LA REPARACION CIVIL EN LA VIOLENCIA ECONOMICA: 1 La reparación civil en la ley 3

To answer Research Question 1, that is; “How can an on-line simulation, which provides estimates of bed demand, be developed for the operational management of hospital beds at the ward level?”, six stages of development

have been described within this chapter, including a novel method for conducting “black-box” type validation of an online model, prior to its “real-world” implementation, and before any connection to the real system is established.

In the first stage of development, the requirements of an online simulation are discussed, to assess the feasibility of online modelling in the hospital context. At the second stage, a conceptual model of the hospital is developed at a level of detail which is capable answering questions associated with ward-level bed management, such as the likelihood of reaching a given ward’s maximum capacity. The conceptual model developed at this stage is not dissimilar from a conceptual model developed for an offline or non-terminating simulation, although special attention is paid to temporal level-of-detail modelling decisions, in addition to structural level-of-detail modelling decisions, since the outputs of the eventual online model are necessarily time-dependent. This includes decisions regarding the frequency at which results are to be collected from the model, along with the time-scale of the possible decision variables which could be used to run alternative scenarios.

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In the third stage of development, the conceptual model is implemented in the Micro Saint Sharp simulation package, and the PA data used to parameterise the model is analysed for the existence of time-dependent patterns which might affect the midnight census at the finest temporal level-of-detail (one day). Statistically significant relationships are found between emergency patient arrival rates and day-of-the-week, along with patient length-of-stay and weekday of admission when both patient types are pooled, therefore these relationships are included in the offline model.

The parameterised offline model is then run for the entire observation period, and the summary statistics generated by the realisations of midnight occupancy are compared with those observed in the PA data, after discarding the results from the warm-up period. These checks of offline model validity represent the fourth stage of model development which are intended to provide an indication that the model is performing as expected, by analysing simulation outputs generated by greater run lengths than the online model is likely to use. No statistically significant differences are found when comparing the mean midnight occupancy generated by the offline model with the PA data for each admission type (emergency/elective) across all wards. The variability of the model also seems comparable with the time-series of observed midnight occupancy for each admission type, with 88.3% of emergency patient censes falling within their corresponding 90% prediction interval, and 90.9% of elective patient censes doing the same (Section 4.5.3).

The penultimate stage of development sees the offline model augmented with the ability to be loaded with observed system states at initialisation. For the

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model to be used in practice, Requirement 2 calls for these states to be loaded via an online connection to the real system, however, for the purpose validating the online model, a connection is made to a historic set of system states instead. The ability to load these states necessitates the inclusion of conditional length of stay distributions from which realisations of remaining length of stay can be drawn.

Finally, methods for black-box validation of the online model are developed by assuming a sensible length for the planning horizon, and re-initialising the online model using system states observed in the PA data at the beginning of each planning horizon period. These methods contribute towards clarifying Requirement 1 in terms of obtaining a validated model for online use and offer techniques for comparisons of the distribution of the performance indicators, rather than comparing summary statistics. This type of online validation is distinct from the “auto-validation” sometimes associated with online models in the literature, since it allows for the assessment of the model’s performance in an “online way” prior to its connection with the real system, while it is still possible to make complex adjustments to the model, if needed.

As mentioned in Section 4.7.3, the development of the Δℎ-occupancy random variable used to compare the distributions of midnight occupancy as they evolve over time, is a by-product of the discrete nature of the performance indicator (midnight census). This situation is not unique to the hospital setting; therefore, this method could be generalised to any online simulation in which the performance measure can be thought of as a discrete quantity. Although this method pools observations generated under different initial conditions (on

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which each distribution of simulated midnight occupancy is known to depend), it goes further than typical validation techniques, by evaluating the fit of the model with the observed data over time. For models with continuous

performance indicators, it is possible to pool the simulated and observed data in such a way the initial conditions are accounted for, by first normalising the data, using the percentiles method described in Section 4.7.3. The validation method in the continuous-case assesses the agreement in distribution (as does

Δℎ-occupancy), rather than simply assessing the similarity of summary statistics.

With Δ_ℎ-occupancy defined, the quality of the fit of the distribution of the performance measure (midnight census) from the simulation is assessed against that of the data, for each time ℎ (in days) from initialisation. While the quality of the fit does not change significantly with ℎ, differences worthy of consideration are found to exist on wards which are more likely to be found at high levels of midnight bed occupancy, relative to their maximum capacity. The midnight occupancies generated for these wards by the online simulation are found to have higher sample variances than their PA data counterparts – a likely consequence of using uncapacitated simulation nodes to model wards in which the maximum capacity is more regularly encountered, coupled with the inability of the simulation to distribute patient load among free beds on other wards.

Research Question 1 has been answered in this chapter, through the development and validation of an online simulation for ward-level bed management. However, the development of additional model components remains to be discussed. Specifically, a method for modelling patient diversions

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during times of peak bed demand is proposed and evaluated in the next chapter. While these components could be viewed as part of the model development process, they also contribute to answering Research Questions 2 and 3 and are therefore discussed in the chapters which follow.

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Chapter 5