VIGENCIA DE LAS MEDIDAS DE PROTECCION Y MEDIDAS CAUTELARES DICTADAS PARA LA PROTECCION DE LAS VICTIMAS

Once a patient has been assigned to a ward bed (by either admission or transfer from another ward), the bed is occupied for some period of time before the patient is either discharged or transferred to another ward. The amount of time

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a patient occupies a bed is known as the patient’s length-of-stay (LOS) and this can potentially be influenced by a number of factors. The most obvious of these is the type and severity of a patient’s condition, but others might include bed blocking, (the patient is required to wait until space on a more suitable ward becomes available) or the hospital’s ability to discharge the patient (in cases where the patient requires help leaving the hospital).

Naturally, not all factors which influence a patient’s LOS are recorded in the PA data, and even if very detailed information was available, it would not rule out uncertainty in LOS altogether. For this reason, LOS for both the emergency and elective patients are treated as discrete random variables which represent the number of midnights a patient will stay on a particular ward.

While it may be unreasonable to expect that detailed LOS information (such as delays caused by bed blocking) is recorded in the PA data, other standard information is available. As has already been mentioned, the PA data contains patient stay records with specialty, ward and admission type information along with the times at which the status of any of these changes. This means the pool of patient level LOS records can be disaggregated to form samples of similar patients from which LOS distributions can be derived.

Since the purpose of the model is to provide estimates of ward-level bed demand, the pool of all LOS observations is first disaggregated by ward. This also goes some way towards grouping patients of similar specialty, although it is not uncommon for wards to provide beds for multiple specialties. The next disaggregation occurs at the admission type level, meaning LOS for elective and emergency patients on the same ward will be drawn from distinct

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distributions. Further disaggregation by specialty is theoretically possible by using the specialty categorisation in the PA data; however, each level of disaggregation has the effect of diminishing the sample size of each patient group, making any statistical inference (such as analysing the relationship between midnight occupancy and transition probability) less meaningful. Therefore, discrete empirical LOS distributions for the number of midnights spent on each ward are derived at the ward and admission type (emergency/elective) level.

As has already been shown in Section 4.4.2, it is likely that some day-of-the- week dependent effect exists for the distribution of emergency arrivals. In a similar way, it might be reasonable to expect that a patient’s LOS is also affected by the day of the week on which he or she is admitted. Such an analysis has already been carried out by the UK Audit Commission (Audit Commission, 2003) in which LOS records generated by NHS Trusts across England and Wales were grouped by weekday of admission. The Audit Commission found that patients admitted on a Thursday stayed in hospital for a significantly longer period than patients admitted on any other day of the week, citing the reduced availability of support and diagnostic departments, along with reduced numbers of senior staff capable of making discharge decisions over the weekend as likely causes.

If evidence suggests that a relationship exists between LOS and weekday of admission in the AGH being modelled, then capturing this relationship has the potential to improve bed demand estimates. In Figure 4.4, the Total LOS observations (that is, the amount of time spent as an inpatient from admission

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to discharge, regardless of ward placement) are grouped by weekday of admission to investigate the likelihood of such a relationship.

Figure 4.4: Mean Total LOS for emergency and elective patients in the observation period. Error bars are 95% confidence intervals for the means. K-W testing has been used since homogeneity of variance across weekday groups is not assumed.

On average, Total LOS appears to be greatest for patients admitted on a Friday, closely followed by those admitted on a Thursday, and these patients stay in hospital for approximately one day more than those arriving on a Monday or a Tuesday. The weekly LOS pattern is similar to the pattern reported by the Audit Commission (2003), indicating that the AGH may also suffer from a lack of resources and staff over the weekend, resulting in a decreased rate of discharge. The Kruskal-Wallis test has been used to test the null hypothesis that the distribution of LOS is not dependent on weekday of admission, and this hypothesis is rejected with a significance level of 0.0005.

4 4.5 5 5.5 6 6.5 7 7.5 8

Monday Tuesday Wednesday Thursday Friday Saturday Sunday Mean Total LOS (Midnights in Bed) by Weekday of Admission Kruskal-Wallis Test

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Because the relationship between weekday of admission and the distribution of total LOS is statistically significant and likely to have an impact on midnight bed occupancy numbers, it makes sense to model this relationship in the simulation. However, it is worth noting that although the analysis of this relationship was based on Total LOS (all wards) and both admission types, LOS in the simulation is modelled at a lower level of detail. Rather than carrying out the analysis for each of the ward and admission type combinations, the findings of this pooled analysis are treated as being valid for all levels of detail, since disaggregation would result in smaller sample sizes and potentially insufficient statistical power on which to base a conclusion.

With 10 modelled wards, 2 admission types and 7 possible admission days, each ward LOS can be drawn from one of 140 possible LOS distributions. The LOS generation process has been simplified by assuming that each ward LOS draw is independent of all other simulated patients and any time spent on other wards. It should also be noted that although elective (planned) arrivals are treated as deterministic, their LOS is treated as a random variable at this stage of model development.