Fitting the distributions of length of stay by parametric models

Deconstructing the effects of stochasticity on transmission of hospital-acquired infections in ICUs

The inherent stochasticity in transmission of hospital-acquired infections (HAIs) has complicated our understanding of transmission pathways. It is particularly difficult to detect the impact of changes in the environment on acquisition rate due to stochasticity. In this study, we investigated the impact of uncertainty (epistemic and aleatory) on nosocomial transmission of HAIs by evaluating the effects of stochasticity on the detectability of seasonality of admission prevalence. For doing so, we developed an agent-based model of an ICU and simulated the acquisition of HAIs considering the uncertainties in the behaviour of the healthcare workers (HCWs) and transmission of pathogens between patients, HCWs, and the environment. Our results show that stochasticity in HAI transmission weakens our ability to detect the effects of a change, such as seasonality patterns, on acquisition rate, particularly when transmission is a low-probability event. In addition, our findings demonstrate that data compilation can address this issue, while the amount of required data depends on the size of the said change and the degree of uncertainty. Our methodology can be used as a framework to assess the impact of interventions and provide decision-makers with insight about the minimum required size and target of interventions in a healthcare facility.

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.

Modeling COVID-19 hospital admissions and occupancy in the Netherlands

We describe the models we built for predicting hospital admissions and bed occupancy of COVID-19 patients in the Netherlands. These models were used to make short-term decisions about transfers of patients between regions and for long-term policy making. For forecasting admissions we developed a new technique using linear programming. To predict occupancy we fitted residual lengths of stay and used results from queueing theory. Our models increased the accuracy of and trust in the predictions and helped manage the pandemic, minimizing the impact in terms of beds and maximizing remaining capacity for other types of care.

Semi-parametric time-to-event modelling of lengths of hospital stays

Length of stay (LOS) is an essential metric for the quality of hospital care. Published works on LOS analysis have primarily focused on skewed LOS distributions and the influences of patient diagnostic characteristics. Few authors have considered the events that terminate a hospital stay: Both successful discharge and death could end a hospital stay but with completely different implications. Modelling the time to the first occurrence of discharge or death obscures the true nature of LOS. In this research, we propose a structure that simultaneously models the probabilities of discharge and death. The model has a flexible formulation that accounts for both additive and multiplicative effects of factors influencing the occurrence of death and discharge. We present asymptotic properties of the parameter estimates so that valid inference can be performed for the parametric as well as nonparametric model components. Simulation studies confirmed the good finite-sample performance of the proposed method. As the research is motivated by practical issues encountered in LOS analysis, we analysed data from two real clinical studies to showcase the general applicability of the proposed model.

Impact of Income Disparity on Utilization of Home-Based Care Services Among Older Adults in Japan: A Retrospective Cohort Study

This study aimed to determine whether there are disparities in the utilization of home-based care services according to income level among people aged 75 years or older in Japan. The research team used administrative claims data from April 2014 to March 2018 for people aged 75 years or older in Fukuoka Prefecture. Subjects were categorized according to income level using medical insurance claim data. Associations between income level and usage days of inpatient care, outpatient care, home medical care, and usage number of home-based long-term care (LTC) services were evaluated. Furthermore, medical and LTC costs were evaluated and adjusted for gender, age, and level of LTC needs. The team used generalized linear models (GLMs) to estimate medical and LTC services utilization, as well as the potential influence of gender, age, care needs level, and death as risk factors. The study analyzed 31,322 subjects, among whom 17,288 were in low-, 12,755 were in middle-, and 1399 were in high-income groups. The results of GLMs showed the number of home medical care days was 59.45, 62.24, and 69.66 days for users from low-, middle-, and high-income groups, respectively. Correspondingly, the number of home-based LTC services used was 668.84, 709.59, and 833.14 times. This study suggests that older adults with lower incomes had relatively low utilizations of home-based care services and high utilizations of nonhome-based LTC services. Policymakers should implement policies focused on people who need care to tackle socioeconomic inequalities in home-based care.

Decision support tool for hospital resource allocation during the COVID-19 pandemic

The SARS-CoV-2 (COVID-19) pandemic has placed unprecedented demands on entire health systems and driven them to their capacity, so that health care professionals have been confronted with the difficult problem of ensuring appropriate staffing and resources to a high number of critically ill patients. In light of such high-demand circumstances, we describe an open web-accessible simulation-based decision support tool for a better use of finite hospital resources. The aim is to explore risk and reward under differing assumptions with a model that diverges from most existing models which focus on epidemic curves and related demand of ward and intensive care beds in general. While maintaining intuitive use, our tool allows randomized "what-if" scenarios which are key for real-time experimentation and analysis of current decisions' down-stream effects on required but finite resources over self-selected time horizons. While the implementation is for COVID-19, the approach generalizes to other diseases and high-demand circumstances.

