The normative modelling framework for traumatic brain injury

Abstract

This review examines the principles, applications and methodological foundations of normative modelling, emphasizing its potential to assist in mitigating longstanding challenges in traumatic brain injury (TBI) research and management. TBI remains a major global health concern, with an incidence exceeding 50–60 million cases worldwide. Progress in research and clinical practice has been hindered by the complex and heterogeneous nature of TBI, arising from diverse aetiologies, injury mechanisms and pathophysiological processes that lead to variable clinical presentations.

A significant obstacle, particularly present within neuroimaging, is the continued reliance on classification scales and analytical models that do not account for nuanced differences among patients. For example, the Glasgow Coma Scale and many prevalent models categorize injury severity levels by assuming homogeneity within groups, which inevitably results in heterogeneity and obscures individual variability. Similarly, traditional case-control research designs separate injury and control groups to conduct group difference testing, diluting valuable individual data by focusing on mean comparisons.

We advocate for a paradigm shift towards normative modelling—a flexible framework that assesses individual differences by comparing patients to a reference cohort. This approach moves beyond traditional methods that emphasize group differences, addressing the limitations of conventional classification by avoiding the aggregation of TBI patients into heterogeneous categories based on simplistic measures. By capturing the full spectrum of variability, normative modelling has the potential to improve patient selection in clinical trials and foster more personalized treatment strategies. Adopting this innovative approach aims to enhance outcomes for TBI patients by emphasizing individual variability rather than relying on broad group classifications. Normative modelling promises to transform the translation of TBI research into clinical practice, ultimately driving progress towards more effective, tailored interventions.

Mitchell et al. explore normative modelling as a transformative approach to traumatic brain injury. By comparing individuals to reference cohorts, this method overcomes the limitations of traditional classification systems, enabling personalized treatment strategies, better clinical trials, and improved patient outcomes.

Introduction

Traumatic brain injury (TBI) is one of the more prevalent forms of either acute or acquired brain injury, imposing a significant burden on global health. The incidence of TBI has increased over the past few decades, with estimates rising from approximately 18 million annual cases in 1990 to 50–60 million by 2017.^1,2 Of particular concern are TBI-related fatalities; in the United States alone, mortality rates reach 69 000 annually, equating to nearly 190 deaths per day.³

Beyond mortality, TBI leads to a broad spectrum of long-term consequences. Survivors may experience significant physical impairments, cognitive deficits and psychiatric disturbances.⁴ Emerging evidence also implicates TBI as a contributor to accelerated brain ageing, potentially leading to cognitive decline and increasing the risk for neurodegenerative diseases.^5,6 These high rates of mortality and morbidity underscore the urgent need for improved prevention and intervention strategies to mitigate both the immediate and long-term impacts of TBI on individuals and society.

TBI encompasses any external force that disrupts normal brain function.⁷ However, this disruption manifests uniquely in each individual, resulting in highly individualized neuropathophysiological profiles influenced by various neurobiological factors that lead to individualized recovery trajectories and outcomes. Some researchers suggest that heterogeneity should be viewed not merely as a limitation but as a hallmark of TBI.⁸ Factors contributing to variability in TBI outcomes include pre-injury characteristics such as age, sex, home and family support, and medical comorbidities.⁹ The mechanism of injury also plays a vital role; different types of impact—such as direct blows, acceleration-deceleration forces or skull penetration—lead to distinct neurological consequences.¹⁰ The presence of extracranial injury is a factor that influences different bodily functions, largely affecting outcome.¹¹ Additionally, the location and severity of brain impact influence the specific neurological deficits observed, reinforcing the complexity and heterogeneity of TBI.

Despite the substantial societal burden posed by TBI, there remains a lack of clear and accurate diagnostic criteria, even with recent developments in prognostic tools. Clinicians face considerable challenges in managing TBI patients due to the complexity and variability of injury presentations. The Glasgow Coma Scale (GCS) remains the clinical standard for categorizing TBI severity, yet it potentially oversimplifies the injury by neglecting individual differences and assuming uniformity within and across severity categories (Box 1).¹² Clinicians also face limited acute intervention strategies post-TBI, which could potentially be due to heterogeneous factors present within research (Box 2).

Box 1 Challenge of classification.

Accurate early classification is pivotal for guiding acute management and framing expectations after traumatic brain injury (TBI). Clinically, severity is still most often gauged with the Glasgow Coma Scale (GCS), which rates eye-opening, verbal and motor responses to give a score from 3 to 15.^13,14 Although indispensable at the bedside, the GCS was designed to capture ‘momentary’ neurological status, not to serve as a surrogate for long-term prognosis. Its thresholds, mild (14–15), moderate (9–13) and severe (3–8), compress a biologically heterogeneous disorder into three broad bins and are frequently applied inconsistently in both research and practice.

Many studies omit one or more GCS components or record the score at variable time points, undermining reproducibility.¹⁵ Unsurprisingly, outcome studies show high variability within any given GCS band: among ‘severe’ injuries (scores 3–8), reported mortality ranges from 0% to 100%, while subdividing ‘mild’ TBI (e.g. 13–14 versus 15) often fails to reveal meaningful differences in symptoms, imaging findings or neuropsychological performance.^16,17

Recognizing these limitations, several groups have mounted efforts to modernise TBI taxonomy. The National Institutes of Health (NIH)/National Institute of Neurological Disorders and Stroke (NINDS) International Initiative is developing a multidimensional, data-driven framework that combines acute clinical metrics (pupillary reactivity, advanced neuroimaging), physiological parameters and early neurobehavioural assessments such as the Westmead Post-Traumatic Amnesia Scale.^18,19 For post-acute and chronic phases, alternative systems have emerged: the American Congress of Rehabilitation Medicine’s criteria for mild TBI refine diagnostic boundaries, while the International Initiative for TBI Research (InTBIR)/NIH Common Data Elements and latent-class phenotyping studies capture persistent symptom clusters and disability profiles.²⁰ These schemes acknowledge that classification must be dynamic, evolving with injury stage and analytic capability.

However, even the newest proposals retain an element of categorical grouping. By design, any threshold-based system risks masking the very heterogeneity that drives outcome variability and frustrates treatment trials. A framework that can incorporate continuous, multimodal descriptors, such as deviation scores from normative models, may therefore be critical for transcending static categories, capturing the full spectrum of injury biology and ultimately delivering precision rehabilitation.

