Intercept Estimation of Semi‐Parametric Joint Models in the Context of Longitudinal Data Subject to Irregular Observations
Longitudinal data are often subject to irregular visiting times, with outcomes and visit times influenced by a latent variable. Semi‐parametric joint models that account for this dependence have been proposed; among these, the Sun model is the most suitable for count data as it employs a multiplicat...
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| Published in: | Biometrical journal Vol. 67; no. 6; p. e70088 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01.12.2025
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| ISSN: | 0323-3847, 1521-4036, 1521-4036 |
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| Abstract | Longitudinal data are often subject to irregular visiting times, with outcomes and visit times influenced by a latent variable. Semi‐parametric joint models that account for this dependence have been proposed; among these, the Sun model is the most suitable for count data as it employs a multiplicative link function. Semi‐parametric joint models define an intercept function as the mean outcome when all covariates are set to zero; this is differenced out in the course of estimation and is consequently not estimated. The Sun estimator thus provides estimates of relative covariate effects, but is unable to provide estimates of absolute effects or of longitudinal prognosis in the absence of covariates. We extend the Sun model by additionally estimating the intercept term, showing that our extended estimator is consistent and asymptotically Normal. In simulations, our estimator outperforms the original Sun estimator in terms of bias and standard error and is also more computationally efficient. We apply our estimator to a longitudinal study of tumor recurrence among bladder cancer patients. Provided the intercept term can be adequately captured using splines, we recommend that our extended Sun estimator be used in place of the original estimator, since it leads to smaller bias, smaller standard errors, and allows estimation of the mean outcome trajectories. |
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| AbstractList | Longitudinal data are often subject to irregular visiting times, with outcomes and visit times influenced by a latent variable. Semi-parametric joint models that account for this dependence have been proposed; among these, the Sun model is the most suitable for count data as it employs a multiplicative link function. Semi-parametric joint models define an intercept function as the mean outcome when all covariates are set to zero; this is differenced out in the course of estimation and is consequently not estimated. The Sun estimator thus provides estimates of relative covariate effects, but is unable to provide estimates of absolute effects or of longitudinal prognosis in the absence of covariates. We extend the Sun model by additionally estimating the intercept term, showing that our extended estimator is consistent and asymptotically Normal. In simulations, our estimator outperforms the original Sun estimator in terms of bias and standard error and is also more computationally efficient. We apply our estimator to a longitudinal study of tumor recurrence among bladder cancer patients. Provided the intercept term can be adequately captured using splines, we recommend that our extended Sun estimator be used in place of the original estimator, since it leads to smaller bias, smaller standard errors, and allows estimation of the mean outcome trajectories.Longitudinal data are often subject to irregular visiting times, with outcomes and visit times influenced by a latent variable. Semi-parametric joint models that account for this dependence have been proposed; among these, the Sun model is the most suitable for count data as it employs a multiplicative link function. Semi-parametric joint models define an intercept function as the mean outcome when all covariates are set to zero; this is differenced out in the course of estimation and is consequently not estimated. The Sun estimator thus provides estimates of relative covariate effects, but is unable to provide estimates of absolute effects or of longitudinal prognosis in the absence of covariates. We extend the Sun model by additionally estimating the intercept term, showing that our extended estimator is consistent and asymptotically Normal. In simulations, our estimator outperforms the original Sun estimator in terms of bias and standard error and is also more computationally efficient. We apply our estimator to a longitudinal study of tumor recurrence among bladder cancer patients. Provided the intercept term can be adequately captured using splines, we recommend that our extended Sun estimator be used in place of the original estimator, since it leads to smaller bias, smaller standard errors, and allows estimation of the mean outcome trajectories. Longitudinal data are often subject to irregular visiting times, with outcomes and visit times influenced by a latent variable. Semi‐parametric joint models that account for this dependence have been