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Abstract: Improving the efficiency of A&E departments is a priority for the NHS and new targets are being introduced to assist this. In Northern Ireland the new target states that by April 2008, 95% of all patients should spend no longer than 4 hours in total in the department. Analysis of a local hospital dataset, recording all new A&E attendances over a one year period, indicates that currently, only 80% of patients are meeting this target.

Identifying heterogeneity

From the dataset it was possible to identify patient pathways and two streams of patient passing through the department - patients who require a decision to admit to hospital (DTA patients) and patients who don't have a decision to admit (no DTA patients). The results indicated that the DTA patients spend significantly longer in A&E than no DTA patients (p-value <0.001). Therefore, when considering total time in A&E, the two streams should be accounted for and modelled separately.

Patient pathway through A&E

Figure 1 Two groups of patients in the community following discharge from hospital.

Results

It was found that a lognormal distribution with probability density function (pdf) math formula

where s and l are parameters estimated from the data and t represents waiting times, gave the best fit to waiting times for no DTA patients (Figure 2(a)). For patients with a DTA, a 4-phase Coxian phase-type distribution gave the best fit to the data (Figure 2(b)). The Coxian phase-type distribution is a probability distribution function capable of describing the movement of patients between a series of ordered phases (pathways). For the DTA patients, the pdf describing their waiting time can be given by f(t) = p exp{Qt}q. p is a matrix of initial probabilities and Q and q are matrices consisting of the parameters of a 4-phase model, which are estimated from the waiting time data.

Current work involves studying classification methods as a possible way for predicting patient streams, and the development of more accurate models of waiting times.

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Figure 2 Results of fitting a log-normal model to the total time in A&E for patients with no decision to admit.

Figure 3. Results of fitting a 4-stage Coxian phase-type model to the total time in A&E for patients with a decision to admit.

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