Clustering of longitudinal data: A tutorial on a variety of approaches

Teuling, Niek Den; Pauws, Steffen; Heuvel, Edwin van den

doi:10.48550/arxiv.2111.05469

Cited by 4 publications

(3 citation statements)

References 128 publications

(205 reference statements)

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“…KML enables us to find trajectories that do not follow polynomial curves, which may remain hidden with parametric methods (Genolini & Falissard, 2010), such as a peaks after the transition to secondary school. KML has also been demonstrated to work especially well in exploratory contexts such as ours (Teuling et al, 2021).…”

Section: Identifying Absence Trajectoriesmentioning

confidence: 90%

School absence trajectories and their consequences for achievement

Dräger¹,

Klein²,

Sosu³

2023

Preprint

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In this study, we examined the joint trajectories of authorised and unauthorised absences from first year of primary to the end of secondary school, and their consequence for educational achievement. Our sample consisted of linked data from the Millennium Cohort Study and the National Pupil Database in England (N=7093). Employing k-medians clustering for longitudinal data, we identified seven distinct absence trajectories. Five of these clusters had very low levels of unauthorised absences but different levels and dynamics of authorised absences (constantly low, constantly moderate, decreasing, slightly increasing, dramatically increasing), while two clusters were characterised by moderately and dramatically increasing unauthorised absences in the last years. Next, using a regression-with-residuals approach to adjust for time-varying confounders, we found that absence trajectories had significant consequences for pupils’ achievement, with a large effect size. The largest disadvantages appear for pupils with dramatically increasing unauthorised absences followed by dramatically increasing authorised, and moderately increasing unauthorised absence trajectories. These pupils were between 25 and 40 percentage points less likely to obtain 5 GCSEs. Even low to moderate absence trajectories were significantly detrimental to achievement. Our findings suggest a need to pay equal attention to all forms and levels of absences throughout the educational life course.

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Section: Identifying Absence Trajectoriesmentioning

confidence: 90%

School absence trajectories and their consequences for achievement

Dräger¹,

Klein²,

Sosu³

2023

Preprint

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“…Each trajectory was represented by the coefficients of an individually fitted linear regression model. The trajectories are then clustered based on the coefficients using k-means clustering ( 15 , 16 ). The best number of clusters was determined by multiple metrics including log likelihood value, Bayesian information criterion (BIC), and Akaike's information criterion (AIC).…”

Section: Methodsmentioning

confidence: 99%

Identifying Novel Clusters of Patients With Prolonged Mechanical Ventilation Using Trajectories of Rapid Shallow Breathing Index

Yang

Chen²,

Lin³

et al. 2022

Front. Med.

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ObjectivePatients with prolonged mechanical ventilation (PMV) are comprised of a heterogeneous population, creating great challenges for clinical management and study design. The study aimed to identify subclusters of PMV patients based on trajectories of rapid shallow breathing index (RSBI), and to develop a machine learning model to predict the cluster membership based on baseline variables.MethodsThis was a retrospective cohort study conducted in respiratory care center (RCC) at a tertiary academic medical center. The RCC referral criteria were patients with mechanical ventilation for at least 21 days with stable hemodynamic and oxygenation status. Patients admitted to the RCC from April 2009 to December 2020 were screened. Two-step clustering through linear regression modeling and k-means was employed to find clusters of the trajectories of RSBI. The number of clusters was chosen by statistical metrics and domain expertise. A gradient boosting machine (GBM) was trained, exploiting variables on RCC admission, to predict cluster membership.ResultsA total of 1371 subjects were included in the study. Four clusters were identified: cluster A showed persistently high RSBI; cluster B was characterized by a constant low RSBI over time; Cluster C was characterized by increasing RSBI; and cluster D showed a declining RSBI. Cluster A showed the highest mortality rate (72%), followed by cluster D (63%), C (62%) and B (61%; p = 0.005 for comparison between 4 clusters). GBM was able to predict cluster membership with an accuracy of > 0.95 in ten-fold cross validation. Highly ranked variables for the prediction of clusters included thyroid-stimulating hormone (TSH), cortisol, platelet, free thyroxine (T4) and serum magnesium.ConclusionsPatients with PMV are composed of a heterogeneous population that can be classified into four clusters by using trajectories of RSBI. These clusters can be easily predicted with baseline clinical variables.

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“…McNicholas (2016) provides a comprehensive review of finite mixture model based clustering (MBC) including clustering longitudinal data. Teuling et al (2021) provides a tutorial on a selection of methods for longitudinal clustering, including group-based trajectory modeling (GBTM), growth mixture modeling (GMM), and k-means based modelling for longitudinal data clustering (KML, cf. Genolini and Falissard, 2010;Genolini et al 2015).…”

Section: Introductionmentioning

confidence: 99%

Clustering Longitudinal Data for Growth Curve Modelling by Gibbs Sampler and Information Criterion

Fei,

Li,

et al. 2024

J Classif

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Clustering longitudinal data for growth curve modelling is considered in this paper, where we aim to optimally estimate the underpinning unknown group partition matrix. Instead of following the conventional soft clustering approach, which assumes the columns of the partition matrix to have i.i.d. multinomial or categorical prior distributions and uses a regression model with the response following a finite mixture distribution to estimate the posterior distribution of the partition matrix, we propose an iterative partition and regression procedure to find the best partition matrix and the associated best growth curve regression model for each identified cluster. We show that the best partition matrix is the one minimizing a recently developed empirical Bayes information criterion (eBIC), which, due to the involved combinatorial explosion, is difficult to compute via enumerating all candidate partition matrices. Thus, we develop a Gibbs sampling method to generate a Markov chain of candidate partition matrices that has its equilibrium probability distribution equal the one induced from eBIC. We further show that the best partition matrix, given a priori the number of latent clusters, can be consistently estimated and is computationally scalable based on this Markov chain. The number of latent clusters is also best estimated by minimizing eBIC. The proposed iterative clustering and regression method is assessed by a comprehensive simulation study before being applied to two real-world growth curve modelling examples involving longitudinal data clustering.

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Clustering of longitudinal data: A tutorial on a variety of approaches

Cited by 4 publications

References 128 publications

School absence trajectories and their consequences for achievement

School absence trajectories and their consequences for achievement

Identifying Novel Clusters of Patients With Prolonged Mechanical Ventilation Using Trajectories of Rapid Shallow Breathing Index

Clustering Longitudinal Data for Growth Curve Modelling by Gibbs Sampler and Information Criterion

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