*Result*: A Tobit Partly Linear Mixed and Mixture Cure Model for the Joint Analysis of Interval-Bounded Longitudinal Measurements and Survival Times With Cure Proportion.
Title:
A Tobit Partly Linear Mixed and Mixture Cure Model for the Joint Analysis of Interval-Bounded Longitudinal Measurements and Survival Times With Cure Proportion.
Authors:
Wang Z; Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei, China., Shen Z; Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei, China., Ming R; School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China., Tu D; Canadian Cancer Trials Group, Queen's University, Kingston, Ontario, Canada.
Source:
Pharmaceutical statistics [Pharm Stat] 2026 Mar-Apr; Vol. 25 (2), pp. e70072.
Publication Type:
Journal Article
Language:
English
Journal Info:
Publisher: Wiley Country of Publication: England NLM ID: 101201192 Publication Model: Print Cited Medium: Internet ISSN: 1539-1612 (Electronic) Linking ISSN: 15391604 NLM ISO Abbreviation: Pharm Stat Subsets: MEDLINE
Imprint Name(s):
Original Publication: Chichester, UK : Wiley, c2002-
MeSH Terms:
Models, Statistical*, Breast Neoplasms/drug therapy ; Breast Neoplasms/mortality ; Breast Neoplasms/therapy ; Clinical Trials as Topic/statistics & numerical data ; Clinical Trials as Topic/methods ; Humans ; Longitudinal Studies ; Female ; Linear Models ; Survival Analysis ; Computer Simulation ; Likelihood Functions
References:
R. Elashoff, G. Li, and N. Li, Joint Modeling of Longitudinal and Time‐to‐Event Data (CRC Press, 2016).
D. Rizopoulos, Joint Models for Longitudinal and Time‐to‐Event Data: With Applications in R (CRC Press, 2023).
H. Song, Y. Peng, and D. Tu, “Jointly Modeling Longitudinal Proportional Data and Survival Times With an Application to the Quality of Life Data in a Breast Cancer Trial,” Lifetime Data Analysis 23, no. 2 (2017): 183–206.
Z. Wang, H. Xu, H. Liu, H. Song, and D. Tu, “A Joint Model for Longitudinal Outcomes With Potential Ceiling and Floor Effects and Survival Times, With Applications to Analysis of Quality of Life Data From a Cancer Clinical Trial,” Stat 11, no. 1 (2022): e412.
B. Yu, “A Frailty Mixture Cure Model With Application to Hospital Readmission Cata,” Biometrical Journal 50, no. 3 (2008): 386–394.
V. Rondeau, J. P. Pignon, and S. Michiels, “A Joint Model for the Dependence Between Clustered Times to Tumour Progression and Deaths: A Meta‐Analysis of Chemotherapy in Head and Neck Cancer,” Statistical Methods in Medical Research 24, no. 6 (2011): 711–729.
R. Tawiah, G. McLachlan, and S. Ng, “A Bivariate Joint Frailty Model With Mixture Framework for Survival Analysis of Recurrent Events With Dependent Censoring and Cure Fraction,” Biometrics 76, no. 3 (2020): 753–766.
Y. Peng and B. Yu, Cure Models: Methods, Applications, and Implementation (CRC Press, 2021).
L. Yang, H. Song, Y. Peng, and D. Tu, “Joint Analysis of Longitudinal Measurements and Survival Times With a Cure Fraction Based on Partly Linear Mixed and Semiparametric Cure Models,” Pharmaceutical Statistics 20, no. 2 (2021): 362–374.
H. Song, Y. Peng, and D. Tu, “Joint Modeling of Longitudinal Proportional Measurements and Survival Time With a Cure Fraction,” Science China Mathematics 59, no. 12 (2016): 2427–2442.
D. Rizopoulos, G. Verbeke, and E. Lesaffre, “Fully Exponential Laplace Approximations for the Joint Modelling of Survival and Longitudinal Data,” Journal of the Royal Statistical Society. Series B, Statistical Methodology 71, no. 3 (2009): 637–654.
E. F. Vonesh, “A Note on the Use of Laplace's Approximation for Nonlinear Mixed‐Effects Models,” Biometrika 83, no. 2 (1996): 447–452.
T. Hastie, R. Robert Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer, 2009).
J. Shao and D. Tu, The Jackknife and Bootstrap (Springer Science & Business Media, 2012).
Z. Wang, Y. Wu, and L. Zhao, “Approximation by Randomly Weighting Method in Censored Regression Model,” Science in China, Series A: Mathematics 52, no. 3 (2009): 561–576.
Z. Wang, S. Yao, and Y. Wu, “A Randomly Weighting Approximation Approach for Two‐Tailed Censored Regression Model,” Scientia Sinica Mathematica 48 (2018): 955–968.
