Influence analysis for skew‐normal semiparametric joint models of multivariate longitudinal and multivariate survival data

Tang, An Min; Tang, Nian; Zhu, Hongtu

doi:10.1002/sim.7211

Cited by 8 publications

(18 citation statements)

References 25 publications

(45 reference statements)

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“…Here, a penalized splines method is adopted to approximate g ( t ). Following Lang and Brezger 6 and Tang et al, 10 the polynomial splines approximation of g ( t ) has the form

g (t) \approx α_{0} + α_{1} t + \dots + α_{q} t^{q} + \sum_{k = 1}^{K} α_{q + k} {(t - 𝒦_{k})}_{+}^{q} = B {(t)}^{⊤} α,

where q is the degree of the polynomial component, K is the number of knots ( K knots divide the possible values of g ( t ) into K + 1 regression intervals),

α = {(α_{0}, α_{1}, \dots, α_{q + K})}^{⊤}

is a ( q + K )‐vector of unknown coefficients, and

B (t) = {(1, t, \dots, t^{q}, {(t - 𝒦_{1})}_{+}^{q}, \dots, {(t - 𝒦_{K})}_{+}^{q})}^{⊤}

with

a_{+}^{q} = {\max (0, a)}^{q}

, and

𝒦_{k}

is the location of the k th knot and is usually set as the {( k + 1)/( K + 2)}th quantile of the unique dataset { t i : i = 1, … , n } for k = 1, … , K or equidistantly set in the interval (

\min t_{}

…”

Section: Model and Bayesian Adaptive Lassomentioning

confidence: 99%

Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

Tang

2021

Statistics in Medicine

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Alzheimer's disease can be diagnosed by analyzing brain images (eg, magnetic resonance imaging, MRI) and neuropsychological tests (eg, mini‐mental state examination, MMSE). A partially linear mean shift model (PLMSM) is here proposed to investigate the relationship between MMSE score and high‐dimensional regions of interest in MRI, and detect the outliers. In the presence of high‐dimensional data, existing Bayesian approaches (eg, Markov chain Monte Carlo) to analyze a PLMSM take intensive computational cost and require huge memory, and have low convergence rate. To address these issues, a variational Bayesian inference is developed to simultaneously estimate parameters and nonparametric functions and identify outliers in a PLMSM. A Bayesian P‐splines method is presented to approximate nonparametric functions, a Bayesian adaptive Lasso approach is employed to select predictors, and outliers are detected by the classification variable. Two simulation studies are conducted to assess the finite sample performance of the proposed method. An MRI dataset with elderly cognitive ability is provided to corroborate the proposed method.

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“…Here, a penalized splines method is adopted to approximate g ( t ). Following Lang and Brezger 6 and Tang et al, 10 the polynomial splines approximation of g ( t ) has the form

g (t) \approx α_{0} + α_{1} t + \dots + α_{q} t^{q} + \sum_{k = 1}^{K} α_{q + k} {(t - 𝒦_{k})}_{+}^{q} = B {(t)}^{⊤} α,

where q is the degree of the polynomial component, K is the number of knots ( K knots divide the possible values of g ( t ) into K + 1 regression intervals),

α = {(α_{0}, α_{1}, \dots, α_{q + K})}^{⊤}

is a ( q + K )‐vector of unknown coefficients, and

B (t) = {(1, t, \dots, t^{q}, {(t - 𝒦_{1})}_{+}^{q}, \dots, {(t - 𝒦_{K})}_{+}^{q})}^{⊤}

with

a_{+}^{q} = {\max (0, a)}^{q}

, and

𝒦_{k}

is the location of the k th knot and is usually set as the {( k + 1)/( K + 2)}th quantile of the unique dataset { t i : i = 1, … , n } for k = 1, … , K or equidistantly set in the interval (

\min t_{}

…”

Section: Model and Bayesian Adaptive Lassomentioning

confidence: 99%

Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

Tang

2021

Statistics in Medicine

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“…Four indicators of QOL, that is, physical well-being (lousy-good), mood (miserable-happy), appetite (none-good), and perceived coping (“how much effort does it cost you to cope with your illness?” (a great deal-none)), were observed at baseline and months 3 and 18 after randomization to assess the treatment effect. Tang et al 12 pointed out that the QOL observations (in natural log scale) for 832 patients are highly skewed. To this end, as an alternative to the traditional JMLSs, some new JMLSs have developed to accommodate non-normal longitudinal data in recent years.…”

