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PhD Research

What is the added value of using non-linear models to explore complex healthcare datasets?

Under the supervision of Professor Frances Griffiths, Dr Nick Parsons and Professor Margaret Thorogood .

Warwick PhD Theses are available via the Warwick Research Archive Portal (WRAP). Mine is here: Dr Martine J. Barons

Three publications arising from my PhD research are here:


Health care is a complex system and it is therefore expected to behave in a non-linear manner. It is important for the delivery of health interventions to patients that the best possible analysis of available data is undertaken. Many of the conventional models used for health care data are linear. This research compares the performance of linear models with non-linear models for two health care data sets of complex interventions.

Logistic regression, latent class analysis and a classification artificial neural network were each used to model outcomes for patients using data from a randomised controlled trial of a cognitive behavioural complex intervention for non-specific low back pain. A Cox proportional hazards model and an artificial neural network were used to model survival and the hazards for different sub-groups of patients using an observational study of a cardiovascular rehabilitation complex intervention.

The artificial neural network and an ordinary logistic regression were more accurate in classifying patient recovery from back pain than a logistic regression on latent class membership. The most sensitive models were the artificial neural network and the latent class logistic regression. The best overall performance was the artificial neural network, providing both sensitivity and accuracy. Survival was modelled equally well by the Cox model and the artificial neural network, when compared to the empirical Kaplan-Meier survival curve. Long term survival for the cardiovascular patients was strongly associated with secondary prevention medications, and fitness was also important. Moreover, improvement in fitness during the rehabilitation period to a fairly modest 'high fitness' category was as advantageous for long-term survival as having achieved that same level of fitness by the beginning of the rehabilitation period. Having adjusted for fitness, BMI was not a predictor of long term survival after a cardiac event or procedure. The Cox proportional hazards model was constrained by its assumptions to produce hazard trajectories proportional to the baseline hazard. The artificial neural network model produced hazard trajectories that vary, giving rise to hypotheses about how the predictors of survival interact in their influence on the hazard.

The artificial neural network, an exemplar non-linear model, has been shown to match or exceed the capability of conventional models in the analysis of complex health care data sets.


For this project there were two data sets from two types of study.

1. The BeST data set is a randomised contolled trial of a new complex intervention for back pain which includes a cognitive behavioural element in the treatment arm of the trial (BeST 2010). A complex intervention is defined as one with many elements which may operate independently or interdependently.

Subgroup analysis concluded that lower fear avoidance gave a greater treatment effect , those with moderately troublesome pain seemed to benefit CBT more than those with severely troublesome pain, and the length of time the condition had been preexisting was not significant.

Many of the measurements in this trial are psychosocial, self-reported and measured on a Likert scale which causes a different kind of uncertainty than objectively measured data.

As a randomised contolled trial, this data can answer questions about the effectiveness of treatment compared to those that did not receive it.

The outcome for the randomised contolled trial was improvement or cure of a chronic condition.

The results of the trial were published in The Lancet in February 2010. Press release here, article here: The Lancet.

2. The Alton and Basingstoke cardiovascular rehabilitation data set is an observational study of around 3000 individuals with coronary heart disease passing through the Alton & Basingstoke rehabilitation programme (Turner 2007). Its uniqueness lies in the fact that previous studies are mainly small randomised contolled trials of middle-aged men, whilst this cohort encompassed all age groups and both genders in sufficiently significant numbers to draw legitimate conclusions. This is a right censored data set, i.e. the date of death for some patients is known only to be beyond a certain date, as at that date they were still living. The question here is about validating the cardiovascular rehabilitation approach, finding out which elements are the most helpful, and for whom.

The study used objective measurements, e.g. of blood pressure and fitness, with attendant measurement error, combined with some subjective assessments such as depression score.

The observational study can answer questions about the differences of response between the recipients of the treatment.

The outcome of the observational study was survival duration.


How this work contributes:

1. The BeST trial has established that a new complex intervention for the treatment of lower back pain, which includes a cognitive behavioural element, is both effective on average and cost effective. This work seeks to maximise the benefits of this new treatment by identifying those patient characteristics which predict benefit, and to eliminate waste by identifying patient characteristics which predict no benefit. It may also identify patient characteristics which predict harm, if any.

2. The Alton and Basingstoke cardiovascular rehabilitation observational study data is unusual in its size and the inclusion of women. The first analysis has shown that a higher fitness level was associated with improved survival and that low fitness and depression predicted increased risk of non-completion of the rehabilitation programme.

The unique nature of the dataset makes it imperative that the full range of possible analysis is applied to fully understand the benefits of the current rehabilitation regime and the other factors which predict survival, in order to asses for whom this regime is beneficial, and if possible, how it may be adapted to better serve different patient types.


This project seeks to address next generation healthcare in the tailoring of treatments to patients through investigating the mechanisms for identifying patient – treatment pairs.








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