Implication of excessive length of stay of asthma patient with heterogenous status attributed to air pollution

OBJECTIVE

Air pollution has potential risk on asthma patients, further prolongs the length of stay. However, it is unclear that the impact of air pollution on excessive length of stay (ELoS) of heterogeneous asthma patients. In this study, we proposed a K-Nearest Neighbor (KNN) embedded approach incorporating with patient status to analyze the impact of short-term air pollution on the ELoS of asthma patients.

METHODS

The KNN embedded approach includes two stages. Firstly, the KNN algorithm was employed to search for the most similar patient community and approximate kernel proxy of each index patient by Euclidean distance. Then, we built the differential fixed-effect linear model to estimate the risk of air pollution to the ELoS.

RESULTS

We analyzed 6563 asthma patients' medical insurance records in a large city of China from January to December in 2014. It was found that when the duration of exposure to air pollution (i.e., PM2.5, PM10, SO2, NO2, and CO) reaches around 4-5 days, the risk of increasing the ELoS becomes the largest. But only O3 shows the opposite effect. What's more, CO is the dominant risk to increase the ELoS. With a 1 mg/m3 increment of CO average concentration in 5 days, the ELoS will go up by 0.8157 day (95%CI:0.72,0.9114). Based on the kernel proxy in the top 1% similar patient community, the additional financial burden posed on each patient increases by RMB 488.6002 (95%CI:430.1962,547.0043) due to the ELoS.

CONCLUSIONS

The KNN embedded approach is an innovative method that takes into account the heterogeneous patient status, and effectively estimates the impact of air pollution on the ELoS. It is concluded that air pollution poses adverse effects and additional financial burdens on asthma patients. Heterogeneous patients should adopt different strategies in health management to reduce the risk of increasing the ELoS due to air pollution, and improve the efficiency of medical resource utilization.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s40201-020-00584-8.

Comparison of care utilisation and medical institutional death among older adults by home care facility type: a retrospective cohort study in Fukuoka, Japan

OBJECTIVES

We compared the care services use and medical institutional deaths among older adults across four home care facility types.

DESIGN

This was a retrospective cohort study.

SETTING

We used administrative claims data from April 2014 to March 2017.

PARTICIPANTS

We included 18 347 residents of Fukuoka Prefecture, Japan, who received home care during the period, and aged ≥75 years with certified care needs of at least level 3. Participants were categorised based on home care facility use (ie, general clinics, Home Care Support Clinics/Hospitals (HCSCs), enhanced HCSCs with beds and enhanced HCSCs without beds).

PRIMARY AND SECONDARY OUTCOME MEASURES

We used generalised linear models (GLMs) to estimate care utilisation and the incidence of medical institutional death, as well as the potential influence of sex, age, care needs level and Charlson comorbidity index as risk factors.

RESULTS

The results of GLMs showed the inpatient days were 54.3, 69.9, 64.7 and 75.0 for users of enhanced HCSCs with beds, enhanced HCSCs without beds, HCSCs and general clinics, respectively. Correspondingly, the numbers of home care days were 63.8, 51.0, 57.8 and 29.0. Our multivariable logistic regression model estimated medical institutional death rate among participants who died during the study period (n=9919) was 2.32 times higher (p<0.001) for general clinic users than enhanced HCSCs with beds users (relative risks=1.69, p<0.001).

CONCLUSIONS

Participants who used enhanced HCSCs with beds had a relatively low inpatient utilisation, medical institutional deaths, and a high utilisation of home care and home-based end-of-life care. Findings suggest enhanced HCSCs with beds could reduce hospitalisation days and medical institutional deaths. Our study warrants further investigations of home care as part of community-based integrated care.

Impact of high-sensitivity cardiac troponin implementation on emergency department length of stay, testing, admissions, and diagnoses

OBJECTIVE

While high-sensitivity (hs) troponin (cTn) has been associated with shorter emergency department (ED) length of stay (LOS) and decreased hospital admissions outside the United States (US), concerns have been raised that it will have opposite effects in the US. In this study, we aimed to compare ED LOS, admissions, and acute coronary syndrome (ACS) diagnoses before and after the implementation of hs-cTn.

