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

Functional principal component analysis for identifying the child growth pattern using longitudinal birth cohort data

Background

Longitudinal studies are important to understand patterns of growth in children and limited in India. It is important to identify an 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. In this research study, we employed functional principal component analysis (FPCA) as a statistical method to find the pattern of growth data. The purpose of this study is to describe the longitudinal child growth trajectory pattern under 3 years of age using functional principal component method.

Methods

Children born between March 2002 and August 2003 (n = 290) were followed until their third birthday in three neighbouring slums in Vellore, South India. Field workers visited homes to collect details of morbidity twice a week. Height and weight were measured monthly from 1 month of age in a study-run clinic. Longitudinal child growth trajectory pattern were extracted using Functional Principal Component analysis using B-spline basis functions with smoothing parameters. Functional linear model was used to assess the factors association with the growth functions.

Results

We have obtained four FPCs explained by 86.5, 3.9, 3.1 and 2.2% of the variation respectively for the height functions. For height, 38% of the children’s had poor growth trajectories. Similarly, three FPCs explained 76.2, 8.8, and 4.7% respectively for the weight functions and 44% of the children’s had poor growth in their weight trajectories. Results show that gender, socio-economic status, parent’s education, breast feeding, and gravida are associated and, influence the growth pattern in children.

Conclusions

The FPC approach deals with subjects’ dynamics of growth and not with specific values at given times. FPC could be a better alternate approach for both dimension reduction and pattern detection. FPC may be used to offer greater insight for classification.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01566-0.

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

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.

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

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.

Bayesian Scalar on Image Regression With Nonignorable Nonresponse

Medical imaging has become an increasingly important tool in screening, diagnosis, prognosis, and treatment of various diseases given its information visualization and quantitative assessment. The aim of this article is to develop a Bayesian scalar-on-image regression model to integrate high-dimensional imaging data and clinical data to predict cognitive, behavioral, or emotional outcomes, while allowing for nonignorable missing outcomes. Such a nonignorable nonresponse consideration is motivated by examining the association between baseline characteristics and cognitive abilities for 802 Alzheimer patients enrolled in the Alzheimer's Disease Neuroimaging Initiative 1 (ADNI1), for which data are partially missing. Ignoring such missing data may distort the accuracy of statistical inference and provoke misleading results. To address this issue, we propose an imaging exponential tilting model to delineate the data missing mechanism and incorporate an instrumental variable to facilitate model identifiability followed by a Bayesian framework with Markov chain Monte Carlo algorithms to conduct statistical inference. This approach is validated in simulation studies where both the finite sample performance and asymptotic properties are evaluated and compared with the model with fully observed data and that with a misspecified ignorable missing mechanism. Our proposed methods are finally carried out on the ADNI1 dataset, which turns out to capture both of those clinical risk factors and imaging regions consistent with the existing literature that exhibits clinical significance. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.