The impact of model assumptions in scalar‐on‐image regression

Happ, Clara; Greven, Sonja; Schmid, Volker

doi:10.1002/sim.7915

Cited by 7 publications

(6 citation statements)

References 57 publications

(144 reference statements)

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“…In addition to the bias induced by the regularisation, another potential issue related to the functional coefficient is its sensitivity to the modelling strategy used. As extensively studied in Happ et al. (2018) , the smoothness induced by splines could lead to different estimates with respect to other approaches (e.g.…”

Section: Discussion and Further Researchmentioning

confidence: 99%

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Quantifying uncertainty in brain-predicted age using scalar-on-image quantile regression

et al. 2020

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Prediction of subject age from brain anatomical MRI has the potential to provide a sensitive summary of brain changes, indicative of different neurodegenerative diseases. However, existing studies typically neglect the uncertainty of these predictions. In this work we take into account this uncertainty by applying methods of functional data analysis. We propose a penalised functional quantile regression model of age on brain structure with cognitively normal (CN) subjects in the Alzheimer’s Disease Neuroimaging Initiative (ADNI), and use it to predict brain age in Mild Cognitive Impairment (MCI) and Alzheimer’s Disease (AD) subjects. Unlike the machine learning approaches available in the literature of brain age prediction, which provide only point predictions, the outcome of our model is a prediction interval for each subject.

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Section: Discussion and Further Researchmentioning

confidence: 99%

“…In our context we call it scalar-on-image regression . The non-identifiability problem ( Happ et al., 2018 ) arising from having sample size lower than the number of voxels for each image can be attenuated by imposing some assumptions on the data generating process (for example smoothness).…”

Section: Introductionmentioning

confidence: 99%

Quantifying uncertainty in brain-predicted age using scalar-on-image quantile regression

et al. 2020

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“…[12,[14][15][16][17][18]. Outlier detection visualizing tools such as Functional version of Box plot and outliergram were used to identify an abnormal function in both outcomes [17][18][19][20]. There are two types of variability in the functions: (i) amplitude variation and (ii) phase variation.…”

Section: Smoothing Outlying Function and Fpcamentioning

confidence: 99%

Identifying longitudinal child growth curve pattern using Functional Principal Component Analysis from birth cohort study in South India

Karuppusami¹,

Antonisamy²,

Premkumar³

2021

Preprint

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Background: Human growth studies has long been of interest to researchers and health authorities. Predominantly, the study of physical growth in children is a challenging and complex issue. The goal of a variety of studies from across the world is to develop overall health and well-being in children. It is therefore important that we need to identify an accurate and reliable approach for characterising growth trajectories to distinguish between children who have healthy growth and those growth is poor. Many statistical approaches are available to assess the longitudinal growth data and which are difficult to recognize the pattern. The purpose of this study is to identify the longitudinal child growth trajectory pattern and factors association on the growth function using an advanced statistical technique. Methods: This longitudinal birth cohort study (n=290) was conducted in three nearby urban slums communities in Vellore, South India. Pregnant women were identified during a survey conducted in 2002 and infants were recruited from birth between the period of March 2002 and August 2003 following written informed consent from the mother. Growth outcomes of height and weight measurements were recorded for each child continuously in first 36 months. Functional Principal Component Analysis was used to classify the longitudinal child growth trajectory pattern. Functional linear model was used to assess the factors association with the growth functions. Results: We have obtained four functional principal components explained by 86.5%, 3.9%, 3.1% and 2.2% of the variation respectively for the height functions. 38% of the children’s had poor growth trajectories in height. Similarly, we have obtained three functional principal components explained 76.2%, 8.8%, and 4.7% respectively for the weight functions. 44% of the children’s had poor growth in their weight trajectories. The study shows that gender, socio-economic status, parent’s education, breast feeding, and gravida are associated and, influence the growth pattern in children. Conclusions: The advanced FPC approach deals with subjects’ dynamics of growth and not with specific values at given times. FPCA may be a better alternative approach in the sense of both dimension reduction and pattern detection. FPCA may be used to offer greater insight for classification.

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“…In practice, it is generally assumed that theoretical conditions for identifiability are satisfied when estimating β(t) in model (1). In scalar-on-image regression models, Happ et al [12] studied the impact of structural assumptions of the parameter image, such as smoothness and sparsity, on the model estimates, as well as measures to assess to what degree the assumptions are satisfied.…”

Section: Number Of Independent Pieces Of Information In a Flmmentioning

confidence: 99%

On the Number of Independent Pieces of Information in a Functional Linear Model with a Scalar Response

Montoya

2020

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In a functional linear model (FLM) with scalar response, the parameter curve quantifies the relationship between a functional explanatory variable and a scalar response. While these models can be ill-posed, a penalized regression spline approach may be used to obtain an estimate of the parameter curve. The penalized regression spline estimate will be dependent on the value of a smoothing parameter. However, the ability to obtain a reasonable parameter curve estimate is reliant on how much information is present in the covariate functions for estimating the parameter curve. We propose to quantify the information present in the covariate functions to estimate the parameter curve. In addition, we examine the influence of this information on the stability of the parameter curve estimator and on the performance of smoothing parameter selection methods in a FLM with a scalar response.

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The impact of model assumptions in scalar‐on‐image regression

Cited by 7 publications

References 57 publications

Quantifying uncertainty in brain-predicted age using scalar-on-image quantile regression

Quantifying uncertainty in brain-predicted age using scalar-on-image quantile regression

Identifying longitudinal child growth curve pattern using Functional Principal Component Analysis from birth cohort study in South India

On the Number of Independent Pieces of Information in a Functional Linear Model with a Scalar Response

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