Eilers PHC, Marx BD. Practical Smoothing : The Joys of P-Splines. Cambridge University Press; 2021. Accessed March 6, 2025. https://doi.org/10.1017/9781108610247
Rigorous and robust statistical analysis lies at the heart of scientific endeavour. It provides the means to draw reliable conclusions from data, quantify uncertainty and distinguish genuine effects from random variation. Within epidemiology, modelling repeated measures in the same individuals over time helps us understand how people grow and develop over time and identify when adverse changes in people’s growth and development might occur. This allows researchers to identify when monitoring or support might be needed to improve people’s life course trajectory.
The challenge of growth modelling
Dr Ahmed Elhakeem, a Research Fellow in Epidemiology at the Bristol Medical School, is an expert in statistical techniques which can identify change in physical and psychological health trajectories.
Dr Elhakeem was recently awarded an MRC-NIHR Better Methods, Better Research New Investigator Research grant. The grant, ‘SITAR enhancements to support state of the art analysis on individual growth curves and their correlates’, is worth £540k over the next three years, was submitted in collaboration with Dr Richard Parker and Professor Kate Tilling and external collaborators in the UK, USA, and Canada.
Many developmental processes display non-linear patterns of change with age, especially during the growing years, which makes it challenging to accurately model their trajectories. One method that Dr Elhakeem uses is splines, which are flexible mathematical functions used for smoothing and interpolation of data in regression modelling, as Dr Elhakeem explains:
“Historically, the standard approach has been to make use of polynomial functions to approximate nonlinear curves. However, these can struggle when trying to reproduce complex patterns of change. Splines are highly flexible cutting-edge tools for analysing complex nonlinear change – they are made up of piecewise polynomials that are joined together at break/turning points called knots”.
Dr Elhakeem’s MRC-NIHR grant builds on collaborations and expertise developed using funding from the Elizabeth Blackwell Institute Discovery Research Support Scheme, which supports early career biomedical researchers in developing their research to explore and implement cutting edge methodologies.
Visiting researcher
“The Elizabeth Blackwell Institute Discovery Research Support Scheme allowed me to develop collaboration with Dr Li, an expert in splines, who was completing a Fellowship at Simon Fraser University. We invited him over as a visiting researcher to the Bristol Medical School in October 2022,” said Dr Elhakeem. “He kindly agreed to deliver a 1-day workshop to BMS on applied spline analysis for epidemiologists. The workshop was restricted to 20 attendees to allow productive interactions and hands-on practice, and all workshop material and code was made available to interested researchers.”
Following the well-received workshop, Dr Elhakeem, Dr Li and co-applicants are working on a number of papers using the technique; for example, assessing the association of birth weight on early life growth trajectories. Dr Elhakeem elaborates:
Early life growth dynamics
“This paper investigates the association between birthweight for gestational age centiles and infant and child growth curve features. It’s an ideal example to fully realise the value of spline methodology given the rapid and complex changes in body size during the first few years of life, that has limited previous research.”
Continued collaborations
“Dr Li and I continue to work together and collaborate on research projects and larger follow-on funding applications” said Dr Elhakeem.
“Collaboration with Dr Li has enabled me develop skills in implementing cutting edge methods of analysing complex change trajectories” said Dr Elhakeem. “I have been actively promoting and supporting use of splines by epidemiologists in workshops and tutorials. In 2023 I ran a session called “What is nonlinear trajectory modelling with splines?” at the 2023 National Centre for Research Methods Research Methods e-Festival. This included a segment on the knowledge gained in this project.”
Dr Elkaheem continued, “I am also building an interdisciplinary network, starting from the workshop, and extending to online tools beyond this grant, thereby generating a new activity pipeline around splines and future developments to ‘trajectory/change’ analyses, as well as co-supervising PhD candidates.”