proposed; among these, the Sun model is the most suitable for count data as it employs a multiplicative link function. Semi‐parametric joint models define an intercept function as the mean outcome when all covariates are set to zero; this is differenced out in the course of estimation and is consequently not estimated. The Sun estimator thus provides estimates of relative covariate effects, but is unable to provide estimates of absolute effects or of longitudinal prognosis in the absence of covariates. We extend the Sun model by additionally estimating the intercept term, showing that our extended estimator is consistent and asymptotically Normal. In simulations, our estimator outperforms the original Sun estimator in terms of bias and standard error and is also more computationally efficient. We apply our estimator to a longitudinal study of tumor recurrence among bladder cancer patients. Provided the intercept term can be adequately captured using splines, we recommend that our extended Sun estimator be used in place of the original estimator, since it leads to smaller bias, smaller standard errors, and allows estimation of the mean outcome trajectories. |
| Author | Pullenayegum, Eleanor Ledesma, Luis |
| Author_xml | – sequence: 1 givenname: Luis surname: Ledesma fullname: Ledesma, Luis organization: Department of Medicine McMaster University Hamilton Canada – sequence: 2 givenname: Eleanor orcidid: 0000-0003-4265-1330 surname: Pullenayegum fullname: Pullenayegum, Eleanor organization: Child Health Evaluative Sciences The Hospital for Sick Children Toronto Canada, Dalla Lana School of Public Health University of Toronto Toronto Canada |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/41199501$$D View this record in MEDLINE/PubMed |
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| Keywords | estimating equations semi‐parametric models irregular observation longitudinal data |
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| References | Liang Y. (e_1_2_9_9_1) 2009; 65 Byar D. (e_1_2_9_4_1) 1980 Andersen P. K. (e_1_2_9_2_1) 1982; 10 Buzkova P. (e_1_2_9_3_1) 2010; 171 Hall A. (e_1_2_9_8_1) 2005 Coulombe J. (e_1_2_9_5_1) 2021; 77 Sun L. (e_1_2_9_12_1) 2011; 27 Wang M.‐C. (e_1_2_9_13_1) 2001; 96 Pullenayegum E. M. (e_1_2_9_10_1) 2023; 42 Diggle P. J. (e_1_2_9_6_1) 2002 Pullenayegum E. M. (e_1_2_9_11_1) 2016; 25 Efron B. (e_1_2_9_7_1) 1994 |
| References_xml | – volume: 42 start-page: 2361 issue: 14 year: 2023 ident: e_1_2_9_10_1 article-title: Causal Inference With Longitudinal Data Subject to Irregular Assessment Times publication-title: Statistics in Medicine doi: 10.1002/sim.9727 – volume-title: Generalized Method of Moments year: 2005 ident: e_1_2_9_8_1 – volume: 27 start-page: 29 issue: 1 year: 2011 ident: e_1_2_9_12_1 article-title: Semiparametric Analysis of Longitudinal Data With Informative Observation Times publication-title: Acta Mathematicae Applicatae Sinica, English Series doi: 10.1007/s10255-011-0037-2 – volume: 96 start-page: 1057 issue: 455 year: 2001 ident: e_1_2_9_13_1 article-title: Analyzing Recurrent Event Data With Informative Censoring publication-title: Journal of the American Statistical Association doi: 10.1198/016214501753209031 – volume: 77 start-page: 162 issue: 1 year: 2021 ident: e_1_2_9_5_1 article-title: Weighted Regression Analysis to Correct for Informative Monitoring Times and Confounders in Longitudinal Studies publication-title: Biometrics doi: 10.1111/biom.13285 – volume-title: An Introduction to the Bootstrap year: 1994 ident: e_1_2_9_7_1 doi: 10.1201/9780429246593 – volume: 25 start-page: 2992 issue: 6 year: 2016 ident: e_1_2_9_11_1 article-title: Longitudinal data subject to Irregular Observation: A Review of Methods With a Focus on Visit Processes, Assumptions, and Study Design publication-title: Statistical Methods in Medical Research doi: 10.1177/0962280214536537 – volume: 65 start-page: 377 issue: 2 year: 2009 ident: e_1_2_9_9_1 article-title: Joint Modeling and Analysis of Longitudinal Data With Informative Observation Times publication-title: Biometrics doi: 10.1111/j.1541-0420.2008.01104.x – volume: 10 start-page: 1100 issue: 4 year: 1982 ident: e_1_2_9_2_1 article-title: Cox's Regression Model for Counting Processes: a Large Sample Study publication-title: The Annals of Statistics doi: 10.1214/aos/1176345976 – volume: 171 start-page: 189 issue: 2 year: 2010 ident: e_1_2_9_3_1 article-title: Longitudinal Data Analysis for Generalized Linear Models Under Participant‐Driven Informative Follow‐Up: an Application in Maternal Health Epidemiology publication-title: American Journal of Epidemiology doi: 10.1093/aje/kwp353 – volume-title: Analysis of Longitudinal Data year: 2002 ident: e_1_2_9_6_1 doi: 10.1093/oso/9780198524847.001.0001 – start-page: 363 volume-title: Bladder Tumors and Other Topics in Urological Oncology year: 1980 ident: e_1_2_9_4_1 doi: 10.1007/978-1-4613-3030-1_74 |
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| Title | Intercept Estimation of Semi‐Parametric Joint Models in the Context of Longitudinal Data Subject to Irregular Observations |
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