Box 2 Limitations of current evidence for acute interventions after traumatic brain injury: pharmacological and beyond.

Treating traumatic brain injury (TBI), particularly through pharmacological means, presents numerous challenges, many stemming from the difficulty of capturing neurobiological diversity. Despite increased investment by the US National Institutes of Health, there has not been a corresponding rise in successful clinical trials. A 2021 review of ClinicalTrials.gov found that, of 44 studies reporting results, only one showed statistically significant outcomes in its treatment arm.^21,22 Notably, this trial targeted sialorrhoea across various neurological disorders in children, not exclusively TBI. Of the remaining studies, only four published results; two demonstrated weak associations with improved TBI-related outcomes, while the other two reported promising preliminary findings that require follow-up analysis.^23-26 Most studies, however, did not report positive therapeutic outcomes.

The challenges in conducting clinical trials are complex and multifaceted, leading to frequent failures. Pharmaceutical clinical trials often focus on neuroprotective strategies, aiming to mitigate the secondary phase of injury—which includes inflammation, oxidative stress and neurotransmitter imbalances—resulting from the mechanical impact of TBI.²⁷ Despite some promising phase III and phase IV trials, there are currently no approved pharmacological treatments for managing either acute or chronic TBI recovery.²⁸ This could be due to trials targeting specific signalling pathways disrupted by TBI, neglecting the fact that the injury induces heterogeneous changes in brain physiology.²⁹ The inherent variability in the neurobiological response to TBI further compounds the challenges for researchers. While novel neuroprotective approaches are crucial for patients and their families, the research community has struggled to make significant advancements in therapeutic interventions.

Non-pharmacological treatments face comparable challenges. Physiotherapy protocols vary widely, and few randomized trials provide definitive efficacy data.³⁰ Neurosurgical procedures, while lifesaving in selected cases, are supported mainly by observational studies, prompting calls for more rigorous trials to define indications and timing.³¹ Blood-product strategies illustrate the same uncertainty: a recent meta-analysis of red blood cell transfusion in TBI concluded that, despite benefits in other critically ill populations, heterogeneity across studies precludes firm recommendations.³²

Addressing the complexity of TBI at both the biological and individual level remains a critical hurdle for improving patient outcomes. It is highly likely that a predominant cause of these failures is the incorrect collapsing of injury severity in clinical trials based on groups that are not homogeneous. When models like the Glasgow Coma Scale are used in clinical trials, they largely influence researchers’ decisions—whether in the investigation of specific pharmacological therapies or in measuring how treatments affect different aspects of this complex injury. When TBI models are too heterogeneous, it becomes difficult to derive statistically meaningful outcomes due to the remarkable heterogeneity present at every level of TBI—from individual genetic factors to the variability within a patient's medical condition.³³ Therefore, it stands to reason that more specific measures of injury could improve the success rates of clinical trials in TBI.

This review advocates for the leveraging of normative models—principally within neuroimaging studies of the sub-acute and chronic phases of TBI, where empirical work is most mature, as an additional framework to understand heterogeneity. By better accounting for the inherent diversity in TBI cases, these models have the potential to guide more personalized and effective interventions. The purpose of this review is not to prescribe a definitive set of target or predictor variables; rather, we outline the conceptual framework of normative modelling, describe its construction and validation, and discuss emerging applications within neuroimaging and TBI.

Heterogeneity in TBI

The core challenge in managing and researching TBI stems from its inherently heterogeneous nature. This complexity, shaped by various factors, makes rehabilitation efforts and research outcomes variable and difficult to standardise. The individualistic aspects of trauma make isolating specific target variables a major challenge, often rendering it impractical. This review briefly addresses a range of factors unique to each person and injury, all likely influencing how TBI manifests.

Mechanism of trauma

Variability in injury mechanisms leads to a wide range of outcomes and manifestations. In high-income countries, falls are the most common mechanism of injury among older adults, while road traffic accidents are more prevalent in younger populations.³³ In contrast, low- and middle-income countries report the highest rates of road traffic injuries among younger age groups. Other frequent mechanisms include assault, blast-related TBI and sports-related concussions.²

Biomechanical consequences vary significantly among these injuries. For instance, falls are often experienced in older adults, commonly linked to altered cerebrovascular physiology following TBI.³⁴ Road traffic accidents often involve rapid deceleration of the brain, causing additional damage due to sudden velocity changes.³⁵ Blast-related TBI typically starts with a direct impact to the head, followed by overpressure waves.³⁶ Injuries can also be categorized by loading mechanisms: impact injuries involve both contact and inertial loading due to forceful impacts, while impulsive injuries are characterized by inertial loading without direct impact.³⁷

Each trauma mechanism results in distinct neurobiological signatures, adding to the variability of post-trauma outcomes. This complexity poses significant challenges for researchers seeking meaningful findings, especially since current investigative methods lack effective strategies for addressing the heterogeneity of trauma mechanisms. Further, the response of the younger versus older brain to the various mechanisms of trauma likely contributes to heterogeneity in outcome.

Pre-injury

Highly individualized pre-injury factors critically influence TBI management and outcomes. Factors such as personality traits, substance use, medications, history of prior TBI, socioeconomic status, genetic predisposition, resilience, access to healthcare and support and anthropometric characteristics all affect the trajectory of TBI.^38-59 Among these, age, sex and comorbidities are the most significant contributors to neurobiological variability.