Section: Introductionmentioning

confidence: 99%

Variable selection for joint models of multivariate skew-normal longitudinal and survival data

Tang

2023

Stat Methods Med Res

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Many joint models of multivariate skew-normal longitudinal and survival data have been presented to accommodate for the non-normality of longitudinal outcomes in recent years. But existing work did not consider variable selection. This article investigates simultaneous parameter estimation and variable selection in joint modeling of longitudinal and survival data. The penalized splines technique is used to estimate unknown log baseline hazard function, the rectangle integral method is adopted to approximate conditional survival function. Monte Carlo expectation-maximization algorithm is developed to estimate model parameters. Based on local linear approximations to conditional expectation of likelihood function and penalty function, a one-step sparse estimation procedure is proposed to circumvent the computationally challenge in optimizing the penalized conditional expectation of likelihood function, which is utilized to select significant covariates and trajectory functions, and identify the departure from normality of longitudinal data. The conditional expectation of likelihood function-based Bayesian information criterion is developed to select the optimal tuning parameter. Simulation studies and a real example from the clinical trial are used to illustrate the proposed methodologies.

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“…(i) Most joint models focus on a single longitudinal variable associated with a time-to-event outcome (Henderson et al, 2000 ; Brown and Ibrahim, 2003 ; Tsiatis and Davidian, 2004 ; Rizopoulos, 2011 , 2012 ). However, in practice, many studies often collect multiple longitudinal outcomes (Lin et al, 2002 ; Brown et al, 2005 ; Chi and Ibrahim, 2006 ; Fieuws and Verbeke, 2006 ; Albert and Shih, 2010 ; Rizopoulos and Ghosh, 2011 ; Kim and Albert, 2016 ; Chen and Wang, 2017 ; Tang et al, 2017a , b ; Proudfoot et al, 2018 ; Chen et al, 2021 ) which may be significantly correlated. For example, the weight and height repeated measures presented in Figure 1 (left and middle panels) show significant correlation and it may lead to biased estimation if their correlation is ignored.…”

Section: Introductionmentioning

confidence: 99%

“…Alternatively, the skew-elliptical (SE) distributions including skew-normal (SN) distribution (Sahu et al, 2003 ) should be more appropriate to model the skewed data (Azzalini and Capitanio, 2003 ; Sahu et al, 2003 ; Arellano-Valle and Genton, 2005 ; Huang and Dagne, 2011 ). Although a few studies investigated multivariate joint (MVJ) models (Chi and Ibrahim, 2006 ; Albert and Shih, 2010 ; Rizopoulos and Ghosh, 2011 ; Kim and Albert, 2016 ; Chen and Wang, 2017 ; Tang et al, 2017a , b ; Chen et al, 2021 ), they have not considered non-normal features of longitudinal data.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Joint Modeling of Multivariate Longitudinal and Survival Data With an Application to Diabetes Study

Huang

Chen

et al. 2022

Front. Big Data

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Joint models of longitudinal and time-to-event data have received a lot of attention in epidemiological and clinical research under a linear mixed-effects model with the normal assumption for a single longitudinal outcome and Cox proportional hazards model. However, those model-based analyses may not provide robust inference when longitudinal measurements exhibit skewness and/or heavy tails. In addition, the data collected are often featured by multivariate longitudinal outcomes which are significantly correlated, and ignoring their correlation may lead to biased estimation. Under the umbrella of Bayesian inference, this article introduces multivariate joint (MVJ) models with a skewed distribution for multiple longitudinal exposures in an attempt to cope with correlated multiple longitudinal outcomes, adjust departures from normality, and tailor linkage in specifying a time-to-event process. We develop a Bayesian joint modeling approach to MVJ models that couples a multivariate linear mixed-effects (MLME) model with the skew-normal (SN) distribution and a Cox proportional hazards model. Our proposed models and method are evaluated by simulation studies and are applied to a real example from a diabetes study.

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Influence analysis for skew‐normal semiparametric joint models of multivariate longitudinal and multivariate survival data

Cited by 8 publications

References 25 publications

Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

Variable selection for joint models of multivariate skew-normal longitudinal and survival data

Bayesian Joint Modeling of Multivariate Longitudinal and Survival Data With an Application to Diabetes Study

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