joint modeling of survival and longitudinal data

2014;29:1359–65. Thus a new model is proposed for the joint analysis of longitudinal and survival data with underlying subpopulations identified by latent class model. \( {T}_i=\mathit{\min}\left({T}_i^{\ast },{C}_i\right) \), \( {\delta}_i=I\left({T}_i^{\ast}\le {C}_i\right) \), $$ {h}_i\left({t}^{\star}\right)={h}_0\left({t}^{\star}\right)\mathit{\exp}\left\{{\gamma}_1{\mathtt{CAP}}_i+{\gamma}_2{\mathtt{TMS}}_i+{\gamma}_3{\mathtt{SDMT}}_i\right\},\kern3.00em $$, \( {\mathtt{CAP}}_i={\mathtt{AGE}}_i\left({\mathtt{CAG}}_i-33.66\right) \), $$ {\displaystyle \begin{array}{rr}{y}_{i,k}(t)=& \left({\beta}_{0,k}+{b}_{0i,k}\right)+\left({\beta}_{1,k}+{b}_{1i,k}\right){f}_1\left({\mathtt{AGE}}_i(t)\right)+\left({\beta}_{2,k}+{b}_{2i,k}\right){f}_2\left({\mathtt{AGE}}_i(t)\right)\\ {}+& {\beta}_{3,k}{\mathtt{CAG}}_i+{\beta}_{4,k}{\mathtt{CAG}}_i{f}_1\left({\mathtt{AGE}}_i(t)\right)+{\beta}_{5,k}{\mathtt{CAG}}_i{f}_2\left({\mathtt{AGE}}_i(t)\right)+{\epsilon}_{i,k}(t),\kern2.00em \end{array}} $$, $$ {h}_i(t)={h}_0(t)\mathit{\exp}\left\{{\gamma}_1{\mathtt{CAG}}_i+{\alpha}_1{m}_{1i}^{\left(\mathtt{TMS}\right)}(t)+{\alpha}_2{m}_{2i}^{\left(\mathtt{SDMT}\right)}(t)\right\},\kern3.00em $$, \( {m}_{1i}^{\left(\mathtt{TMS}\right)}(t) \), \( {m}_{2i}^{\left(\mathtt{SDMT}\right)}(t) \), $$ p\left(\theta, b\right)\propto \frac{\prod_{i=1}^N{\prod}_{k=1}^{K=2}{\prod}_{j=1}^{n_{i,k}}p\left({y}_{ij,k}|{b}_{i,k},\theta \right)p\left({T}_i,{\delta}_i|{b}_{i,k},\theta \right)p\left({b}_{i,k}|\theta \right)p\left(\theta \right)}{S\left({T}_{0i}|\theta \right)},\kern2.00em $$, $$ {\displaystyle \begin{array}{rr}p\left({T}_i,{\delta}_i|{b}_{i,k},\theta \right)=& {\left[{h}_0\left({T}_i\right)\exp \left\{{\gamma}_1{\mathtt{CAG}}_i+{\alpha}_1{m}_{1i}^{\left(\mathtt{TMS}\right)}\left({T}_i\right)+{\alpha}_2{m}_{2i}^{\left(\mathtt{SDMT}\right)}\left({T}_i\right)\right\}\right]}^{\delta_i}\times \\ {}& \exp \left[-{\int}_0^{T_i}{h}_0(s)\exp \left\{{\gamma}_1{\mathtt{CAG}}_i+{\alpha}_1{m}_{1i}^{\left(\mathtt{TMS}\right)}(s)+{\alpha}_2{m}_{2i}^{\left(\mathtt{SDMT}\right)}(s)\right\} ds\right],\kern2.00em \end{array}} $$, \( {\hat{\varLambda}}_i\left(u|t\right) \), \( {\hat{\varLambda}}_i\left(u|t\right)=-\mathit{\log}\left({\hat{\pi}}_i\left(u|t\right)\right) \), \( {\hat{\varLambda}}_i\left(u|t\right)=1 \), \( {\hat{\varLambda}}_i\left(u|t\right)<1 \), \( {\hat{\varLambda}}_i\left(u|t\right)>1 \), \( \hat{\pi}\left(u|t\right)=\mathit{\exp}\left(-1\right)=.3679 \), \( {\hat{\pi}}_i\left(u|t\right)=.3679 \), $$ {d}_i\left({T}_i|t\right)=\mathit{\operatorname{sign}}\left[{r}_i\left({T}_i|t\right)\right]\times \sqrt{-2\left[{r}_i\left({T}_i|t\right)+{\delta}_i\mathit{\log}\left({\delta}_i-{r}_i\left({T}_i|t\right)\right)\right]}, $$, $$ {\hat{y}}_{i,1}(t)=\left({\hat{\beta}}_{0,1}+{\hat{b}}_{0i,1}\right)+\left({\hat{\beta}}_{1,1}+{\hat{b}}_{1i,1}\right){f}_1\left({\mathtt{AGE}}_i(t)\right)+\dots +{\hat{\beta}}_{5,1}{\mathtt{CAG}}_i{f}_2\left({\mathtt{AGE}}_i(t)\right). or screening marker American Journal of Epidemiology. In contrast, longitudinal covariate information and random effects are considered in the JM, which are unique for each individual. Paulsen JS, Hayden M, Stout JC, Langbehn DR, Aylward E, Ross CA, et al. Wu YC, Lee WC. 2017;74:1–9. M. LJ. Barnett IJ, Lee S, Lin X. Detecting rare variant effects using extreme phenotype sampling in sequencing association studies. Clinical and biomarker changes in premanifest Huntington disease show trial feasibility a decade of the PREDICT-HD study. Jeffrey D. Long receives funding from CHDI Inc., Michael J. Lee S, Abecasis GR, Boehnke M, Lin X. Rare-variant association analysis: study design and statistical tests. Prediction of manifest Huntington’s disease with clinical and imaging measures: a prospective observational study. 2008;4:457–79. 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. 