On Estimating the Relationship between Longitudinal Measurements and Time-to-Event Data Using a Simple Two-Stage Procedure

Biostatistics and Bioinformatics Branch, Division of Epidemiology, Statistics, and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, Maryland 20892, USA.
Biometrics (Impact Factor: 1.57). 09/2010; 66(3):983-7; discussion 987-91. DOI: 10.1111/j.1541-0420.2009.01324_1.x
Source: PubMed


Ye, Lin, and Taylor (2008, Biometrics 64, 1238-1246) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual's random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al. (2008), an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.

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    • "Tsiatis and Davidian (2004) [5] provided a very thorough overview of early work on joint models, including those of De Gruttola and Tu (1994) [6], Wulfsohn and Tsiatis (1997) [4], Henderson et al. (2000) [7], and Wang and Taylor (2001) [8], among others. More recent work, including Ding and Wang (2008) [9], Nathoo and Dean (2008) [10], Ye et al. (2008) [11], Albert and Shih (2010) [12], Jacqmin-Gadda et al. (2010) [13], Rizopoulos, (2012) [14], Wu et al. (2010) [15], and Huang et al. (2011) [16], have extensively discussed the development, estimation and applications of joint models. Yi-Kuang Tseng et al., [17] used a joint modeling (graphic approach) to model survival time and time dependent CD4 count simultaneously for AIDS patients in Taiwan. "
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    ABSTRACT: Lately, joint modeling has been reckoned as a very efficient technique for studying combinations of longitudinal and survival data generated from medical studies. In this paper we have developed a joint model to simultaneously study the longitudinal repeated measures on CD4 cell counts and the time to event (event being defined as loss to follow up) process of HIV/AIDS patients undergoing Anti-retroviral therapy (ART) treatment at Dr. Ram Manohar Lohia Hospital's ART centre, New Delhi, India. Apart from increasing the risk of the HIV infection to progress to AIDS, the event of loss to follow up in patients undergoing ART seriously interferes with the development, improvement, and validation of treatment techniques being used in the therapy. The fact that the problem of loss to follow up from ART has been understated in studies based on ART centers in India has motivated us to investigate the effect of various clinical, socioeconomic and demographic factors on the hazard of loss to follow up in patients undergoing ART treatment. The results of the joint model have been compared with those of the separate analyses of the longitudinal and the survival data. The parameter estimates of both methods are consistent; however, the joint analysis supports the dependence of the hazard of lost to follow up from ART treatment on the rate of change in CD4 counts, apart from the patient's baseline CD4 count. The estimated overall survival probability for HIV/AIDS patients retained on antiretroviral therapy was 0.81; 95%CI (0.76-0.87).
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    • "This basic structure was later extended by Xu and Zeger (2001) to a variety of data situations. Other noteworthy method developments and significant data applications were presented by De Gruttola and Tu (1994), Nathoo and Dean (2008), and Albert and Shih (2010). Notably missing in this literature is variable selection. "
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    ABSTRACT: Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects is essential for practical data analysis. Simultaneous selection of variables in both longitudinal and survival components functions as a necessary safeguard against model misspecification. However, variable selection in such models has not been studied. No existing computational tools, to the best of our knowledge, have been made available to practitioners. In this article, we describe a penalized likelihood method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for simultaneous selection of fixed and random effects in joint models. To perform selection in variance components of random effects, we reparameterize the variance components using a Cholesky decomposition; in doing so, a penalty function of group shrinkage is introduced. To reduce the estimation bias resulted from penalization, we propose a two-stage selection procedure in which the magnitude of the bias is ameliorated in the second stage. The penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. Simulation study showed excellent selection results in the first stage and small estimation biases in the second stage. To illustrate, we analyzed a longitudinally observed clinical marker and patient survival in a cohort of patients with heart failure.
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