate the effect of drug titration on the treatment effects of lamotrigine and carbamazepine on the mode of treatment failure. Notwithstanding the vastly different association structures, we show that the inference from each model is consistent, namely, that there is a beneficial effect of lamotrigine on unacceptable adverse events over carbamazepine and a non-significant effect on the hazard of inadequate seizure control. The association between anti-epileptic drug titration and treatment failure was significant in most models. To allow for the routine adoption of joint modelling of competing risks and longitudinal data in the analysis of clinical data sets, further work is required on the development of model diagnostics to aid model choice.
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Tài liệu tham khảo
Andrinopoulou, 2016, Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures, Statist. Med., 35, 4813, 10.1002/sim.7027
Andrinopoulou, 2014, Joint modeling of two longitudinal outcomes and competing risk data, Statist. Med., 33, 3167, 10.1002/sim.6158
Andrinopoulou, 2017, Combined dynamic predictions using joint models of two longitudinal outcomes and competing risk data, Statist. Meth. Med. Res., 26, 1787, 10.1177/0962280215588340
Asar, 2015, Joint modelling of repeated measurement and time-to-event data: an introductory tutorial, Int. J. Epidem., 4, 334, 10.1093/ije/dyu262
Bakoyannis, 2012, Practical methods for competing risks data: a review, Statist. Meth. Med. Res., 21, 257, 10.1177/0962280210394479
Blanche, 2015, Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks, Biometrics, 71, 102, 10.1111/biom.12232
Chen, 2011, Sample size and power determination in joint modeling of longitudinal and survival data, Statist. Med., 30, 2295, 10.1002/sim.4263
Commission on Antiepileptic Drugs, 1998, Considerations on designing clinical trials to evaluate the place of new antiepileptic drugs in the treatment of newly diagnosed and chronic patients with epilepsy, Epilepsia, 39, 799, 10.1111/j.1528-1157.1998.tb01167.x
Cox, 1972, Regression models and life-tables (with discussion), J. R. Statist. Soc., 34, 187, 10.1111/j.2517-6161.1972.tb00899.x
Cross, 2007, Old versus new antiepileptic drugs: the SANAD study, Lancet, 370, 314, 10.1016/S0140-6736(07)61151-9
Deslandes, 2010, Joint modeling of multivariate longitudinal data and the dropout process in a competing risk setting: application to ICU data, BMC Med. Res. Methodol., 10, 69, 10.1186/1471-2288-10-69
Elashoff, 2007, An approach to joint analysis of longitudinal measurements and competing risks failure time data, Statist. Med., 26, 1999, 10.1002/sim.2749
Elashoff, 2008, A joint model for longitudinal measurements and survival data in the presence of multiple failure types, Biometrics, 64, 762, 10.1111/j.1541-0420.2007.00952.x
Faught, 2007, Epilepsy drugs: getting it right the first time, Lancet Neurol., 6, 476, 10.1016/S1474-4422(07)70115-1
Fine, 1999, A proportional hazards model for the subdistribution of a competing risk, J. Am. Statist. Ass., 94, 496, 10.1080/01621459.1999.10474144
Gould, 2015, Joint modeling of survival and longitudinal non-survival data: current methods and issues: Report of the DIA Bayesian joint modeling working group, Statist. Med., 34, 2181, 10.1002/sim.6141
Gueorguieva, 2012, Joint modelling of longitudinal outcome and interval-censored competing risk dropout in a schizophrenia clinical trial, J. R. Statist. Soc., 175, 417, 10.1111/j.1467-985X.2011.00719.x
Henderson, 2000, Joint modelling of longitudinal measurements and event time data, Biostatistics, 1, 465, 10.1093/biostatistics/1.4.465
Hickey, 2016, Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues, BMC Med. Res. Methodol., 16, 1, 10.1186/s12874-016-0212-5
Hogan, 1997, Model-based approaches to analysing incomplete longitudinal and failure time data, Statist. Med., 16, 259, 10.1002/(SICI)1097-0258(19970215)16:3<259::AID-SIM484>3.0.CO;2-S
Hu, 2016, Joint multiple imputation for longitudinal outcomes and clinical events that truncate longitudinal follow-up, Statist. Med., 35, 2991, 10.1002/sim.6590
Hu, 2009, A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data, Statist. Med., 28, 1601, 10.1002/sim.3562
Hu, 2012, Nonparametric multistate representations of survival and longitudinal data with measurement error, Statist. Med., 31, 2303, 10.1002/sim.5369