Age impacts both primary and secondary aspects of TBI. Older individuals (65 years and older) have the highest rates of hospital admissions (43.9%) and deaths (38.4%), followed by children and adolescents.^60,61 Studies show that older adults may experience slower recovery times, poorer cognitive and functional outcomes and increased dependency on caregivers.^62-66

Sex influences various neurological sequelae following TBI. Men experience nearly double the incidence rate compared to women (151 per 100 000 versus 86 per 100 000), although TBI rates among women increase with age, with higher incidences in women over 85.^67,68 However, intimate partner violence is highly skewed towards being directed against women, with a global prevalence of one in three, often including blows to the head.⁶⁹ Despite having similar injuries, women are less likely to visit a hospital or be admitted to intensive care and more likely to be discharged.⁷⁰ Women also tend to have more severe mental health and worse post-concussion symptoms following similar injury, especially following mild TBI.^70,71

Comorbidities further complicate injury manifestation. The presence of additional diseases, including neurological conditions, can exacerbate TBI outcomes. Comorbidities are common, particularly in older individuals, with 80% of the US population over 65 living with one chronic illness and 50% with two or more.⁷² Psychiatric disorders like depression or anxiety are relatively common comorbidities, affecting the rehabilitation and injury trajectory.^73,74 In research, such conditions likely confound symptom presentation post-TBI, making it difficult to delineate outcomes specific to TBI. This contributes to the chronic under-researching of vulnerable cohorts in an effort to maintain homogeneous samples.

Individual neuroimaging neuropathology

Regardless of the trauma mechanism, neuropathological manifestations are highly individualized. The label TBI encompasses diverse lesion subtypes—such as epidural haematoma (EDH), subdural haematoma (SDH), subarachnoid haemorrhage (SAH), focal contusion, and diffuse axonal injury (DAI)—all grouped under a homogeneous title. Often, these lesion categories co-occur in patients, the patterns of which are informative.^10,75 Each of these lesion subtypes requires specific interventions with different processes and recovery outcomes. For example, a patient with a large EDH has a high risk of mortality unless rapidly evacuated, but when the lesion is identified and evacuated early, it is associated with a good prognosis.^76,77 However, DAI often requires supportive care, focusing on preventing secondary injury through anti-inflammatories or other neuroprotective drugs.⁷⁸ The broad label TBI thus obscures significant heterogeneity in neuropathology.

Extracranial injury

The presence of any polytrauma in addition to TBI affects clinical treatment decisions, which adds to the complex and heterogeneous nature of TBI. Damage to other parts of the body, including the thoracic region, extremities and spinal cord, is relatively common in TBI.^79,80 These extracranial injuries can be widespread, having a large effect on the outcome of TBI.⁸¹ Initial damage to these regions can often lead to the disruption of functioning in multiple bodily systems, like the immune, autonomic nervous and haemostasis systems.^11,82 The extent of extracranial injury has been associated with a strong prognostic factor in mortality rates and unfavourable outcomes.^83,84 Extracranial injuries add to the remarkable heterogeneity present in TBI, largely affecting outcome.⁸⁵

Rehabilitation

The vast individual differences in neuropathology contribute to heterogeneity in TBI recovery. Predicting outcomes is challenging when research frameworks are developed for the ‘average’ patient, often stemming from categorical severity classification systems used to separate TBI groups. This creates a disconnect between how rehabilitation strategies are developed, tested and implemented.

Rehabilitation programmes are complex, requiring clinicians to address various facets of consciousness, cognition and physical recovery based on individual patient needs.^86,87 Clinicians depend on research that is easily transferable to practice, but the individuality of neurobiological responses to trauma is often overlooked in current research.

The complexity of informed decision-making is amplified by diverse pre-injury factors, injury mechanisms and varied neuropathologies. This places immense pressure on clinicians navigating these challenges to provide care. In response, recent efforts within the TBI field have shifted towards developing more individualized, patient-centred models of injury, focusing on capturing and addressing the variability inherent in TBI.^2,8

Reliance on group-difference models

One of the many prevailing frameworks in TBI research is case-control designs, where individuals with TBI (cases) are compared to similar individuals without the injury (controls).⁸⁸ Particularly within neuroimaging, where the majority of research approaches injury using group averages.^89-91 Studies often further stratify cases by injury severity and compare group averages across cohorts, implicitly assuming homogeneity within and between groups (Fig. 1).⁹² While effective in studying rare diseases and identifying risk factors, this approach may not be suitable for understanding the complex, heterogeneous nature of TBI.

Figure 1.

The assumptions of the case-control approach versus the reality of TBI. This figure contrasts the theoretical assumptions of case-control studies with the heterogeneous nature of TBI. (A) A representation of the traditional case-control approach, where the groups (TBI cases and healthy controls) are considered homogeneous, with a distinct separation between them. (B) A more realistic depiction of TBI research, where the boundary between groups is blurred, with notable overlap in characteristics between the TBI and control groups. (C) The idealized assumption in case-control studies, portraying TBI as a homogeneous condition, where comparisons between TBI and control brains are expected to apply universally to all patients. (D) A more accurate depiction of TBI’s heterogeneity, showing that collapsing a broad spectrum of injuries into a single case group results in findings that are less applicable to any individual patient, thereby oversimplifying the complex nature of the condition. TBI = traumatic brain injury.

Group-averaging methodologies provide robust statistical power but inherently discount individual variability and relies on between-group similarity in controllable factors like age and sex. In TBI—where neuropathology manifests differently across different individuals—this limitation is particularly pronounced. Although such methods have yielded valuable insights, they risk producing findings not fully applicable to the diverse TBI population. The pursuit of a ‘magic bullet’ treatment may overshadow the need to account for individual differences. By focusing on group-level analyses, researchers may inadvertently obscure meaningful individual variations, creating results that are broadly generalizable but applicable to no one in particular. Consequently, current research paradigms may fail to address the neurobiological heterogeneity defining TBI, hindering the development of more personalized, patient-centred approaches. Therefore, normative modelling is being put forward as an alternative method to move beyond group averaging.

Advancing precision medicine in TBI research

In many areas of medicine, patient care often follows a generalized, one-size-fits-all approach—a model that has also prevailed in TBI management. The limitations of current research methodologies highlight the need for better ways to measure and interpret individual variability in TBI. Understanding this vast heterogeneity presents an opportunity to develop more personalized approaches to treatment and rehabilitation.

Precision medicine offers a promising solution by tailoring healthcare based on the unique characteristics of each patient, accounting for individual variability in health status. It is a data-driven, patient-specific recovery strategy—including drug treatments and rehabilitation approaches—that evolves over time. By using updated patient information to guide therapeutic decisions throughout disease or injury progression, clinicians can select treatments that yield the best outcomes while minimizing unnecessary side effects. While physicians already aim to provide patient-specific care, precision medicine in research incorporates underutilized individual data, transforming what is often regarded as statistical ‘noise’ into valuable information.

