Extending the linear mixed modelling framework for method comparison studies involving functional responses with applications in elite sports
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Date
2023-01-10Embargo Date
2025-01-09
Author
Das, Kishor
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Abstract
A method comparison study compares two or more different methods measuring some
quantity of interest and the aim is to determine the level of agreement between the
methods. Most of the methodological developments in this research area have focused
on studies where the response variable of interest is a univariate continuous response.
More recently there has been interest on method comparison studies where the response
is functional in nature (i.e. a discrete realisations of an underlying functional form).
This is still a new and growing field of research in Statistics with many open questions.
The specific aim of this thesis is to extend the Linear Mixed Modelling (LMM)
framework to method agreement studies i) involving a continuous response when the
observed bias between the methods of measurement is non-linear and ii) where the
response variable is functional in nature.
Initially the focus is on method comparison studies involving a univariate continuous
response where the LMM is used to extend the “classical” Bland and Altman approach
to account for non-linear bias between two methods of measurement.
Following this, a further extension of the LMM framework is proposed for method
comparison studies (of increasing design complexity) involving functional responses.
A natural alternative analytical approach to consider is the use of Functional Data
Analysis (FDA), given the nature of the response. A detailed description of the use of
FDA in method comparison studies is given including a new functional equivalent to
the Bland-Altman plot. An approach to adapt the LMM framework to accommodate
functional responses is then given and the benefits of this approach for study designs
with increasing complexity are discussed. The computational issues that arise when
fitting a nonparametric LMM are highlighted and a new elegant solution to circumvent this problem is proposed using an eigenbasis for the random-effects regressor matrix.
A simulation study is presented to investigate the performance of the FDA and
LMM when used to generate functional limits of agreement in studies with no replicates.
The performance of the eigenbasis approach to a full B-spline basis implementation is
compared in terms of coverage and computational time.
All the graphical and analytical approaches proposed are demonstrated using data
from two case studies in elite sports: one relating to blood biomarkers with a univariate
continuous responses and the other a comparison of two motion capture systems with
functional responses.