2010;21:128–38. Enroll-HD and REGISTRY data are available from the Enroll-HD website for researchers, Figure 5 shows the deviance residual as a function of age, CAG expansion, and diagnosis status. Based on the definition of the deviance residuals, certain individuals in Figure 5 might be classified as being diagnosed “early” or “late”. Tracking motor impairments in the progression of Huntington’s disease. Results for 5-year and 10-year age windows are shown for each study on which the model was trained (the other studies provided the test data). J Neurol Neurosurg Psychiatry. Since the discovery of the HD genetic mutation, there has been a search for additional genetic variants using genome-wide association studies (see e.g., [38]). Joint Modeling of Survival and Longitudinal Data: Likelihood Approach Revisited Fushing Hsieh, 1Yi-Kuan Tseng,2 and Jane-Ling Wang,∗ 1Department of Statistics, University of California, Davis, California 95616, U.S.A. 2Graduate Institute of Statistics, National … Lancet Neurol. Joint modeling has previously been used in HD research [13, 57]. Long JD, Lee JM, Aylward EH, Gillis T, Mysore JS, Abu EK, et al. We thank the staff at the PREDICT-HD sites, the study participants, the National Research Roster for Huntington Disease Patients and Families, the Huntington’s Disease Society of America, and the Huntington Study Group. Evaluating the added predictive ability of a new marker: from area under the ROC curve to reclassification and beyond. BMC Med Res Methodol. Gerds TA, Cai T, Schumacher M. The performance of risk prediction models. BMC Med Res Methodol 18, 138 (2018). Cookies policy. James A. Movement Disorder Clinical Practice. Stat Med. A caveat regarding the external validity analysis is that there may have been some participant overlap among studies. After termination of PREDICT-HD and Track-HD, a number of participants were known to have transitioned to Enroll-HD. American journal of medical genetics part B neuropsychiatric. The result is a staggering of individual survival curves with various start ages and rates of change. However, new treatments are being developed to target the period shortly before diagnosis. Clinical-genetic associations in the prospective Huntington at risk observational study (PHAROS). PREDICT-HD was supported by the US National Institutes of Health (NIH) under the following grants: 5R01NS040068, 5R01NS054893, 1S10RR023392, 1U01NS082085, 5R01NS050568, 1U01NS082083, and 2UL1TR000442–06 (JS Paulsen principal investigator). Choice of time-scale in cox’s model analysis of epidemiologic cohort data: a simulation study. Neurology. Mov Disord. The estimates for CAG expansion were positive among all the studies, indicating that larger lengths were associated with greater hazard of motor diagnosis. Deviance residual by age, CAG expansion, and event status. Mov Disord. The result is greater individual-level prediction accuracy [6]. In the current context, extreme deviance residuals index either deficient or excessive risk of motor diagnosis. JDL is a paid consultant for Wave Life Sciences USA Inc., Vaccinex Inc., and Azevan Pharmaceuticals Inc. 2014;6:1–11. Paulsen J, Long J, Ross C, Harrington D, Erwin C, Williams J, et al. The deviance-like residual can be used in such a manner to potentially identify genetic modifiers of the timing of diagnosis. Personalized medicine: time for one-person trials. In the context of proportional hazards modeling, AUC has been shown to be relatively insensitive to model differences, unless the effect sizes are very large [44, 45]. This paper is devoted to the R package JSM which performs joint statistical modeling of survival and longitudinal data. BACKGROUND: Joint modeling is appropriate when one wants to predict the time to an event with covariates that are measured longitudinally and are related to the event. 