At the heart of precision medicine is a continuous feedback loop: deep phenotyping leads to diagnostic and prognostic models, resulting in more accurate predictions of treatment outcomes. As individual data accumulate, biomarkers become identifiable, guiding more effective therapeutic interventions. This mechanism aligns directly with clinical experience, where decisions are made on an individual basis. Unfortunately, current management strategies and rehabilitation programs for TBI are often based on research derived from the ‘average’ patient, leading to a disconnect between research findings and clinical application. Precision medicine, by contrast, embraces heterogeneity and individual differences as essential assets rather than obstacles.

Although the ideal of precision medicine is not yet fully realized, notable successes exist in other fields. For example, Slamon et al.⁹³ discovered that breast cancer patients with overexpressed HER2 genes (present in 25%–30% of cases) responded positively to trastuzumab, a HER2-targeted monoclonal antibody, when added to their chemotherapy regimen. This personalized treatment significantly improved outcomes, including longer survival rates and reduced disease progression compared to chemotherapy alone. The ultimate goal of precision medicine is to compile sufficient relevant data to guide clinicians in selecting the most effective treatment for each patient based on their unique profile.

In TBI, however, progress towards precision medicine has been slow. The lack of clear definitions of TBI pathology hinders the development of this feedback loop in research, where individuality is pivotal to decision-making. The field urgently requires tools that can address the interplay between the complex heterogeneity of TBI and its clinical manifestations. Developing frameworks that enable meaningful, individual-level measurements is critical to better uncovering the characteristics of TBI neuropathology.

Normative modelling

The recent Lancet Neurology Commission on TBI underscores the necessity for integrated, person-centred assessments to better capture the complex individuality inherent in TBI cases.² Serving as a roadmap for the field, this document emphasizes the importance of approaches that value interindividual variability rather than dismissing it. In this context, normative modelling is emerging as a promising method for evaluating diseases and injuries, as it acknowledges and utilizes variations between individuals.

Normative modelling is a statistical method that differentiates individuals from a reference cohort by focusing on deviations from the expected norm (Fig. 2). By capturing individual differences relative to this reference group, it provides valuable insights into how an individual diverges from the ‘normal’ range.⁹⁴  Z-scores or percentiles are typically used to represent these deviations from the mean or median, allowing for a nuanced understanding of both healthy variation and the progression of injury or disease across the lifespan.⁹⁴ Crucially, this method enables researchers to make statistical inferences at the level of the individual, without minimizing the inherent variability within a dataset.

Figure 2.

Illustrating normative models: understanding individual variability. This figure presents an example of a normative model, where each brain represents an individual. The quantile curves indicate z-scores, with a z-score of 0 representing the expected value (mean). In this case, researchers have determined that a z-score of ±2 indicates an extreme deviation from the norm. The brain outlined in red visually represents an individual with such an extreme deviation within the model, highlighting the capacity of normative models to identify and interpret significant variations in individual characteristics. TBI = traumatic brain injury.

In a clinical context, the strength of normative modelling lies in its ability to function without requiring predefined subgroups of disease or injury, offering a deeper, individualized understanding of post-injury outcomes.⁹⁵ Furthermore, its adaptability makes it a versatile tool for assessing individual differences across a wide range of measures. By altering the variables being modelled, researchers can explore complex relationships between diverse factors, providing a comprehensive view of where an individual stands within a larger framework.

TBI research is particularly well-suited to the application of normative models, given the pronounced neuropathological heterogeneity. There is an opportunity to enhance the overall characterization of TBI, especially in research settings, potentially leading to more specific trials and outcomes. By approaching the characterization of TBI in an individualistic manner, we hold the potential to overcome one of the field’s greatest challenges: accurately capturing and measuring individual differences in injury outcomes.

The impact of normative modelling in healthcare

Normative modelling has a long history of enhancing clinical decision-making, with one of the earliest and most impactful examples being the establishment of developmental growth charts. Growth charts were utilized as early as the late 18th century, consistently being used to measure normal developmental growth.⁹⁶ Becoming more clinically prevalent when introduced by the National Center for Health Statistics (NCHS) in 1977, these growth charts became essential tools for clinicians to track a child’s physical development against societal norms.⁹⁷ The NCHS collected data from a large cohort of children, measuring height and weight from ages 2 to 18, which allowed for the creation of growth trajectories and provided a standard reference for typical physical development. Today, growth charts remain indispensable in paediatric care for diagnosing growth disorders, assessing nutritional status and ensuring children are developing as expected. In 2022, the Centers for Disease Control and Prevention updated these charts to include revised body mass index (BMI) percentiles, demonstrating their ongoing relevance and utility in modern healthcare.⁹⁸ These growth charts are now advancing beyond the white Caucasian model to include other racial groups.⁹⁹ The ease with which clinicians can access individualized patient data from these charts continues to support more accurate, data-driven decisions when growth deviates from expected trajectories.

Normative modelling also plays a crucial role in psychology, particularly in neuropsychology, where clinicians use normative data to compare an individual’s performance on cognitive tests. The norms for these measures are typically derived from group cognitive scores, adjusting for age, then fitting a parametric distribution over the residuals.¹⁰⁰ This method helps to assess cognitive impairments, differentiate normal variation from pathology and develop tailored treatment plans that address specific cognitive strengths and weaknesses. However, most of the time, this method of generating norms is not matched demographically to the cohorts they are used on. Despite this, normative models allow clinicians to track cognitive changes over time, offering a powerful tool for monitoring progress and adjusting interventions as needed. In research, these models validate assessment tools and enhance our understanding of cognitive processes and disorders by providing robust comparisons to normative data. Normative modelling has played a key role in laboratory medicine for decades, where laboratory tests are interpreted as normal or abnormal based on a representative reference group.¹⁰¹

These frameworks are currently being developed and tested in neuroimaging and psychiatric conditions. Researchers like Verdi et al.¹⁰² are utilizing normative modelling to analyse neuroimaging datasets in other heterogeneous diseases, specifically Alzheimer’s disease. This framework is also being applied and further explored through neuroimaging in psychiatric disorders like schizophrenia, attention-deficit hyperactivity disorder (ADHD) and depression.^94,103,104

Advancements in technological accessibility for normative modelling in TBI

Recent technological advancements and the rise of open science have paved the way for implementing normative models across the medical field. In the context of TBI, the Lancet Neurology Commission advocates for the adoption of federated science, emphasizing the open sharing of TBI data to enhance the development of machine learning techniques.² This recommendation aligns with the growing capabilities of machine learning, where systems learn and adapt model parameters from datasets through experience.¹⁰⁵

Machine learning involves learning statistical regularities from data, aiming to generalize to future samples. This enables researchers to explore large, federated datasets, uncovering relationships between variables that are often hidden or challenging to identify. Consequently, this facilitates the creation of specific, person-centred descriptions of current patient states that are both reliable and easy to interpret.

