Optimal Designs for Longitudinal and Functional Data

Ji, Hao; Müller, Hans‐Georg

doi:10.1111/rssb.12192

Cited by 25 publications

(32 citation statements)

References 31 publications

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“…It is of interest to extend the proposed methods to select schedules that optimize power to detect associations between the longitudinal profiles and its correlates. While Ji and Müller () use predictive criteria for continuous outcomes to advance this area, we demonstrated that our proposed methods have power to detect associations between the profile and correlates even though the correlate was not specified in the design. Retout et al () evaluate the influence of designs on the power the Wald test has to detect a treatment effect in PMM.…”

Section: Discussionmentioning

confidence: 92%

“…In B.1 and B.2, we de‐trend the data using local linear regression and only use the FPCA design method. Since in B.1 and B.2 the PMM is not applicable, use Ji and Müller ()'s idea to compare the FPCA to a ”random design.” Here, a random design consists of m times chosen from S at random without replacement. For all approaches, we use the Metropolis–Hastings algorithm described in Section to obtain

T_{ℓ}^{*}

for each preliminary data set.…”

Section: Simulation Studymentioning

confidence: 99%

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FPCA-based Method to Select Optimal Sampling Schedules That Capture Between-subject Variability in Longitudinal Studies

Diez‐Roux

Raghunathan

et al. 2017

Biometrics

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Summary A critical component of longitudinal study design involves determining the sampling schedule. Criteria for optimal design often focus on accurate estimation of the mean profile, although capturing the between-subject variance of the longitudinal process is also important since variance patterns may be associated with covariates of interest or predict future outcomes. Existing design approaches have limited applicability when one wishes to optimize sampling schedules to capture between-individual variability. We propose an approach to derive optimal sampling schedules based on functional principal component analysis (FPCA), which separately characterizes the mean and the variability of longitudinal profiles and leads to a parsimonious representation of the temporal pattern of the variability. Simulation studies show that the new design approach performs equally well compared to an existing approach based on parametric mixed model (PMM) when a PMM is adequate for the data, and outperforms the PMM-based approach otherwise. We use the methods to design studies aiming to characterize daily salivary cortisol profiles and identify the optimal days within the menstrual cycle when urinary progesterone should be measured.

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Section: Discussionmentioning

confidence: 92%

T_{ℓ}^{*}

for each preliminary data set.…”

Section: Simulation Studymentioning

confidence: 99%

FPCA-based Method to Select Optimal Sampling Schedules That Capture Between-subject Variability in Longitudinal Studies

Diez‐Roux

Raghunathan

et al. 2017

Biometrics

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show abstract

“…Otherwise, if

p

is large, Ferraty et al . (), Ji & Müller () and Berrendero et al . () used a greedy search algorithm, and Wu et al () proposed a Metropolis sampling method.…”

Section: Methodsmentioning

confidence: 94%

“…While

{\overset{σ}{true}}_{ϵ}^{2}

might be close to zero in practice, we have not noticed such a case in the simulation studies and the real data applications. Should a very small estimate of error variance occur, we offer two options: (i) one may follow the approach in Ji & Müller () and select the estimate of error variance using cross‐validation of classification accuracy and (ii) approximate

{\overset{bold∑}{true}}^{- 1} = {false{\overset{r}{true} false(boldt, boldt false) + {\overset{σ}{true}}_{ϵ}^{2} {boldI}_{p} false}}^{- 1}

\sum_{k = 1}^{\overset{K}{true}} {\overset{λ}{true}}_{k}^{- 1} {\overset{bold-italicφ}{true}}_{k} {\overset{bold-italicφ}{true}}_{k}^{'}

, where

{\overset{bold-italicφ}{true}}_{k} = {false{{\overset{φ}{true}}_{k} false(t_{1} false), \dots, {\overset{φ}{true}}_{k} false(t_{p} false) false}}^{'}

and select

\overset{K}{true}

by cross‐validating the classification accuracy.…”

Section: Methodsmentioning

confidence: 99%

Optimal design for classification of functional data

Cai

Xiao

2019

Can J Statistics

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We study the design problem for the optimal classification of functional data. The goal is to select sampling time points so that functional data observed at these time points can be classified accurately. We propose optimal designs that are applicable to either dense or sparse functional data. Using linear discriminant analysis, we formulate our design objectives as explicit functions of the sampling points. We study the theoretical properties of the proposed design objectives and provide a practical implementation. The performance of the proposed design is evaluated through simulations and real data applications. The Canadian Journal of Statistics 48: 285–307; 2020 © 2019 Statistical Society of Canada

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“…Whereas our study of relative efficiency has taken the design matrix X (and Z ) as given and considered av G ( ρ ) as a function of ρ , the field of optimal design is concerned with the choice of X . Depending on the choice of G and of nomenclature, av G (0) might be the criterion for an I ‐, V ‐ or I V ‐optimal or Q ‐optimal cross‐sectional design; see Ji and Müller and Park et al for recent contributions to optimal design for functional data. In neuroimaging and other biomedical studies of growth trajectories, we generally cannot “optimally design” the participants' ages.…”

Section: Discussionmentioning

confidence: 99%

Cross‐sectional versus longitudinal designs for function estimation, with an application to cerebral cortex development

Reiss

2018

Statistics in Medicine

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Motivated by studies of the development of the human cerebral cortex, we consider the estimation of a mean growth trajectory and the relative merits of cross-sectional and longitudinal data for that task. We define a class of relative efficiencies that compare function estimates in terms of aggregate variance of a parametric function estimate. These generalize the classical design effect for estimating a scalar with cross-sectional versus longitudinal data, and are shown to be bounded above by it in certain cases. Turning to nonparametric function estimation, we find that longitudinal fits may tend to have higher aggregate variance than cross-sectional ones, but that this may occur because the former have higher effective degrees of freedom reflecting greater sensitivity to subtle features of the estimand. These ideas are illustrated with cortical thickness data from a longitudinal neuroimaging study.

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Optimal Designs for Longitudinal and Functional Data

Cited by 25 publications

References 31 publications

FPCA-based Method to Select Optimal Sampling Schedules That Capture Between-subject Variability in Longitudinal Studies

FPCA-based Method to Select Optimal Sampling Schedules That Capture Between-subject Variability in Longitudinal Studies

Optimal design for classification of functional data

Cross‐sectional versus longitudinal designs for function estimation, with an application to cerebral cortex development

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