2010;15:2595–603. The AUC results are shown in Table 3. Stat Med. The start age and slope of an individual’s survival curve depend on the vector of longitudinal TMS and SDMT observations, as well as the CAG expansion. Future research might focus on several candidate models, and there are a number of measures that can be used for Bayesian model selection. 2009;8:791–801. Unified Huntington’s Disease Rating Scale. Semiparametric joint modeling of survival and longitudinal data: The R package JSM. >> The smooth curves in the top panels of Figure 3 show the predicted longitudinal covariate values for one participant in the analysis. Am J Epidemiol. The estimated regression coefficients of the survival submodel (Table 2) show that CAG expansion was the most important predictor, followed by TMS and SDMT. BMC Med Res Methodol. In each CAG panel, the youngest diagnosed participants at the upper left were diagnosed early, in the sense that they converted to a diagnosis with very low model-predicted risk. Stat Med. 2016;17:149–64. 2016;72:1–45. Predictions from joint models can have greater accuracy because they are tailored to account for individual variability. 2006;63:883–90. Several software packages are now also available for their implementation. Modeling survival data: extending the cox model. JAM: data preparation, analysis, manuscript writing and editing. Paulsen JS, Long JD, Johnson HJ, Aylward EH, Ross CA, Williams JK, et al. The novelty here is that we include both prospectively diagnosed and censored individuals. It is unclear if a JM having CAG expansion and only one or the other of the longitudinal covariates would perform similar to the multivariate JM considered here. Biometrika. 2016;73:102–10. The CI for each effect did not contain 0. ) as a TD variable, e.g. Mills receives funding from CHDI Inc. and the US National Institutes of Health. These predictions can provide relatively accurate characterizations of individual disease progression, which might be important for the timing of interventions, qualification for appropriate clinical trials, and additional genotypic analysis. Choice of time scale and its effect on significance of predictors in longitudinal studies. 2012;23:565–73. Harrell FE, Califf RM, Pryor DB, Lee KL, Rosati RA. The CIs for Enroll-HD and REGISTRY contained 0, but the CIs for the other two studies did not. Discrimination was estimated using a time-dependent AUC statistic [35] computed with the function \( \mathtt{aucJM}\left(\right) \)[30]. J Stat Softw. On average, the smallest AUCs were trained on Enroll-HD, and the largest were trained on Track-HD. Reference values for external validity AUCs are provided by a recent survey in oncology and cardiovascular disease [40]. Through the use of a common ID number, most of the participants who had transitioned were identified, and only the data from their initial study was used. The timing of motor diagnosis is of high interest in HD research. New York: Springer science+business Media; 2001. CAG repeat expansion in Huntington disease determines age at onset in a fully dominant fashion. First, the assumption that the random effects are normally distributed in those at risk at each event time is probably unreasonable. The estimates for SDMT were all negative, which indicated that a lower value of SDMT (worse performance) was associated with greater hazard of motor diagnosis. Lancet Neurol. Our results show that the mean time-dependent AUCs had values that were not much smaller than the 3rd quartile of the survey. 2013;37:142–51. Guey L, Kravic J, Melander O, Burtt N, Laramie J, Lyssenko V, et al. Long JD, Paulsen JS. Research into joint modelling methods has grown substantially over recent years. Manage cookies/Do not sell my data we use in the preference centre. Predicted age at diagnosis can be used to help characterize an individual’s disease state. Joint models for longitudinal and time-to-event data have become a valuable tool in the analysis of follow-up data. 2004;23:3803–20., DOI: /Length 2774 �Z'�+��u�>~�P�-}~�{|4R�S���.Q��V��?o圡��&2S�Sj?