Several platforms already exist that leverage lifespan cohorts of healthy individuals, providing valuable resources for these advancements. For instance, the Predictive Clinical Neuroscience (PCN) lab has developed an online platform offering openly available MRI scans and a user-friendly interface for conducting normative modelling transformations based on a lifespan reference model.¹⁰⁶ Similarly, Bethlehem, et al.¹⁰⁷ published a study on brain development across the human lifespan, compiling over 123 984 MRI scans and making this dataset accessible through an open-access website. Importantly, they modelled non-linear growth trajectories in T1-weighted scans, with the ability to stratify by sex over the lifespan. Much of the problematic research conducted in the past was hampered by limited sample sizes that, even when paired with well-matched controls, could not resolve inter-individual heterogeneity. Moving forward, federated and privacy-preserving data-sharing frameworks will be essential for assembling the large, multi-site reference cohorts required for normative modelling. Importantly, once these models are established, they can be applied to a single new patient at the point of care, delivering individualized deviation maps without the need for further large-scale data collection or on-site model retraining.

These platforms provide immediate access to extensive datasets, enabling researchers to create normative reference cohorts and derive meaningful insights that can significantly enhance our understanding of brain health and disease. In laboratory medicine, efforts are being made to develop personalized reference intervals to improve the precision of test interpretation.

Key steps in building a normative model

Developing normative models involves several critical steps, especially when handling complex variables.⁹⁵ While specifics may vary depending on the context, some essential steps ensure the construction of a reliable model. The first step is selecting the target variable, predictor variables and a reference cohort. The reference cohort typically represents a subsection of the population within the normative framework, but sometimes a disease cohort can be used to compare individuals with the same condition. If using a population-based reference cohort, it is pivotal to capture a wide range of variation that is representative of the population.⁹⁵ The size of the reference cohort varies depending on the complexity of the variable in question. For example, due to the complexities associated with neuroimaging, the reference cohort used to capture population variability should be large.¹⁰⁷ Whereas other biomarker variables with differing levels of complexity may differ.

Next, an appropriate statistical model must be chosen to capture the variance of the target variable across the predictor. For example, to build a normative model for depressive symptoms (target variable) across age and gender (predictors), a healthy population could serve as the reference cohort, applying a suitable model to assess variance. However, creating a model without evaluating its predictive accuracy is insufficient. To ensure reliability, it is recommended to test the model’s performance on unseen data using metrics like root mean squared error (RMSE), explained variance or standardized error.⁹⁵

Bethlehem, et al.¹⁰⁷ explored additional methods for testing reliability applicable to various estimative models. They assessed the reliability and validity of their brain centiles by introducing new scans to each site’s dataset. The resulting estimative centile scores, derived from study-specific offsets and age-appropriate epochs, displayed high reliability in test-retest datasets.

The resulting normative model will derive deviation scores that can then be explored and transformed to address research questions. For example, Zabihi et al.¹⁰⁸ calculated deviation scores of cortical thickness derived from a normative model for each vertex on T1-weighted MRI scans between those who were neurotypical and participants with autism. These z-scores were then passed into normative probability maps, and for the autism group, an applied spectral clustering with cosine similarity affinity matrix was used to group into sub-clusters. These sub-clusters were analysed alongside phenotyping of clinical, behavioural and genetic measures of autism, subdividing individuals into anatomically different groups. Continually, other researchers have used support vector machines to classify deviation maps in neuropathological conditions such as TBI and schizophrenia.^109,110

As the model’s complexity increases, so do the considerations required, particularly when introducing additional variables and sites. Decisions on how to handle site effects, or analysing non-Gaussian distributions, can be addressed by employing advanced techniques to improve prediction accuracy. These foundational steps provide a structured approach to constructing a normative model while allowing the flexibility needed to accommodate complex data.

Promising normative modelling algorithms for TBI

The selection of an appropriate algorithm or model is critical in building an accurate normative framework. Numerous algorithms exist for assessing deviations within a normative model, but this review focuses on five widely used approaches in neuropsychology and neuroimaging.¹¹¹ These have shown promise in their appropriate fields in measuring neuropathology specific to each individual and are primed to be applied to the field of TBI (Table 1).

Table 1.

Pros and cons of popular normative modelling algorithms for neuroimaging in traumatic brain injury

Algorithm	Pros	Cons
Quantile Regression	Capture non-Gaussian distributions Robust to outliers Computationally efficient	No statistical quantification of the magnitude of deviation from the threshold Lacks predictive uncertainty
Gaussian Process Regression (GPR)	Provides predictive uncertainty Flexible non-parametric modelling	Computationally demanding for large datasets Predictive accuracy may diminish when applied to new datasets
Generalized Additive Models for Location Scale and Shape (GAMLSS)	Transferable to new datasets Flexible distribution functions Suitable for heteroscedastic data	Limited for small datasets Requires expert choice of model specification for accurate predictions
Bayesian Linear Regression (BLR)	Transferable to new datasets Provides predictive uncertainty Flexible model adaptations	Without adaptations, it assumes linearity Struggles with complex datasets
Hierarchical Bayesian Regression (HBR)	Transferable to new datasets Allows for site or subject-level variability Provides predictive uncertainty Does not require pre-defined variance Model flexibility	Computationally demanding

Traditional estimation approaches: quantile regression

Quantile regression is an older method employed to estimate normative models. When assumptions of homoscedasticity are violated or when variables deviate from a normal distribution, quantile regression can be useful. Quantile regression quantifies the association between covariates and variables without being dependent on the underlying distribution.

