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This thesis is motivated by the particular modelling requirements of data collected by a General Practitioner who wished to study the relationship between incidences of asthma and air pollution in Glyn Neath, a small mining village in South Wales. We consider the need to model the function of an individual's peak expiratory flow in such a way that the possible influence of airborne pollutants is testable, using only the binary time series of attacks available for each patient. Korn and Whittemore (1979) presented a threshold model which considered an individual's resistance to an 'onslaught' of pollution. A subtle adaptation of the principles of their research has allowed this methodology to be adapted to the requirements of this thesis. We present a model which is motivated by medically-based criteria and is capable of generating events corresponding to acute episodes of asthma. Statistical analysis of the model introduces correlated random variables with survival probabilities requiring the integration of the appropriate multi-dimensional Normal probability density function. We develop a novel approach for approximating the correlation structure which allows this integration to be reduced to a single dimension. For parameter estimation we consider the method of maximum likelihood and examine the properties of the maximum likelihood estimates. Initial exploration of the estimates indicate that they are substantially biased and hence further refinement of the approximated correlation structure is necessary. The research has achieved its original aim of developing medically based statistical methods.

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