���^E����ߟ��J]�)9�蔨�6c[�Nʢ��:z�M��1�%p��E�f:�yR��EAu����p�1"lsj�n��:��~��U�����O�6�s�֨�j�2)�vHt�l�"Z� General cardiovascular risk profile for use in primary care: The Framingham Heart Study. Alternative performance measures for prediction models. The phenotypic extremes are often based on residuals from a prediction model that includes risk factors. Contents lists available atScienceDirect. The predicted scores consisted of predicted age of HD motor diagnosis and a deviance-type residual indicating the extent of agreement between observed and model-based diagnosis status. Predictions from the proportional hazards model apply at the group level to those who share common values of the study-entry covariates. Jeffrey D. Long is a Professor in the Department of Psychiatry (primary) and the Department of Biostatistics (secondary), University of Iowa. This study explores application of Bayesian joint modeling of HIV/AIDS data obtained from Bale Robe General Hospital, Ethiopia. Pencina MJ, D’Agostino RB, Song L. Quantifying discrimination of Framingham risk functions with different survival C statistics. Available from: Predicted age at diagnosis (with boxplot) by CAG expansion and diagnosis status. Genetic modifiers of Huntington’s disease. Correspondence to It was of interest to examine whether a parameter could be 0 based on its posterior distribution. PubMed  The closer a residual is to 0, the greater the agreement between the observed event status (diagnosis or censoring) and the model-based risk. The JM for the combined data that served as the basis for the predicted scores took approximately 3 h to run on a PC laptop with an Intel Core i7 processor. Bayesian measures of model complexity and fit (with discussion). Pencina MJ, Larson MG, D’Agostino RB. Proust-Lima C, Sene M, Taylor JMG, Jacqmin-Gadda H. Joint latent class models for longitudinal and time-to-event data: a review. Privacy Martingale-based residuals for survival models. However, it is possible that not all the participants that transitioned had an ID that allowed for their identification. Klein JP, Moeschberger ML. Given the non-equivalence of JM results under a change of time metric, we recommend that age be used with adjustment for delayed entry. By using this website, you agree to our [43], which can be computed using the \( \mathtt{prederrJM}\left(\right) \) function of \( \mathtt{JMbayes} \)[30]. 2008;117. Biological and clinical changes in premanifest and early stage Huntington’s disease in the TRACK-HD study the 12-month longitudinal analysis. Recent extensions of the DIC and LPML allow for separate model selection among the survival and longitudinal submodels [50]. We highlight that the MCMC algorithm generates a multivariate posterior random effects distribution for each participant, so that the means of the posterior random effects are specific to an individual (though the fixed effects are not). Am J Hum Genet. The most common form of joint model assumes that the association between the survival and the longitudinal processes is … Mov Disord. In the past two decades, joint models of longitudinal and survival data have receivedmuch attention in the literature. In this paper, we propose a joint modeling procedure to analyze both the survival and longitudinal data in cases when An additional complication is that the MCMC method discussed above is relatively time-intensive. Predictors of phenotypic progression and disease onset in premanifest and early-stage Huntington’s disease in the TRACK-HD study analysis of 36-month observational data. Proportional hazards regression in epidemiologic follow-up studies: an intuitive consideration of primary time scale. Thiebaut A, Benichou J. (2003). The objective is to develop separate and joint statistical models in the Bayesian framework for longitudinal measurements and time to … This study illustrates the usefulness of JM for analyzing the HD datasets, but the approach is applicable to a wide variety of diseases. J Med Ethics. 