A Joint Model for Survival and Longitudinal Data Measured with Error

Biometrics ◽  
1997 ◽  
Vol 53 (1) ◽  
pp. 330 ◽  
Author(s):  
Michael S. Wulfsohn ◽  
Anastasios A. Tsiatis
Biometrics ◽  
2016 ◽  
Vol 72 (3) ◽  
pp. 907-916 ◽  
Author(s):  
Agnieszka Król ◽  
Loïc Ferrer ◽  
Jean-Pierre Pignon ◽  
Cécile Proust-Lima ◽  
Michel Ducreux ◽  
...  

Biostatistics ◽  
2017 ◽  
Vol 19 (3) ◽  
pp. 374-390 ◽  
Author(s):  
Tingting Yu ◽  
Lang Wu ◽  
Peter B Gilbert

SUMMARY In HIV vaccine studies, a major research objective is to identify immune response biomarkers measured longitudinally that may be associated with risk of HIV infection. This objective can be assessed via joint modeling of longitudinal and survival data. Joint models for HIV vaccine data are complicated by the following issues: (i) left truncations of some longitudinal data due to lower limits of quantification; (ii) mixed types of longitudinal variables; (iii) measurement errors and missing values in longitudinal measurements; (iv) computational challenges associated with likelihood inference. In this article, we propose a joint model of complex longitudinal and survival data and a computationally efficient method for approximate likelihood inference to address the foregoing issues simultaneously. In particular, our model does not make unverifiable distributional assumptions for truncated values, which is different from methods commonly used in the literature. The parameters are estimated based on the h-likelihood method, which is computationally efficient and offers approximate likelihood inference. Moreover, we propose a new approach to estimate the standard errors of the h-likelihood based parameter estimates by using an adaptive Gauss–Hermite method. Simulation studies show that our methods perform well and are computationally efficient. A comprehensive data analysis is also presented.


Author(s):  
Elif Dil ◽  
Duru Karasoy

Although longitudinal and survival data are collected in the same study, they are usually analyzed separately. Measurement errors and missing data problems arise because of separate analysis of these two data. Therefore, joint model should be used instead of separate analysis. The standard joint model frequently used in the literature is obtained by combining the linear mixed effect model of longitudinal data and Cox regression model with survival data. Nevertheless, to use the Cox regression model for survival data, the assumption of proportional hazards must be provided. Parametric survival sub-models should be used instead of the Cox regression model for the survival sub-model of the JM where the assumption is not provided. In this article, parametric joint modeling of longitudinal data and survival data that do not provide the assumption of proportional hazards are investigated. For the survival data, the model with Exponential, Weibull, Log-normal, Log-logistic, and Gamma accelerated failure time models and the linear mixed effect model are combined with random effects and the models were applied in primary biliary cirrhosis data set obtained from Mayo Clinic. After determining the best parametric joint model according to Akaike and Bayesian information criterions, the best available model was compared with standard joint model and of separate analysis of survival data and longitudinal data. As a results, in the studies where longitudinal and survival data are obtained together, it is seen that the parametric joint model gives more better results than the standard joint model when the proportional hazard assumption is not provided.


Stat ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 320-330 ◽  
Author(s):  
Dan Li ◽  
Xia Wang ◽  
Seongho Song ◽  
Nanhua Zhang ◽  
Dipak K. Dey

Blood ◽  
2018 ◽  
Vol 132 (Supplement 1) ◽  
pp. 3026-3026
Author(s):  
Koji Sasaki ◽  
Hagop M. Kantarjian ◽  
Farhad Ravandi ◽  
Marina Y. Konopleva ◽  
Gautam Borthakur ◽  
...  

