Joint models with multiple longitudinal outcomes and a time-to-event outcome: a corrected two-stage approach
Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also a...
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Published in | Statistics and computing Vol. 30; no. 4; pp. 999 - 1014 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
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01.07.2020
Springer Nature B.V |
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Abstract | Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a novel approach that enables the fitting of such models with more realistic computational times. The idea behind the approach is to split the estimation of the joint model in two steps: estimating a multivariate mixed model for the longitudinal outcomes and then using the output from this model to fit the survival submodel. So-called two-stage approaches have previously been proposed and shown to be biased. Our approach differs from the standard version, in that we additionally propose the application of a correction factor, adjusting the estimates obtained such that they more closely resemble those we would expect to find with the multivariate joint model. This correction is based on importance sampling ideas. Simulation studies show that this corrected two-stage approach works satisfactorily, eliminating the bias while maintaining substantial improvement in computational time, even in more difficult settings. |
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AbstractList | Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a novel approach that enables the fitting of such models with more realistic computational times. The idea behind the approach is to split the estimation of the joint model in two steps: estimating a multivariate mixed model for the longitudinal outcomes and then using the output from this model to fit the survival submodel. So-called two-stage approaches have previously been proposed and shown to be biased. Our approach differs from the standard version, in that we additionally propose the application of a correction factor, adjusting the estimates obtained such that they more closely resemble those we would expect to find with the multivariate joint model. This correction is based on importance sampling ideas. Simulation studies show that this corrected two-stage approach works satisfactorily, eliminating the bias while maintaining substantial improvement in computational time, even in more difficult settings. Abstract Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a novel approach that enables the fitting of such models with more realistic computational times. The idea behind the approach is to split the estimation of the joint model in two steps: estimating a multivariate mixed model for the longitudinal outcomes and then using the output from this model to fit the survival submodel. So-called two-stage approaches have previously been proposed and shown to be biased. Our approach differs from the standard version, in that we additionally propose the application of a correction factor, adjusting the estimates obtained such that they more closely resemble those we would expect to find with the multivariate joint model. This correction is based on importance sampling ideas. Simulation studies show that this corrected two-stage approach works satisfactorily, eliminating the bias while maintaining substantial improvement in computational time, even in more difficult settings. |
Author | Boersma, Eric Steyerberg, Ewout Rizopoulos, Dimitris Kardys, Isabella Mauff, Katya |
Author_xml | – sequence: 1 givenname: Katya orcidid: 0000-0002-2443-9830 surname: Mauff fullname: Mauff, Katya email: k.mauff@erasmusmc.nl organization: Department of Biostatistics, Erasmus University Medical Center – sequence: 2 givenname: Ewout surname: Steyerberg fullname: Steyerberg, Ewout organization: Center for Medical Decision Making, Department of Public Health, Erasmus Medical Center, Department of Biomedical Data Sciences, Leiden University Medical Center – sequence: 3 givenname: Isabella surname: Kardys fullname: Kardys, Isabella organization: Department of Cardiology, Erasmus University Medical Center – sequence: 4 givenname: Eric surname: Boersma fullname: Boersma, Eric organization: Department of Cardiology, Erasmus University Medical Center – sequence: 5 givenname: Dimitris surname: Rizopoulos fullname: Rizopoulos, Dimitris organization: Department of Biostatistics, Erasmus University Medical Center |
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Cites_doi | 10.1200/JCO.1991.9.1.191 10.1111/j.1541-0420.2007.00952.x 10.2307/2533118 10.1214/09-AOAS251 10.1002/(SICI)1097-0258(19960815)15:15<1663::AID-SIM294>3.0.CO;2-1 10.1002/sim.4205 10.1111/j.1541-0420.2005.00448.x 10.1093/biostatistics/kxp009 10.1111/j.0006-341X.2005.030929.x 10.1080/01621459.2014.931236 10.1002/sim.7027 10.1198/1061860043010 10.1016/j.ahj.2017.10.008 10.1111/j.1541-0420.2010.01546.x 10.1111/j.1541-0420.2007.00983.x 10.1002/sim.6158 10.1111/biom.12814 10.1016/j.jmva.2009.04.008 10.1002/sim.1179 10.1201/b12208 10.1002/sim.6972 10.1016/j.csda.2006.09.027 10.1002/bimj.201600238 |
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Snippet | Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model,... Abstract Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic... |
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SubjectTerms | Artificial Intelligence Computer simulation Computing time Importance sampling Mathematics and Statistics Multivariate analysis Probability and Statistics in Computer Science Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs Survival |
Title | Joint models with multiple longitudinal outcomes and a time-to-event outcome: a corrected two-stage approach |
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