Development of statistical methods for the analysis of single patient data

Questions arise where an individual is to be compared with a population. What proportion of patients suffering from this disease would have a temperature as low as this patient? Is this patient's combination of enzyme levels unusual? Is it rare to have a pulse rate this high with a blood pressure reading this low? This type of comparison can be of interest, not only to the patient and those treating the patient, but also to science. For example, a patient with a brain injury may display a strange combination of abilities that give insight into the architecture of the brain: the patient may be better than most people at performing one task but much worse than most people at a second task, even though the two tasks are apparently similar. This would show that while the two tasks seem similar they are, in fact, performed by different parts of the brain as the brain injury has impaired performance on one task but not the other. As another example, a patient with Alzheimer's disease might appear to have a reduced rate of memory loss for certain tasks after starting a new medication for a different complaint. Then it is important to know whether the patient's results are genuinely unusual for a person with Alzheimer's disease.

Statistical methods are needed to answer these types of question. Good methods have been developed for the simplest situations where only a single attribute is of interest. These methods are well-used by neuropsychologists and neuroscientists. However, better methods are still needed for situations where an individual appears to have an unusual combination of attributes involving several different tasks. Also, when there are three or more tasks the current methods cannot make adjustments to reflect personal characteristics, such as age or gender. The purpose of this project is to develop statistically valid methods for some of these more complex situations. The challenge is to devise methods that are accurate when information is available for just a small sample of people from the population with whom the individual is to be compared.

There are two fundamentally different approaches to statistics, the frequentist approach and the Bayesian approach. The Bayesian approach is easier to implement for the problems addressed in this project but the frequentist approach has some desirable properties. The aim is to develop Bayesian and Bayesian-based methods that have some of the good properties that frequentist methods give. Methods will be implemented in user-friendly software that is freely available and can be run over the web without down-loading it to one's computer, though the latter will be an option.

This project is to develop effective statistical methods for comparing a single patient with a control population. The fundamental questions are whether the patient could be part of the control population and the degree to which the patient is unusual. In recent years a body of work has addressed these questions in a variety of situations, in most of which comparison is based on a single measure. This work will be extended to handle further situations, focusing on those involving two or more measures. Such situations arise commonly as multiple measurements are typically taken on patients, but appropriate statistical methods for their analysis are largely lacking. The methods that are developed will enable a broader range of more flexible hypotheses to be examined by researchers, allowing them to handle multiple indicators, quantify the uncertainty over results using confidence/credible intervals, and take account of covariates.
The new methods will use both frequentist and Bayesian ideas, and combinations of the two that yield Bayesian-based methods with good frequentist properties. Probability-matching priors are one approach that will be considered. Also, the frequentist distributions of statistics from Bayesian posterior distributions will be derived and bias-correction methods examined. A Bayesian equivalent of double-bootstrapping will also be explored as another bias-correction mechanism. Simulation will be used to examine both the properties of methods and the sensitivity of methods to departures from the modelling assumptions. User-friendly software that implements the new methods will be written and made freely available.

Single-patient studies play an important role in advancing knowledge in neuropsychology and neuroscience. The past decade has witnessed a steep rise in the use of single patient studies and a notable expansion in the types of study being undertaken. It is therefore essential that the analysis of single patient studies should be based on sound and versatile statistical methodology. This project will enable a broader range of more flexible hypotheses to be examined. Researchers will be able to handle multiple indicators, quantify the uncertainty over results using confidence/credible intervals, treat regression slopes as the measure of interest, take account of covariates, and test whether a patient's results exhibit unusual variability in repeated testing.

The collaborative work of Crawford and Garthwaite, often with co-researchers (most notably David C. Howell), forms the majority of recent methodological work on the analysis of single patient data. Since 2003 they have co-authored 24 papers in the area and their methods have become the standard methods for the statistical analysis of single patient data in the field of neuropsychology. In 2010 their papers in the field received over 120 citations (Science Citation Index) and Crawford and Garthwaite (2002) has been cited 230 times. The citations mainly arise from their methods being used to analyse data, rather than their work simply being mentioned in other papers. Reasons for the influence of their work are:

(i) They develop good statistical methods for answering questions that commonly arise in single patient studies.
(ii) Crawford, a clinical neuropsychologist, writes in language that is accessible to neuropsychologists, using examples that are meaningful to them.
(iii) Methods are implemented in user-friendly software that is freely available.

These features will be retained in the proposed project. In particular, the motivation for the proposed project is to continue developing good statistical methods for answering questions that commonly arise in single patient studies. The majority of papers will be submitted to neuropsychology and neuroscience journals and these will essentially be written by Crawford. Also, methods will be implemented in user-friendly software that is accessed via the same web-portal as current methods (http://www.abdn.ac.uk/~psy086/dept/WEBPUB_dev.HTM). Consequently, new methods developed in the project will be rapidly adopted by the neuroscience community. The sound statistical work underpinning the methods will raise the quality of the research they produce.

While researchers in neuropsychology and neuroscience are the most obvious beneficiaries of the planned research, situations arise in a variety of other areas where an individual, or individual item, should be compared to a control sample. For example, in applied work in archeology, Jones (a co-investigator on this project) has addressed the task of comparing a stone artifact with samples from rock sources used prehistorically (Jones and Williams-Thorpe, 2001). Our communication plan aims to make more statisticians aware of single patient studies and methods designed for their analysis. Over time, the interaction that occurs between statisticians and other disciplines should lead to wider use of single case methods and the uptake of methods to analyse them effectively, fostering the growth of knowledge.

There will be a post-doctoral Research Fellow on the project, Fadlalla Elfadaly, who is extremely able. In his graduation year he had the highest mark out of 820 students in the Faculty of Economics and Political Science, Cairo University. Currently he is completing a PhD and this project will advance his training in a supportive environment that leads to his being a highly productive researcher.


Crawford, J. R. and Garthwaite, P. H. (2002). Neuropsychologia, 40, 1196-1208.
Jones, M. C. and Williams-Thorpe, O. (2001). Archaeometry, 43, 1-18.