In a study by Lv et al.,¹⁰³ quantile regression was used to analyse the healthy range of brain structure and microstructure in schizophrenia patients. MRI scans of healthy individuals were used to establish normative percentiles, defining values below the 5th percentile as ‘infra-normal’ and above the 95th percentile as ‘supra-normal’. The study found that while many schizophrenia patients exhibited microstructural deviations beyond the healthy range, the variation was heterogeneous, with no single tract showing consistent abnormality across patients. This is a method that has test-retest reliability, first introduced by Fischl and Dale,¹¹² measuring neuroanatomical thickness levels, accurately identifying focal atrophy in those with psychiatric disorders. This approach holds promise to be applied to TBI for researchers measuring volumetric changes in individuals, with smaller datasets and little computational power. Quantile regression has also been used to develop continuous reference intervals for blood-based biomarkers relevant to TBI, including neurofilament light and glial fibrillary acidic protein.^{113  ,114} While quantile regression has proven flexibility, some researchers suggest that machine learning models may be preferable when dealing with larger datasets. This could partly be due to how quantile regression does not make very efficient use of data, resulting in much higher parameter uncertainty than other methods, especially if outer centiles are of interest. Quantile regression results are often interpreted using threshold centiles, leading to binary decisions (e.g. above or below a predefined threshold). This approach has a limitation: it does not allow for the statistical quantification of the magnitude of deviation from the threshold. In other words, while the model can determine whether a value is within or outside the threshold, it cannot measure how far it deviates from it in a statistically meaningful way.

Modern advances in normative modelling

Bayesian methods

Bayesian statistics represent an alternative approach to normative modelling. By incorporating prior knowledge and continuously updating the model as new data is introduced, Bayesian methods provide a dynamic model that aims to coherently manage uncertainty.¹¹¹ The model combines prior knowledge with data to fit a posterior distribution, which helps estimate results for new, unseen data. Unlike traditional methods that assume a single fixed relationship between variables, Bayesian methods also provide a measure of how confident we can be in each prediction.

Gaussian process regression

A Gaussian Process Regression (GPR) model employs a Bayesian non-parametric approach to interpolation, allowing the data to dictate the complexity of the underlying function that relates the input and output variables. The basic GPR model assumes that, for any given input, the distribution of functions used to interpolate the data is smooth. A significant advantage of GPR is its capability to model non-linear relationships while maintaining a fully probabilistic framework, making it particularly well-suited for neuroimaging applications.^94,115 However, a notable drawback is its computational scalability; GPR struggles with larger training datasets (over a few thousand samples) due to the demands on training time and memory allocation.¹¹⁶ Nevertheless, its flexibility allows for model modifications that can enhance sensitivity while reducing computational complexity.¹¹⁷ Wolfers, et al.¹¹⁸ employed GPR to reveal the substantial heterogeneity within schizophrenia and bipolar cohorts by analysing deviation scores in grey matter subregions. Easily translatable to TBI, where grey matter pathology caused by each injury is heterogeneous, this model would provide a substantial improvement in the individual characteristics of neuropathology.

GPR has been utilized extensively in ‘brain age’ studies. Although distinct from normative modelling, these studies involve using imaging-derived features collected from a healthy cohort to predict an individual’s brain age. Once pathologies are introduced into the GPR model, such as through a T1-weighted MRI scan, the predicted brain age is adjusted based on the observed volumetric changes. This approach has proven insightful across various pathologies, including HIV, where studies have reported an increase in predicted brain age despite viral suppression in HIV-positive adults.¹¹⁹

Methods similar to this are now being introduced in TBI. Cole et al.¹²⁰ applied GPR to estimate the ‘predicted age difference’ in brains affected by TBI. This provided a quantifiable measure of the impact of TBI on brain atrophy. Their findings indicated that brain age differences increased with time since injury, suggesting that TBI patients may be at an elevated risk of age-related diseases. This model uncovers more complex relationships between predictors and outcomes, offering a powerful alternative to Bayesian Linear Regression (BLR). However, it is worth noting that its accuracy may diminish when applied to new datasets, emphasizing the importance of validating these models across diverse populations.

Transferability of models

Models that can easily be transferred to new datasets will become increasingly popular alongside recent pushes for big-data. These models can learn the underlying relationship between predictor variables and then be applied to new, unseen datasets from different sites. This will be pivotal to the introduction of normative models across the globe, as within large datasets it is common to have multiple sites included, each site with slight variations in datasets. By using models that can account for these site-specific variations, there is an opportunity to introduce normative modelling to new locations with great efficiency and accuracy.

Generalized Additive Models for Location Scale and Shape

Generalized Additive Models for Location Scale and Shape (GAMLSS) represent a semi-parametric regression framework that incorporates distribution assumptions while allowing for non-parametric smoothing functions for predictor variables.¹²¹ This univariate regression model effectively accommodates multiple explanatory variables, enabling the measurement of location (mean), scale (standard deviation) and shape (skewness and kurtosis).¹²¹

GAMLSS is particularly flexible, as it can model the relationships between explanatory variables across a wide array of parameter distributions without necessitating constant variance. This flexibility has made GAMLSS pivotal in developing growth charts, leveraging the percentiles generated through the model. Furthermore, GAMLSS has been used extensively for neuroimaging applications; once the normative range is established, it can be adapted to new sites, provided recalibration occurs with a small portion of the new data.^122,123

Research has demonstrated the utility of GAMLSS in capturing the individuality of healthy brain ageing in cross-sectional studies and in establishing normative models for hippocampal volume.^124,125 However, several drawbacks must be considered: the requirement for an appropriate choice of parametric distribution for accurate results; the assumption of smooth changes in parametric shape with varying input functions; and its limited applicability to small datasets.¹²²

GAMLSS has already been implemented across neuropsychological disorders, handling complicated datasets from multiple sites. Thus, GAMLSS has the ability to be applied to volumetric data like cortical thickness and white matter volume within different phenotypes, making it extremely appropriate for measuring individualistic neuropathology in TBI. Through extensive testing by Bethlehem et al.,¹⁰⁷ this model is not yet at a stage where it is reliable for implementation in research studies of less than 100 T1-weighted MRI scans or by an individual for clinical practice. However, meaningful results show promise depending on how this model is parameterized. Overall, GAMLSS serves as a valuable tool for estimating normative cohorts, contingent on the correct specification of the underlying parametric distribution.

