Modelling within-individual variation in repeated continuous exposures

Measurements of biological and emotional states are often made repeatedly for the same person. These are used to monitor people with different health problems, or to alert people to health risks. Examples include the measurement of prostate specific antigen (PSA) every 3 months in monitoring of low-risk prostate cancer, and measurement of blood pressure at antenatal appointments to identify risk of pre-eclampsia in pregnant women. Measures are collected at varying intervals, but typically in months (PSA) or weeks (blood pressure during pregnancy) rather than days. Intensively-collected measures are made increasingly possible by new technology, including 'apps' on smartphones such as those which ask about mood at intervals throughout the day. Other examples include blood glucose monitoring in pregnant mothers for detecting and reducing the risk of delivery of a high-birthweight baby, and 24-hour blood pressure monitoring in routine clinical practice.
With these repeated measurements, doctors are often interested in the level of the measure (e.g. does a pregnant woman have high blood pressure), or in how fast the measure is rising (e.g. a rising PSA might indicate a worsening of prostate cancer). However, there is growing interest in whether the variability, or fluctuation, of an individual's measures might also be related to health. For example, how much a person's mood goes up and down, and the timing of these fluctuations, may tell us more about their mental health than just whether they tend to have high or low mood on average. Similarly, someone with blood pressure which varies a lot may be at higher risk of future heart attack or stroke than someone with more stable blood pressure.
There are many separate features of the way a measure varies for an individual which may predict future disease. One could be called the 'amplitude', and is a measure of how many very high and very low values a person experiences (for example, the difference between the very highest and very lowest blood pressures a person experiences during one day). Another is 'variation', and is a measure of how much the person's measure changes for their overall average. Disentangling these features of variation may be important in some situations. For example, it could be that it is the variation in blood pressure which predicts future heart attacks, but the amplitude of blood pressure during pregnancy which predicts problems for mother and child.
There have been many statistical methods developed to relate the level or change in a person's measures to a future disease, but far fewer to look at variation in a person's measurements. In this project, we aim to develop these much-needed statistical methods for modelling fluctuation in measures within an individual, and relating that fluctuation to risk factors and later disease. The developments we will make in this project will allow clinicians to make the best possible use of measures taken repeatedly within people in predicting their future health. We will make sure our new methods are freely available to all scientists in a user-friendly format.
We will apply these methods to two studies that have previously been published. The first is blood pressure readings during pregnancy from mothers whose children were part of ALSPAC, and relating these to the health of the child at birth. The second is a study that monitored blood pressure at 15-minute intervals over one day, and relating variation in this to later cardiovascular health.

Repeated measures of biological variables are used for diagnosis and prognosis in a wide range of clinical settings, with measures collected at varying intervals, but typically in months or weeks rather than days. Technological advances have facilitated the intensive collection of data over shorter time periods, such as real-time glucose monitoring. In many instances, the within-person variation in the repeated measure may be as predictive of future health as the average or rate of change. Although statistical methods for relating the trajectory of such measures to exposures or health outcomes are well-developed, these usually treat within-individual variation as a nuisance. Statistical methods to relate within-individual variability to outcomes are poorly developed and have not been widely used or evaluated.
The proposed research will develop methods for modelling within-individual variation in repeated measures, and relating this variation to distal outcomes. We will derive guidelines for the analysis of within-individual variation for different types of repeated continuous measure (normal, skewed) and different measurement schedules (intense, sparse, regular and irregular). We will extend existing Bayesian and frequentist multilevel methods, and examine their performance, in particular with respect to the number of measures per individual. Methods for estimating other aspects of variability (e.g. range) will be developed and applied. We will also use simulations to examine the conditions under which measurement error and within-individual variation can be disentangled. Data on blood pressure during pregnancy (ALSPAC) and ambulatory blood pressure, as well as other studies available to the co-applicants, and simulated data, will be used to test the generalisibility of our methods and conclusions.

There is increasing use of repeated measures in diagnosis, prognosis and monitoring of health conditions. Technological advances also mean that data is increasingly collected intensively, either by a personally-worn device such as an accelerometer or blood pressure monitor, or by smartphone. We will develop and evaluate methods to help researchers and clinicians take advantage of this wealth of repeated measures data.
Methodological research such as that proposed here will have immediate direct benefits for those in the research community. However, the ability to take advantage of repeatedly collected data in any clinical field clearly also has wider societal benefits, and could result in improved diagnosis and monitoring of health across a wide range of clinical specialties. Benefits could be gained by commercial enterprises which have an interest in the development of technology for measuring data intensively over time. These may include pharmaceutical or biotech companies wishing to develop monitors for use in routine healthcare, or for use in research. The proposed work holds considerable interest to social scientists concerned with variation in social and environmental exposures, how these factors impact on behaviours as well as health.
The development of devices capable of recording physiological measurements in real-time has gathered pace. This has been accompanied by the development of portable multi-use devices (particularly smartphones) capable of recording physiological and behavioural information to satisfy growing demand for devices that empower individuals to monitor their own health and fitness. Our proposed project will enhance the information that can be extracted from the measurements these devices record, and assist in the interpretation of the temporal signals these complex measurements provide. The project will have an impact spanning public, clinical and academic users of such devices, and those involved in the commercial development and manufacture thereof.
The proposed research will have implications for academics in biomedical science, statistics, computing and electronic engineering. To maximise the impact of the proposed research on these stakeholders we will disseminate our findings at national and international conferences, and internationally through publication in peer-reviewed, open-access journals, drawing on the team's established track record of publication in high impact journals. Beyond these traditional approaches to academic dissemination we will utilise the internet to disseminate the project's findings, setting up a project website.
The research assistant working on the project will gain experience in new methodology, and also experience different working environments through working with both the School of Social and Community Medicine and the Centre for Multilevel Modelling in Bristol, and through research visits to Edinburgh and collaboration with Leeds and UCL. Their participation in the wider group of academics interested in this area will enable them to be at the cutting-edge of new methodological developments, and provide an ideal springboard for their development as independent researchers. The wider IEU will also benefit from this methodological development, and researchers within the IEU and the School for Social and Community Medicine will gain exposure to sophisticated statistical methods which will ensure their competitiveness in the research job market.