Huang, 2010, A joint model of longitudinal and competing risks survival data with heterogeneous random effects and outlying longitudinal measurements, Statist. Interfc., 3, 185, 10.4310/SII.2010.v3.n2.a6
Huang, 2011, A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects, Liftim. Data Anal., 17, 80, 10.1007/s10985-010-9169-6
Ibrahim, 2010, Basic concepts and methods for joint models of longitudinal and survival data, J. Clin. Oncol., 28, 2796, 10.1200/JCO.2009.25.0654
Jacqmin-Gadda, 2010, Score test for conditional independence between longitudinal outcome and time to event given the classes in the joint latent class model, Biometrics, 66, 11, 10.1111/j.1541-0420.2009.01234.x
Ko, 2014, Identification of longitudinal biomarkers for survival by a score test derived from a joint model of longitudinal and competing risks data, J. Appl. Statist., 41, 2270, 10.1080/02664763.2014.909789
Latouche, 2013, A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions, J. Clin. Epidem., 66, 648, 10.1016/j.jclinepi.2012.09.017
Li, 2009, Robust joint modeling of longitudinal measurements and competing risks failure time data, Biometr. J., 51, 19, 10.1002/bimj.200810491
Li, 2010, Joint modeling of longitudinal ordinal data and competing risks survival times and analysis of the NINDS rt-PA stroke trial, Statist. Med., 29, 546, 10.1002/sim.3798
Li, 2012, Joint analysis of bivariate longitudinal ordinal outcomes and competing risks survival times with nonparametric distributions for random effects, Statist. Med., 31, 1707, 10.1002/sim.4507
Liu, 2008, Analysis of longitudinal data in the presence of informative observational times and a dependent terminal event, with application to medical cost data, Biometrics, 64, 950, 10.1111/j.1541-0420.2007.00954.x
Marson, 2007, The SANAD study of effectiveness of carbamazepine, gabapentin, lamotrigine, oxcarbazepine, or topiramate for treatment of partial epilepsy: an unblinded randomised controlled trial, Lancet, 369, 1000, 10.1016/S0140-6736(07)60460-7
Philipson, 2017, Package “joineR”
Proust-Lima, 2016, Joint modelling of repeated multivariate cognitive measures and competing risks of dementia and death: a latent process and latent class approach, Statist. Med., 35, 382, 10.1002/sim.6731
Proust-Lima, 2017, Estimation of extended mixed models using latent classes and latent processes: the R package lcmm, J. Statist. Softwr., 78, 1
Proust-Lima, 2012, Joint latent class models for longitudinal and time-to-event data: a review, Statist. Meth. Med. Res., 23, 74, 10.1177/0962280212445839
Putter, 2007, Tutorial in biostatistics: competing risks and multi-state models, Statist. Med., 26, 2389, 10.1002/sim.2712
Rizopoulos, 2010, JM: an R package for the joint modelling of longitudinal and time-to-event data, J. Statist. Softwr., 35, 1
Rizopoulos, 2012, Joint Models for Longitudinal and Time-to-event Data, with Applications in R, 10.1201/b12208
Rizopoulos, 2010, Multiple-imputation-based residuals and diagnostic plots for joint models of longitudinal and survival outcomes, Biometrics, 66, 20, 10.1111/j.1541-0420.2009.01273.x
Rutherford, 2015, The use of restricted cubic splines to approximate complex hazard functions in the analysis of time-to-event data: a simulation study, J. Statist. Computn Simuln, 85, 777, 10.1080/00949655.2013.845890
Sparling, 2006, Parametric survival models for interval-censored data with time-dependent covariates, Biostatistics, 7, 599, 10.1093/biostatistics/kxj028
Tsiatis, 2004, Joint modeling of longitudinal and time-to-event data: an overview, Statist. Sin., 14, 809
Tsiatis, 1995, Modeling the relationship of survival to longitudinal data measured with error—applications to survival and CD4 counts in patients with AIDS, J. Am. Statist. Ass., 90, 27, 10.1080/01621459.1995.10476485
Wang, 2017, A SAS macro for the joint modeling of longitudinal outcomes and multiple competing risk dropouts, Comput. Meth. Progrms Biomed., 138, 23, 10.1016/j.cmpb.2016.10.003
Williamson, 2008, Joint modelling of longitudinal and competing risks data, Statist. Med., 27, 6426, 10.1002/sim.3451
Williamson, 2007, The influence of competing-risks setting on the choice of hypothesis test for treatment effect, Biostatistics, 8, 689, 10.1093/biostatistics/kxl040
Williamson, 2007, Importance of competing risks in the analysis of anti-epileptic drug failure, Trials, 8, 12, 10.1186/1745-6215-8-12
Wulfsohn, 1997, A joint model for survival and longitudinal data measured with error, Biometrics, 53, 330, 10.2307/2533118