Bayesian Linear Regression

BLR applies the Bayesian approach within a linear model, assuming a direct relationship between input and output variables.¹²⁶ BLR is efficient and effective for simpler relationships, allowing methods using, for example, non-linear basis expansion to model linearity, and likelihood warping to model non-Gaussian data, to be developed.^127,128 These extensions enable BLR to handle irregular data more accurately and be applied across different research settings. For example, Barkema et al.¹⁰⁶ used BLR to measure deviations in cortical thickness in patients with schizophrenia. These deviation scores were then fed into another model, a Support Vector Machine (SVM), to help diagnose schizophrenia, resulting in a reasonably strong accuracy score of 0.78. This holds promise if applied to TBI in a similar way; that is, conducting BLR to measure volumetric data that are then fed into a diagnostic algorithm to better distinguish neuropathology specific to TBI.

Hierarchical Bayesian Regression

Hierarchical Bayesian Regression (HBR) integrates prior knowledge into new datasets while allowing for cross-group transferability of coefficients. This normative estimation model is built on a hierarchical linear model, modelling site effects using random slopes and intercepts, whilst also providing a full posterior distribution estimated using sampling methods.

HBR is especially beneficial for studies measuring variables across different sites, as it enhances the model's ability to translate data points to new, unobserved sites.¹²⁹ The advantages of employing HBR for normative modelling are multifaceted and have previously been discussed by Kia et al.¹³⁰ First, it accounts for variability at each data site and acknowledges model uncertainty. Second, it does not require pre-defined variance, allowing the model to identify appropriate variations for each site. Third, HBR supports a wide range of functional forms, including non-linear options. Lastly, it can extend hyper-priors from a reference cohort to new, unseen cohorts, which is useful in contexts where model estimation needs to be done in a decentralized or federated manner. Additionally, de Boer et al.¹³¹ introduced an extension of HBR to model non-Gaussian distributions, being particularly useful for imaging-derived phenotypes. Given these strengths, HBR has proven particularly effective in delineating variations between sites with respect to imaging-derived phenotypes.¹³²

Due to the incredibly high individuality of neuropathology in TBI, it is pivotal that a large dataset is used to derive normative estimations. HBR can bypass the need to share these sensitive data to each individual clinical application, instead being applied directly to a clinical site, making this a readily available tool that can be used in the field of TBI.

The promise of normative models in TBI

The Lancet Neurology Commission² emphasizes the need for individualized management and enhanced characterization of TBI. Normative models offer a promising approach to achieve these goals. By utilizing a normative modelling framework, researchers can conduct flexible and robust analyses of targeted variables, effectively parsing the heterogeneity of TBI to produce detailed and specific summaries of injury.

Implementing normative models can transform TBI measurement by classifying injuries as deviations from or position within a normal range, rather than simply distinguishing between healthy and injured individuals. This approach not only accommodates but leverages heterogeneity to create a more accurate representation of individual differences. Such models address recommendations from the Lancet review, calling for improved measurement of TBI severity across the injury spectrum.²

Normative models have the potential to evolve similarly to growth charts, continually updating to reflect individual neurobiology while providing valuable insights into a patient's current status. Techniques such as HBR can be applied across multiple sites, offering consistent feedback and supporting the development of tailored rehabilitation and recovery strategies. This flexible framework allows analysis of a wide range of clinically relevant variables, addressing the challenge of TBI heterogeneity and leveraging previously overlooked neurobiological variability.

The challenges of normative modelling in neuroimaging

Normative modelling rests on the availability of a reference cohort that mirrors the population of interest. However, building such a cohort in TBI may be uniquely difficult. Early studies have relied on large groups of healthy volunteers matched only on age and sex, but TBI rarely occurs in isolation.^{94,102  ,106  ,127,133} In real-world settings, an individual’s history of prior injuries, cardiovascular and psychiatric comorbidities, genetic risk variants (for example, APOE ε4), socio-economic status and even patterns of healthcare access can meaningfully shape brain structure and function.^45,51,56 Each of these factors can interact with injury severity, recovery trajectory and treatment exposure, so a reference dataset that omits them risks misclassifying biologically meaningful deviations as ‘normal’. Expanding recruitment to capture these variables is logistically demanding—particularly for under-represented groups such as older adults with poly-morbidity—but it is essential if normative models are to support precision rehabilitation. Pragmatically, reference cohorts will need to evolve iteratively, with models re-estimated as new covariates are added and as longitudinal follow-ups become available, so that temporal changes in brain metrics are disentangled from cohort effects.

A second hurdle is the absence of consensus on which MRI sequences, acquisition parameters and analytic pipelines should underpin target variables. Cortical thickness derived from a 3-T T1-weighted scan processed in FreeSurfer represents a very different data-generation pathway from neurite density obtained with multi-shell diffusion MRI.¹³⁴ Scanner vendors, field strengths, gradient non-linearities and reconstruction algorithms all introduce site-specific variance that can easily distort individual-level effects. Statistical harmonization techniques such as ComBat and common quality-control frameworks (e.g. BIDS) offer partial solutions, but they add layers of complexity that must themselves be validated. Normative models, therefore, need to be designed for modularity, allowing variables to be swapped in or out, and for transfer-learning approaches that can adapt previously trained models to new data modalities with minimal loss of calibration. On this point, the field may, in time, need to replace measures that are currently in use, for normative modelling to work going forward.

Lesion burden adds a further layer of intricacy. Focal contusions, haemorrhages and postsurgical cavities disrupt the assumptions built into most neuroimaging software, which were trained on brains without gross pathology.^134-136 When tissue is absent or signal is pathologically altered, automated parcellations can fail, leading to spurious outliers that propagate into the normative-modelling stage. Lesion-filling methods together with robust registration strategies that down-weight abnormal voxels are beginning to mitigate these failures, but they remain under active development and require careful visual inspection.¹³⁷ Even with these tools, DAI—arguably the hallmark of moderate-to-severe TBI—may only be visible on advanced diffusion or susceptibility-weighted sequences, raising questions about how to incorporate ‘invisible’ pathology into a framework that fundamentally relies on measurable brain-wide features.

