Calculating the need for intensive care beds

Hospital length of stay: A cross-specialty analysis and Beta-geometric model

BACKGROUND

The typical hospital Length of Stay (LOS) distribution is known to be right-skewed, to vary considerably across Diagnosis Related Groups (DRGs), and to contain markedly high values, in significant proportions. These very long stays are often considered outliers, and thin-tailed statistical distributions are assumed. However, resource consumption and planning occur at the level of medical specialty departments covering multiple DRGs, and when considered at this decision-making scale, extreme LOS values represent a significant component of the distribution of LOS (the right tail) that determines many of its statistical properties.

OBJECTIVE

To build actionable statistical models of LOS for resource planning at the level of healthcare units.

METHODS

Through a study of 46, 364 electronic health records over four medical specialty departments (Pediatrics, Obstetrics/Gynecology, Surgery, and Rehabilitation Medicine) in the largest hospital in Thailand (Siriraj Hospital in Bangkok), we show that the distribution of LOS exhibits a tail behavior that is consistent with a subexponential distribution. We analyze some empirical properties of such a distribution that are of relevance to cost and resource planning, notably the concentration of resource consumption among a minority of admissions/patients, an increasing residual LOS, where the longer a patient has been admitted, the longer they would be expected to remain admitted, and a slow convergence of the Law of Large Numbers, making empirical estimates of moments (e.g. mean, variance) unreliable.

RESULTS

We propose a novel Beta-Geometric model that shows a good fit with observed data and reproduces these empirical properties of LOS. Finally, we use our findings to make practical recommendations regarding the pricing and management of LOS.

Optimisation and control of the supply of blood bags in hemotherapic centres via Markov decision process with discounted arrival rate

Running a cost-effective human blood transfusion supply chain challenges decision makers in blood services world-wide. In this paper, we develop a Markov decision process with the objective of minimising the overall costs of internal and external collections, storing, producing and disposing of blood bags, whilst explicitly considering the probability that a donated blog bag will perish before demanded. The model finds an optimal policy to collect additional bags based on the number of bags in stock rather than using information about the age of the oldest item. Using data from the literature, we validate our model and carry out a case study based on data from a large blood supplier in South America. The study helped achieve an overall increase of 4.5% in blood donations in one year.

Trends in long-stay admissions to a UK paediatric intensive care unit

OBJECTIVE

Prolonged admission to a paediatric intensive care unit (PICU) consumes significant healthcare resource. An increase in the number of long-stay admissions and bed utilisation has been reported elsewhere in the world but not in the UK. If an increasing trend of long-stay admissions is evident, this may have significant implications for provision of paediatric intensive care in the future.

DESIGN/SETTING/PATIENTS

We retrospectively analysed prospectively collected data from Birmingham Children's Hospital, UK, over a 20-year period from 1998 to 2017. PICU admissions, bed-days, length of stay and mortality trends were analysed and reported over four different epochs (1998-2002, 2003-2007, 2008-2012 and 2013-2017) for long-stay admissions (PICU length of stay ≥28 days) and others. Differences in patient demographics, diagnostic categorisation and hospital utilisation were also analysed.

RESULTS

In total, 24 203 admissions accounted for 131 553 bed-days over the 20-year period. 705 (2.9%) long-stay admissions accounted for 42 312 (32%) bed-days. Proportion of long-stay admissions and corresponding bed-days increased from 1.6% and 20.5% in 1998-2002 to 4.5% and 42.6%, respectively, in 2013-2017 (p<0.001). Long-stay patients had a significantly higher number of hospital admissions (median: 4 vs 2, p<0.001) per patient and overall hospital length of stay (median: 98 vs 15, p<0.001) bed-days compared with other patients. Long-stay admissions were associated with significantly higher crude mortality (23% vs 6%, p<0.001) compared with other admissions.

CONCLUSIONS

A significant increase in the proportion of prolonged PICU admissions with disproportionately high resource utilisation and mortality is evident over two decades.

A Novel Method to Identify the Start and End of the Winter Surge in Demand for Pediatric Intensive Care in Real Time

OBJECTIVE

Implementation of winter surge management in intensive care is hampered by the annual variability in the start and duration of the winter surge. We aimed to develop a real-time monitoring system that could identify the start promptly and accurately predict the end of the winter surge in a pediatric intensive care setting.

DESIGN

We adapted a method from the stock market called "Bollinger bands" to compare current levels of demand for pediatric intensive care services to thresholds based on medium-term average demand. Algorithms to identify the start and end of the surge were developed using Bollinger bands and pragmatic considerations. The method was applied to a specific pediatric intensive care service: the North Thames Children's Acute Transport Service using eight winters of data (2005-2012) to tune the algorithms and one winter to test the final method (2013/2014).

SETTING

A regional specialized pediatric retrieval service based in London, United Kingdom.

MEASUREMENTS AND MAIN RESULTS

The optimal Bollinger band thresholds were 1.2 and 1 SDs above and below a 41-day moving average of demand, respectively. A simple linear model was found to predict the end of the surge and overall surge demand volume as soon as the start had been identified. Applying the method to the validation winter of 2013/2014 showed excellent performance, with the surge identified from November 18, 2013, to January 4, 2014.

CONCLUSIONS

We have developed and tested a novel method to identify the start and predict the end of the winter surge in emergency demand for pediatric intensive care.