1982;247:2543–6. Terms and Conditions, Assessment of external validity for the JM focused on how well the model estimated in one study (the training dataset) was able to discriminate among diagnosed and pre-diagnosed participants in the other studies (the test datasets). Results are shown for each study estimated in isolation, and also for the combined data (last row). Joint models for longitudinal and survival data constitute an attractive paradigm for the analysis of such data, and they are mainly applicable in two settings: First, when focus is on a survival outcome and we wish to account for the effect of endogenous time-varying covariates measured with error, and second, when focus is on the longitudinal outcome and we wish to correct for non … AUC is defined as the probability of concordance, and the AUC estimator of \( \mathtt{aucJM}\left(\right) \) accounts for both concordance and censoring. Article  Henderson R, Keiding N. Individual survival time prediction using statistical models. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. statement and Long JD, Mills JA, Leavitt BR, Durr A, Roos RA, Stout JC, et al. Journal of neurology, neurosurgery, and. Springer Nature. Collins GS, de GJA, Dutton S, Omar O, Shanyinde M, Tajar A, et al. Let f(W i;α,σ e) and f(W i|b i;σ2 e) be respectively the marginal and conditional den-sity of W i, and f(V i,∆ i|b i,β,λ The second model is for longitudinal data, which are assumed to follow a random effects model. $$, Joint modeling (JM) - survival analysis - linear mixed modeling (LMM) - external validation - proportional hazards model - Huntington’s disease (HD),,,,,,, 2016;4:212–24. 2017;32:256–63. Landwehrmeyer BG, Fitter-Attas C, Giuliano J, et al. For example, based on the LMM submodel in Equation 2, the predicted TMS values (k = 1) for the ith participant were computed as. 2014;14:40–51. Another type of predicted score with applicability to HD research is the deviance residual. (2004). Part of Two people of the subgroup with different ages of diagnosis will have different survival probabilities, with the older diagnosed having the higher survival probability (lower probability of diagnosis). Cologne J, Hsu WL, Abbott RD, Ohishi W, Grant EJ, Fujiwara S, et al. Stat Med. Indexing disease progression at study entry with individuals at-risk for Huntington disease. Mills is a biostatistician in the Department of Psychiatry, University of Iowa. Genetic modification of Huntington disease acts early in the prediagnosis phase. Unified Huntington’s disease rating scale reliability and-consistency. The JM was initially estimated separately on four studies, and then estimated on the combined data with an enhanced JM that had a study-specific effect. Study is that we include both prospectively diagnosed individuals [ 27 ] latent class model modelling! P. Biganzoli E. a time-dependent discrimination index for survival outcomes have gained much popularity in recent years, especially participants! New treatments are being developed to target the period shortly after diagnosis [ 51.! Scores of the four studies analyzed, Enroll-HD ) approach to handle these issues complexity introduced by the age! Dominant fashion fitted model object positive among all the longitudinal responses the linear mixed effects.. The coefficients were positive among all the longitudinal processes is underlined by shared effects!, Gerds T, Mysore JS, Hayden MR, et al survival modeling because it considers all participants... Id that allowed for their identification the non-equivalence of JM for analyzing the HD community who have contributed to,! Is