An investigation into the use of shrinkage methods to alleviate over-fitting of prognostic models for independent and clustered data with few events

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Clinicians, health service researchers and epidemiologists often wish to predict a future health outcome for patients and the public. Examples of such outcomes include development of coronary heart disease, the occurrence of in-hospital mortality following surgery, and the onset of depression. These predictions are used by clinicians to determine the prognosis of patients to plan their treatment, to detect high risk patients, and to provide information to patients enabling them to make decisions about their treatment options. Policy makers often use these predictions to assess the performance of hospitals and general practices and identify under performing institutions.Statistical models using patients' clinical and demographic characteristics are typically used to make these predictions. These models are referred to as prognostic models. To develop such models, information is collected on patients or relevant subjects, regarding their risk factors and the health outcome they experienced. The relationship between the risk factors and the outcome is quantified using a statistical model, which can then be used to make predictions for new patients. Models are usually presented in the form of a risk algorithm. This algorithm is then tested on new patients to ensure that it makes reliable predictions. If its performance is found to be satisfactory, it is recommended for use by clinicians in practice. Examples of risk algorithms used in practice include the Framingham risk score to predict the 10 year risk of coronary heart disease, Euroscore to predict in-hospital mortality following cardiac surgery and the PREDICT score to predict the risk of developing depression. When the health outcome of interest is rare it is often problematic to develop a risk algorithm that will both predict risk accurately and be able to classify patients into high and low risk groups. This is a common problem in health research and is often not alleviated by collecting patient data from many centres, or over a long period of time. A further statistical problem occurs with data from many centres as there may be variability in the outcomes between the centres. Robust models exist for relatively common events such as coronary heart disease, in-hospital mortality following cardiac surgery, and depression. However reliable prognostic models are scarce, or not available, for rarer health outcomes, for example death or recurrence following diagnosis of rare types of cancer, and the onset of Parkinson's disease. There is a similar problem when trying to develop prognostic models for common events in relatively small subgroups of people, for example, a model to predict coronary heart disease in people who have severe mental health problems. Some methodological research has been done to handle the problem of fitting statistical models for rare outcomes in genetic studies. However, limited work has been done to develop methods to produce reliable prognostic models with rare outcomes in clinical settings such as public health and health services research. Moreover, the methods that have been developed to date are not used routinely because of lack of software and adequate evaluation. There are currently no guidelines regarding how statisticians and other researchers should be using these methods in practice. The proposed research will evaluate the existing statistical methodology that is available to handle risk predictions when the health outcome of interest is rare, and will develop new methods where necessary. The proposed research will make recommendations regarding the use of these methods in practice. Additionally, the methods developed in this research project will be implemented in widely available statistical software to enable their routine use. The prognostic models developed using these methods should enable clinicians and policy makers to make predictions for patients regarding health outcomes, in these settings even if the outcome is rare