L. Xiao, B. Hou, Z. Wang, and Y. Wu, “Random Weighting Approximation for Tobit Regression Models With Longitudinal Data,” Computational Statistics & Data Analysis 79 (2014): 235–247.
D. Rizopoulos, Joint Models for Longitudinal and Time‐to‐Event Data: With Applications in R (CRC Press, 2023).
H. Song, Y. Peng, and D. Tu, “Jointly Modeling Longitudinal Proportional Data and Survival Times With an Application to the Quality of Life Data in a Breast Cancer Trial,” Lifetime Data Analysis 23, no. 2 (2017): 183–206.
Z. Wang, H. Xu, H. Liu, H. Song, and D. Tu, “A Joint Model for Longitudinal Outcomes With Potential Ceiling and Floor Effects and Survival Times, With Applications to Analysis of Quality of Life Data From a Cancer Clinical Trial,” Stat 11, no. 1 (2022): e412.
B. Yu, “A Frailty Mixture Cure Model With Application to Hospital Readmission Cata,” Biometrical Journal 50, no. 3 (2008): 386–394.
V. Rondeau, J. P. Pignon, and S. Michiels, “A Joint Model for the Dependence Between Clustered Times to Tumour Progression and Deaths: A Meta‐Analysis of Chemotherapy in Head and Neck Cancer,” Statistical Methods in Medical Research 24, no. 6 (2011): 711–729.
R. Tawiah, G. McLachlan, and S. Ng, “A Bivariate Joint Frailty Model With Mixture Framework for Survival Analysis of Recurrent Events With Dependent Censoring and Cure Fraction,” Biometrics 76, no. 3 (2020): 753–766.
Y. Peng and B. Yu, Cure Models: Methods, Applications, and Implementation (CRC Press, 2021).
L. Yang, H. Song, Y. Peng, and D. Tu, “Joint Analysis of Longitudinal Measurements and Survival Times With a Cure Fraction Based on Partly Linear Mixed and Semiparametric Cure Models,” Pharmaceutical Statistics 20, no. 2 (2021): 362–374.
H. Song, Y. Peng, and D. Tu, “Joint Modeling of Longitudinal Proportional Measurements and Survival Time With a Cure Fraction,” Science China Mathematics 59, no. 12 (2016): 2427–2442.
D. Rizopoulos, G. Verbeke, and E. Lesaffre, “Fully Exponential Laplace Approximations for the Joint Modelling of Survival and Longitudinal Data,” Journal of the Royal Statistical Society. Series B, Statistical Methodology 71, no. 3 (2009): 637–654.
E. F. Vonesh, “A Note on the Use of Laplace's Approximation for Nonlinear Mixed‐Effects Models,” Biometrika 83, no. 2 (1996): 447–452.
T. Hastie, R. Robert Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer, 2009).
J. Shao and D. Tu, The Jackknife and Bootstrap (Springer Science & Business Media, 2012).
Z. Wang, Y. Wu, and L. Zhao, “Approximation by Randomly Weighting Method in Censored Regression Model,” Science in China, Series A: Mathematics 52, no. 3 (2009): 561–576.
Z. Wang, S. Yao, and Y. Wu, “A Randomly Weighting Approximation Approach for Two‐Tailed Censored Regression Model,” Scientia Sinica Mathematica 48 (2018): 955–968.
L. Xiao, B. Hou, Z. Wang, and Y. Wu, “Random Weighting Approximation for Tobit Regression Models With Longitudinal Data,” Computational Statistics & Data Analysis 79 (2014): 235–247.
Grant Information:
12371277 National Natural Science Foundation of China; 12231017 National Natural Science Foundation of China; Characteristic Preponderant Discipline of Key Construction Universities in Zhejiang Province; SZJ2022B004 Collaborative Innovation Center of Statistical Data Engineering Technology Application, and Digital+ Discipline Construction and Management Project of Zhejiang Gongshang University; Natural Sciences and Engineering Research Council of Canada
Contributed Indexing:
Keywords: Tobit model; interval bounded; longitudinal data; mixture cure model; random weighting
Entry Date(s):
Date Created: 20260131 Date Completed: 20260131 Latest Revision: 20260131
Update Code:
20260131
DOI:
10.1002/pst.70072
PMID:
41618521
Database:
MEDLINE
*Further Information*
*Motivated by the analysis of data from a clinical trial on patients with early breast cancer, we propose in this paper a new joint model that uses a Tobit partly linear mixed model for longitudinal measurements which are bounded in an interval and have a nonlinear relationship with the observation times and a semiparametric mixture cure model that incorporates a B-spline baseline hazard for survival times with cure proportion. A procedure is developed for estimating parameters in the proposed model using the partial likelihood and Laplace approximation. Additionally, a method of random weighting is proposed to compute the variances of the parameter estimators. The performance of the proposed model and the inference procedures is evaluated through simulation studies and data from the clinical trial that motivated this study.
(© 2026 John Wiley & Sons Ltd.)*