Discriminant Function Analysis for Longitudinal Data: Applications in Medical Research (DiALog)

Identifying the correct diagnosis as early as possible, especially before the patient presents clear structural and/or functional changes, is key for a successful treatment. For example, delays in the treatment of patients with suspected encephalitis can have a devastating impact, including severe cognitive disability. Hence, it is not surprising that in most medical disciplines research focuses on identifying biomarkers and risk factors, some of them measured over time, to correctly predict patient outcomes. We propose to develop a novel statistical methodology that allows us to identify patients at higher risk of developing a particular disease or condition sooner than is currently achieved, with subsequent benefits for patients, clinicians and for health care system costs.

Delay in the detection of a disease is directly linked to economic burdens of the National Health Service and communities. When mechanisms are put in place to achieve early detection, they however may be economically demanding. Patients with diabetes, for instance, are screened annually for diabetic retinopathy at a considerable cost to the NHS. Bearing in mind that less than 4% of patients with diabetes will develop diabetic retinopathy within a year, there is a great interest in being able to identify patients with a higher risk in order to tailor the screening intervals. In other words, while patients with higher risk should be screened more often than once per year, the low risk group (involving 96% of the study population) could be screened less often than annually, reducing significantly both NHS costs and burden on patients and clinicians. Considering that in the UK alone there will be about 4 million people with diabetes by 2025, individualised screening is vital and it is expected to reduce annual costs to the NHS by more than £100 million without reducing medical screening efficacy.

In addition to the importance of early diagnosis, being able to identify early that someone is likely to show a poor prognosis is also essential to improve clinical management and optimise resources. For example, approximately one third of patients with epilepsy do not achieve remission from seizures following drug therapy. Early identification of this patient group would allow clinicians to focus on alternative treatments (e.g., surgery) as early as possible.

We aim to develop a novel time-dependent approach for discriminant analyss that (a) depends directly on both the individual baseline covariate information and the longitudinal data to achieve a more precise classification, (b) allows us to detect the earliest time point at which successful classification can be achieved (with a predefined error), and (c) can be applied to classify individuals into two or more groups, with unequal variance-covariance matrices among groups and incorporation of costs. Our objectives are divided into 3 main parts: development, implementation and clinical applications.

Identifying the correct diagnosis as early as possible, especially before the patient presents clear structural and/or functional changes, is key for a successful treatment. For example, delays in the treatment of patients with suspected encephalitis can have a devastating impact, including severe cognitive disability. Hence, it is not surprising that in most medical disciplines research focuses on identifying biomarkers and risk factors, some of them measured over time, to correctly predict patient outcomes. We propose to develop a novel statistical methodology that allows us to identify patients at higher risk of developing a particular disease or condition sooner than is currently achieved, with subsequent benefits for patients, clinicians and for health care system costs.

Discriminant function analysis can be used to make predictions of the group to which a patient most likely belongs (e.g., groups defined by high/low risk of developing diabetic retinopathy within a year). The use of longitudinally observed data can be particularly powerful in discriminant analysis. In longitudinal data analysis, responses are recorded at different time points and/or different locations, adding a longitudinal dimension to the data set. A promising approach to discrimination using longitudinal data for clinical applications is via extension of linear mixed models.

We aim to develop a novel time-dependent approach for discriminant analysis that (a) depends directly on both the individual baseline covariate information and the longitudinal data to achieve a more precise classification, (b) allows us to detect the earliest time point at which successful classification can be achieved (with a predefined error), and (c) can be applied to classify individuals into two or more groups, with unequal variance-covariance matrices among groups and incorporation of costs. Our objectives are divided into 3 main parts: development, implementation and clinical applications.

We see this project as a DiALog between clinicians and statisticians leading to a novel methodology that allows us to identify patients at higher risk of developing a particular disease or condition sooner than is currently achieved, with subsequent benefits for patients, clinicians and for health care system costs.
Our proposed research will have a broad range of impacts with different timescales.

Short-term impact (1-3 years and beyond)

Advance of scientific knowledge
We propose to develop a novel methodology in the area of discriminant function analysis that innovatively incorporates recent advancements from longitudinal methods. In a close collaboration with clinicians we will develop a time-dependent approach for discriminatory analysis that will mark a turning point in the way multivariate clinical data are analysed, strengthening evidence-based health decisions. Specifically, it will allow us to give recommendations to clinical researchers on the time points at which data need to be collected to achieve a chosen precision while minimising costs. Furthermore, the new methodology will lead to individualised assessments of risks applicable to any medical area. Finally, in addition to clear advancement of discriminant bio-statistical methods, this project provides a good platform to translate the outcomes into clinical practice (see 'Activities' and 'Medium and long term impact' below).

Development of a freely available statistical package
We will construct a statistical package to be implemented into the software R where the methodology developed and validated in Task1 will be implemented. This package will be freely available for the operating systems: windows, mac and linux. We will make use of the applications to clinical data to create worked-examples tailored to clinical researches for a better understanding of the concepts and assumptions behind the new methods.

Activities:

(i) Workshops: We will design, develop and deliver a workshop so that the state-of-the-art methods and statistical package are effectively disseminated.

(ii) Multidisciplinary research meeting across the UK. We will use our collaboration with the Royal Statistical Society to effectively disseminate the findings in multidisciplinary venues.

(iii) Development of a website for DiALog (to inform of DiALog research activities), which will be updated and maintained during the lifetime of the project.

(iv) Other activities include seminars, conferences, publications and academic visits.


Medium and long-term impact (2-4 years and beyond)
Impact to NHS policies and costs
DiALog will make it possible to identify patients who are at higher risk of developing a disease or condition and does this at the earliest time point possible. This will allow clinicians to act upon it in advance with appropriate preventive measures. Patients with diabetes, for instance, are screened annually for diabetic retinopathy at a considerable cost to the NHS.

Patients
Our fundamental goal with this proposal is to contribute to better health. The applicants of DiALog are either PIs or co-applicants of several medical research projects in areas such as infectious diseases, diabetes and diabetic retinopathy, epilepsy, stroke and cancer among others. We have developed experience in discussion with clinicians and patient groups on how to translate the statistical results into findings that are relevant to them. DIALOG will allow us to develop a platform with new clinical applications, and the clinical findings will be disseminated via meetings, the DiALog website, newsletters, study updates, workshops and conferences, invited talks and publications.