METHODS

We conducted a single-institution, retrospective study of two temporally matched six-month study periods before and after the implementation of hs-cTn. We included consecutive adults presenting with chest pain. The primary outcome was ED LOS, which was log transformed and analyzed using multiple linear regression. Binary secondary outcomes of admissions, cardiac testing, cardiology consultation, and ACS diagnoses were analyzed using multiple logistic regression.

RESULTS

We studied 1589 visits before and 1616 visits after implementation of hs-cTn. Median age and sex ratios were similar between study periods. Median ED LOS was longer in the post-implementation period [post: 384 (interquartile range, IQR 260-577) minutes; pre: 374 (IQR 250-564) minutes; adjusted geometric mean ratio 1.05; 95% confidence interval, CI 1.01-1.10)]. Admissions were lower in the post-implementation period [post: 24% (385/1616) vs. pre: 28% (447/1589); adjusted odds ratio, aOR 0.75 (95% CI 0.64-0.88)]. Cardiac risk stratification testing [pre: 9% (142/1589) vs post: 9% (144/1616); aOR 0.95 (95% CI 0.74-1.22)], cardiology consultation [pre: 13% (208/1589) vs post: 13% (207/1616); aOR 0.91 (95% CI 0.73-1.12)], and ACS diagnoses [pre: 7% (116/1589) vs post: 7% (120/1616); aOR 0.94 (95% CI 0.72-1.24)] were similar between the two study periods.

CONCLUSION

In this single-center study, transition to hs-cTn was associated with an increased ED LOS, decreased admissions, and no substantial change in cardiac risk stratification testing, cardiology consultation, or ACS diagnoses.

Describing Serbian Hospital Activity Using Australian Refined Diagnosis Related Groups: A Case Study in Vojvodina Province

Introduction

AR-DRG system for classification hospital episodes was implemented in Serbia to improve efficiency and transparency in the health system.

Methods

L3H3, IQR, and 10th-95th percentile methods were used to identify outlier episodes in the classification. Classification efficiency and within-group homogeneity were measured by an adjusted reduction in variance (R2) and a coefficient of variation (CV).

Results

There were 246,131 hospital episodes with a total 1,651,913 bed days from 14 hospitals. All episodes were classified into 652 groups of which 441 had CV lower than 100%. "Medical groups" accounted for 51% of groups and for 72% of episodes. Chemotherapy and vaginal delivery were the highest volume groups, with 5% and 4% of total episodes. Major diagnostic category 6 (MDC 6, Diseases of the digestive system) was the highest volume MDC, accounting for 11% of episodes. "Day-cases" and "prolonged hospitalisation" accounted for 21% and 3% of episodes, respectively. The average length of stay varied from 5.6 to 8.2 days. Adjusted R2 was 0.3 for untrimmed data. Trimming by L3H3, IQR, and 10th-95th percentile method improved the value of adjusted R2 to 0.61, 0.49, and 0.51, identifying 24%, 7%, and 7% of total cases as outliers, respectively. Mental diseases (MDC 19) remained the lowest adjusted R2 in untrimmed and trimmed datasets.

Conclusion

A long length of stay and a small percentage of "day-cases" characterized hospital activity in Vojvodina. Trimming methods significantly improved DRG efficiency. Future studies should consider cost data.

COVID-19 length of hospital stay: a systematic review and data synthesis

BACKGROUND

The COVID-19 pandemic has placed an unprecedented strain on health systems, with rapidly increasing demand for healthcare in hospitals and intensive care units (ICUs) worldwide. As the pandemic escalates, determining the resulting needs for healthcare resources (beds, staff, equipment) has become a key priority for many countries. Projecting future demand requires estimates of how long patients with COVID-19 need different levels of hospital care.

METHODS

We performed a systematic review of early evidence on length of stay (LoS) of patients with COVID-19 in hospital and in ICU. We subsequently developed a method to generate LoS distributions which combines summary statistics reported in multiple studies, accounting for differences in sample sizes. Applying this approach, we provide distributions for total hospital and ICU LoS from studies in China and elsewhere, for use by the community.