Finally, high-dimensional models that incorporate dozens of covariates demand larger sample sizes than many single-centre studies can muster, mandating multi-site data sharing and rigorous governance around privacy. Missing data patterns, common in chronic TBI cohorts because of dropout, motion artefact or incompatible legacy scans, must be handled with methods that do not bias deviation scores. Computational requirements rise sharply as models move from univariate Gaussian processes to multivariate deep neural networks, and clinicians will need user-friendly interfaces and clear guidance before such tools can influence decision-making. Despite these challenges, the conceptual advantage of normative modelling remains: by benchmarking each patient against a well-characterized reference distribution, we gain a personalized map of abnormality that can evolve as biomarker science, imaging technology and analytic techniques advance.

Future directions

The application of normative models in TBI research offers numerous possibilities. A critical decision involves selecting predictive variables for the models. A promising direction is the measurement of neural volumetrics. Utilizing open-source lifespan models of brain charts provides an opportunity to develop analogous models that can be applied to TBI. Measures of grey matter, commonly researched across all TBI severity levels, could contribute to understanding individual injuries. Current research often uses a case- control framework, with findings suggesting that cortical thinning is associated with poorer outcomes post TBI.¹³⁸ Predicting brain age shows promise in understanding regionally heterogeneous variables.^5,139-141 However, further work is needed to develop volumetric applications of normative models into robust tools for TBI characterization.

Beyond volumetric measures, normative modelling can be applied to assess microstructural health. Jolly et al.¹⁴² identified fractional anisotropy (FA) abnormalities by comparing TBI participants’ white matter in regions of interest to control reference cohorts, better parsing white matter heterogeneity. Z-scores were derived and converted to P-values, with statistical significance identified at P < 0.05. This personalized approach demonstrated that time since injury significantly reduced FA, presenting another avenue for future studies to analyse white matter abnormalities without facing the challenge of neuropathological heterogeneity in TBI.

The application of normative modelling holds promise outside of purely neuroimaging. In psychiatry, normative models have been applied successfully to neurocognitive assessments and symptom presentation. Similarly, applying these models to TBI could enhance injury characterization (Fig. 3). For instance, Del Giovane et al.¹⁴³ conducted cognitive assessments on TBI participants at least 6 months post-injury, comparing results to a population range. By creating an online assessment tool referencing cognitive scores to a sociodemographic model, they could better identify specific cognitive deficits experienced by each TBI case. Their findings suggest that implementing normative modelling can help rehabilitation therapists address the variability of cognitive impairments in TBI, working towards more personalized and precise rehabilitation plans. Future research could use similar methods to investigate phenotypes that better characterise injury based on cognitive impairments.

Figure 3.

Hypothetical symptom-trajectory curves derived from a normative model of post-TBI recovery. This schematic shows how individual deviation scores (z-scores) could track symptom burden over time since injury. Three exemplar trajectories are depicted: a mild deviation (z ≈ −1.0) that improves rapidly; a moderate deviation (z ≈ −2.0) that resolves more slowly; and a severe deviation (z < −2.0) that remains elevated for many months. Although symptom burden is used here for illustration, any TBI-relevant variable, neurocognitive performance, blood biomarkers, quantitative MRI metrics, can be substituted, allowing clinicians to visualize patient-specific recovery paths against an established reference distribution. TBI = traumatic brain injury.

Incorporating blood biomarkers as predictive variables offers additional potential. Recent studies have explored central nervous system proteins indicative of neuronal or glial damage and inflammation present post TBI.^144,145 These proteins have been shown to improve the accuracy of predicting unfavourable outcomes in those with similar demographic or pre-injury factors.¹⁴⁶ Different biomarkers are elevated at different phases and times since injury.^147,148 Therefore, biomarkers are yet another variable that can aid in guiding clinical decision-making and hold promise. Introducing and applying normative modelling to these emerging biomarkers provides an opportunity to refine injury classification and severity assessment, allowing researchers to achieve a more precise reflection of each individual’s injury.

By providing a new approach that leverages heterogeneity encapsulated within clinical measures like blood biomarkers, neuroimaging and symptoms presentation, there is an opportunity to analyse these measures in a novel way (Fig. 4). The introduction of federated data systems also encourages the utilization of these neurobiological variables on a huge scale. Researchers have an opportunity to discover the discriminations between what neurobiological functions or structures are specific to TBI and what is healthy variation.

Figure 4.

Integrating multimodal variables within a normative-modelling framework for TBI. The diagram depicts a single TBI patient whose data span four domains: blood biomarkers; quantitative MRI (cortical thickness); computer-based neurocognitive testing; and self-reported symptoms. Deviation scores reveal markedly elevated biomarkers and pronounced cortical thinning, yet neurocognitive performance and symptom ratings fall within the reference range. By consolidating heterogeneous information into a common z-score metric, normative modelling highlights pathophysiological abnormalities that might otherwise be overlooked, thereby supporting a more comprehensive and individualized characterization of injury. Federated data platforms are critical for generating the large, diverse reference cohorts required to compute these scores reliably. TBI = traumatic brain injury.

Conclusion

Normative models hold significant potential to revolutionize the diagnosis, management and characterization of TBI, advancing the field towards precision medicine. Currently, TBI research faces substantial challenges in patient management and in obtaining meaningful outcomes from clinical trials. A primary factor contributing to these difficulties is the inherent heterogeneity of TBI, which complicates the interpretation of study results and impedes progress.

The reliance on traditional case-control models has often led to a reductionist view of TBI, treating it as a homogeneous condition and overlooking its diverse manifestations. These conventional approaches assume uniformity within and between groups, which contradicts the reality of TBI’s variability. Consequently, clinicians receive generalized advice, leading to less effective decision-making in rehabilitation.

This review advocates for the adoption of normative models as a transformative approach. By embracing the individual variability inherent in TBI, these models shift the focus from a one-size-fits-all perspective to one that leverages diversity. The application of tailored algorithms to specific variables allows for enhanced accuracy in diagnosis, improved clinical management and more precise characterization of TBI. This approach opens new avenues for understanding and addressing TBI, ultimately leading to more personalized and effective treatment strategies.

Funding

S.R.S. is supported by funding from Michael Smith Health Research BC. No other authors received financial support for authorship, research and/or publication.

Competing interests

The authors report no competing interests.