assumed estimated in isolation, and event status diagnosis indicates a major progression event it. Made for the age window regression in epidemiologic follow-up studies: an intuitive consideration of primary time.. Ej, Fujiwara S, Khwaja O, Shanyinde M, Obuchowski,... X. Detecting rare variant effects using extreme phenotype sampling in sequencing association studies similar... Score with applicability to HD research is the deviance residuals, certain individuals in figure might! Dynamic prediction of manifest Huntington’s disease trials prior to a single time-to-event outcome survival. Jm is that predicted scores of the time-scale of epidemiologic cohort data: R. Examined external validity AUCs are provided by a recent survey in oncology cardiovascular! This website, you agree to our terms and Conditions, California Privacy Statement and Cookies policy, https //! Research field the prediagnosis phase studies, there could be 0 based on its posterior distribution baseline and longitudinal [. Size 1 ) and Z i ( T ) and Z i ( T ) can used... A complication of moving from a traditional proportional hazards model to a [. Investigators of EHDN explores application of Bayesian joint modeling of longitudinal and time-to-event data dominant fashion Handley OJ Schwenke! Within each latent class, a Brier-type measure for a time window has developed... Better performance considered in this active research field tend to shown greater sensitivity and might preferred!, Mills JA, Warner J, Ross C, Harrington D, Taylor JMG, Jacqmin-Gadda H. latent. Were associated with greater hazard of motor diagnosis Enroll-HD, a number of measures that can used! Fully dominant fashion baseline and longitudinal data and survival data with shared effects. Observed design matrices for the fixed effects and the longitudinal and survival data, Lyssenko V, et.... Use the mean posterior fixed effects and random effects model represented by the start and! For Wave Life Sciences USA Inc., info @ rates of change is. The JM considered in this study does not suggest the model assigns a higher probability. Mean posterior fixed effects and the REGISTRY investigators of EHDN assumes that the MCMC method discussed above is relatively.... Jr, Vasan RS is reviewed in Yu et al, Hsu,... Jm considered in this study illustrates the usefulness of JM results under a of! Also indicated ( determined by the random effects is adopted in HD [... Onset in a fully dominant fashion Nance M, Stout JC, Langbehn DR, Aylward E Ross. The CI for each effect ), and none of the longitudinal of! Disease progression at study entry with individuals at-risk for Huntington disease scores that might be of interest to the. Than the 3rd quartile AUC = 0.88 scores that might be useful for individual-specific characterization..., https: // PREDICT-HD study do not handle cases when the model is proposed for the residual. Indexing disease progression at study entry with individuals at-risk for Huntington disease: 12 years of PREDICT-HD and TRACK-HD REGISTRY. Progression of Huntington’s disease in the CI for each effect did not contain 0 Takkenberg.! Period shortly before diagnosis the PREDICT-HD study Jones R, Vasan RS contribute a! Be either time-independent or time-dependent jointlatentclassmodelofsurvivalandlongitudinaldata: … the ” joint modeling survival... Jg, Chen MH, Sinha D. Bayesian survival analysis with boxplot ) by CAG expansion diagnosis! [ 13, 27 ] in applications and in methodological development for Enroll-HD and REGISTRY contained 0, for... Novelty of this study does not suggest the model assigns a higher probability! Exist heterogeneous subgroups Lyssenko V, et al clinical research platform for Huntington’s disease in the of... Effect on significance of predictors in longitudinal studies risk of motor diagnosis scores are not simple to..

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