Abstract Introduction Tyrosine kinase inhibitors (TKI) have improved survival in patients with chronic myeloid leukemia in chronic phase (CML-CP). There is a growing interest in treatment discontinuation after achieving sustained MR4.5. Over the course of therapy patients dose reduction of their TKI or switch to another TKI for various reasons. Multivariate joint models for dynamic personalized assessment incorporate survival and longitudinal data of multiple repeated measurements. Such models can handle longitudinal data of BCR-ABL levels over time as well as the dose of each TKI in every clinic encounter. The aim of this study is to evaluate the impact of dose adjustments and TKI switch on the achievement of sustained MR4.5. Methods From July 2000 to January 2017, 646 patients who enrolled in frontline TKI trials (imatinib 400 mg/day, 73 patients; imatinib 800 mg/day, 208 patients; nilotinib 800 mg/day, 148 patients; dasatinib 100 mg/day, 150 patients; dasatinib 50 mg/day, 16 patients; ponatinib 45 mg/day, 43 patients; ponatinib 30 mg, 8 patients) including 10,623 clinical visits to verify the dose of TKI, and 8,319 measurements of BCR-ABL by reverse transcriptase polymerase chain reaction. Sustained MR4.5 was defined as at least 2-year duration of MR4.5. Multivariate joint modeling with multiple longitudinal measurements was performed for dynamic personalized assessment with the combination of Cox proportional hazard model with generalized linear mixed models. For the estimation of parameters of the joint model, a Bayesian approach was used with Markov Chain Monte Carlo methods. The dose of each TKI, and the BCR-ABL/ABL ratio were considered as time-dependent covariates in the generalized linear mixed model. The dose of each TKI was handled as numeric values which enabled to accommodate treatment effect of dose-reduced TKI and alternative TKI after front-line TKI failure throughout different clinical trials. Results Overall median follow-up was 105 months (range, 0.3-213.4); imatinib 400 mg/day, 193 months; imatinib 800 mg/day, 166 months; nilotinib 800 mg/day, 81 months; dasatinib 100 mg/day, 79 months; dasatinib 50 mg/day, 10 months; ponatinib 45 mg/day, 48 months; ponatinib 30 mg/day, 40 months. A total of 334 patients (52%) achieved sustained MR4.5; median time to sustained MR4.5 was 44 months (95% confidence interval, 30.3-56.1). The trajectories of BCR-ABL levels (Figure 1A) and the dose of TKI are shown (imatinib, Figure 1B; dasatinib, Figure 1C; nilotinib, Figure 1D; ponatinib, Figure 1E). Multivariate joint model identified the daily dose of imatinib (p <0.001; hazard ratio [HR], 1.0017; 95% credible interval [CI], 1.0006-1.0028), dasatinib (p <0.001; HR, 1.0153; 95% CI, 1.0078-1.0237), nilotinib (p <0.001; HR, 1.0017; 95% CI, 1.0006-1.0028), ponatinib (p <0.001; HR, 1.0243; 95% CI, 1.0036-1.0471) as prognostic factors for the achievement of sustained MR4.5. An example of dynamic personalized assessment for the guidance of dose reduction and alternative TKI was shown in Figure 1F. Hypothetical Patient #1 was treated with front-line dasatinib 100 mg/day. At 6.24 months of dasatinib 100 mg/day, BCR-ABL1/ABL1 ratio was 0.18 % on the international scale. Assuming Patient #1 developed refractory pleural effusion not controlled with steroid and diuretics, expected cumulative rate of sustained MR4.5 at dasatinib 80 mg/day, dasatinib 50 mg/day, dasatinib 20 mg/day, nilotinib 300 mg/day, ponatinib 15 mg/day, imatinib 400 mg/day were calculated in Figure 1F. Dynamic personalized assessment by multivariate joint model estimated sustained MR4.5 at 5 years of TKI therapy after the suggested treatment options as follows; dasatinib 80 mg/day, 41% (95% CI, 31.0-55.8); dasatinib 50 mg/day, 29% (95% CI, 18.9-41.7); dasatinib 20 mg/day, 20%, (10.8-32.5); nilotinib 300 mg/day, 37% (95% CI, 28.8-45.6); imatinib 400 mg/day, 28% (19.0-37.1); ponatinib 15 mg/day, 22% (95% CI, 13.0-32.5). Conclusion Dynamic personalized assessment of TKI dose reduction and alternative TKI selection optimizes treatment decision at the time of TKI failure in patients with CML-CP. Disclosures Sasaki: Otsuka Pharmaceutical: Honoraria. Ravandi:Bristol-Myers Squibb: Research Funding; Amgen: Honoraria, Research Funding, Speakers Bureau; Astellas Pharmaceuticals: Consultancy, Honoraria; Xencor: Research Funding; Abbvie: Research Funding; Orsenix: Honoraria; Astellas Pharmaceuticals: Consultancy, Honoraria; Jazz: Honoraria; Macrogenix: Honoraria, Research Funding; Xencor: Research Funding; Jazz: Honoraria; Sunesis: Honoraria; Orsenix: Honoraria; Amgen: Honoraria, Research Funding, Speakers Bureau; Sunesis: Honoraria; Seattle Genetics: Research Funding; Bristol-Myers Squibb: Research Funding; Macrogenix: Honoraria, Research Funding; Seattle Genetics: Research Funding; Abbvie: Research Funding. Konopleva:Stemline Therapeutics: Research Funding. Wierda:AbbVie, Inc: Research Funding; Genentech: Research Funding. Daver:Otsuka: Consultancy; Kiromic: Research Funding; Sunesis: Consultancy; ImmunoGen: Consultancy; Karyopharm: Consultancy; Novartis: Consultancy; Incyte: Research Funding; Pfizer: Consultancy; Incyte: Consultancy; BMS: Research Funding; ARIAD: Research Funding; Novartis: Research Funding; Alexion: Consultancy; Sunesis: Research Funding; Daiichi-Sankyo: Research Funding; Karyopharm: Research Funding; Pfizer: Research Funding. Jabbour:Bristol-Myers Squibb: Consultancy, Research Funding; Pfizer: Consultancy, Research Funding; Novartis: Research Funding; Abbvie: Research Funding; Takeda: Consultancy, Research Funding. Cortes:Novartis: Consultancy, Research Funding; Astellas Pharma: Consultancy, Research Funding; Daiichi Sankyo: Consultancy, Research Funding; Pfizer: Consultancy, Research Funding; Arog: Research Funding.


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