RESULTS

We identified 52 studies, the majority from China (46/52). Median hospital LoS ranged from 4 to 53 days within China, and 4 to 21 days outside of China, across 45 studies. ICU LoS was reported by eight studies-four each within and outside China-with median values ranging from 6 to 12 and 4 to 19 days, respectively. Our summary distributions have a median hospital LoS of 14 (IQR 10-19) days for China, compared with 5 (IQR 3-9) days outside of China. For ICU, the summary distributions are more similar (median (IQR) of 8 (5-13) days for China and 7 (4-11) days outside of China). There was a visible difference by discharge status, with patients who were discharged alive having longer LoS than those who died during their admission, but no trend associated with study date.

CONCLUSION

Patients with COVID-19 in China appeared to remain in hospital for longer than elsewhere. This may be explained by differences in criteria for admission and discharge between countries, and different timing within the pandemic. In the absence of local data, the combined summary LoS distributions provided here can be used to model bed demands for contingency planning and then updated, with the novel method presented here, as more studies with aggregated statistics emerge outside China.

COVID-19 length of hospital stay: a systematic review and data synthesis

BACKGROUND

The COVID-19 pandemic has placed an unprecedented strain on health systems, with rapidly increasing demand for healthcare in hospitals and intensive care units (ICUs) worldwide. As the pandemic escalates, determining the resulting needs for healthcare resources (beds, staff, equipment) has become a key priority for many countries. Projecting future demand requires estimates of how long patients with COVID-19 need different levels of hospital care.

METHODS

We performed a systematic review of early evidence on length of stay (LoS) of patients with COVID-19 in hospital and in ICU. We subsequently developed a method to generate LoS distributions which combines summary statistics reported in multiple studies, accounting for differences in sample sizes. Applying this approach, we provide distributions for total hospital and ICU LoS from studies in China and elsewhere, for use by the community.

RESULTS

We identified 52 studies, the majority from China (46/52). Median hospital LoS ranged from 4 to 53 days within China, and 4 to 21 days outside of China, across 45 studies. ICU LoS was reported by eight studies-four each within and outside China-with median values ranging from 6 to 12 and 4 to 19 days, respectively. Our summary distributions have a median hospital LoS of 14 (IQR 10-19) days for China, compared with 5 (IQR 3-9) days outside of China. For ICU, the summary distributions are more similar (median (IQR) of 8 (5-13) days for China and 7 (4-11) days outside of China). There was a visible difference by discharge status, with patients who were discharged alive having longer LoS than those who died during their admission, but no trend associated with study date.

CONCLUSION

Patients with COVID-19 in China appeared to remain in hospital for longer than elsewhere. This may be explained by differences in criteria for admission and discharge between countries, and different timing within the pandemic. In the absence of local data, the combined summary LoS distributions provided here can be used to model bed demands for contingency planning and then updated, with the novel method presented here, as more studies with aggregated statistics emerge outside China.

COVID-19 length of hospital stay: a systematic review and data synthesis

BACKGROUND

The COVID-19 pandemic has placed an unprecedented strain on health systems, with rapidly increasing demand for healthcare in hospitals and intensive care units (ICUs) worldwide. As the pandemic escalates, determining the resulting needs for healthcare resources (beds, staff, equipment) has become a key priority for many countries. Projecting future demand requires estimates of how long patients with COVID-19 need different levels of hospital care.

METHODS

We performed a systematic review of early evidence on length of stay (LoS) of patients with COVID-19 in hospital and in ICU. We subsequently developed a method to generate LoS distributions which combines summary statistics reported in multiple studies, accounting for differences in sample sizes. Applying this approach, we provide distributions for total hospital and ICU LoS from studies in China and elsewhere, for use by the community.

RESULTS

We identified 52 studies, the majority from China (46/52). Median hospital LoS ranged from 4 to 53 days within China, and 4 to 21 days outside of China, across 45 studies. ICU LoS was reported by eight studies-four each within and outside China-with median values ranging from 6 to 12 and 4 to 19 days, respectively. Our summary distributions have a median hospital LoS of 14 (IQR 10-19) days for China, compared with 5 (IQR 3-9) days outside of China. For ICU, the summary distributions are more similar (median (IQR) of 8 (5-13) days for China and 7 (4-11) days outside of China). There was a visible difference by discharge status, with patients who were discharged alive having longer LoS than those who died during their admission, but no trend associated with study date.

CONCLUSION

Patients with COVID-19 in China appeared to remain in hospital for longer than elsewhere. This may be explained by differences in criteria for admission and discharge between countries, and different timing within the pandemic. In the absence of local data, the combined summary LoS distributions provided here can be used to model bed demands for contingency planning and then updated, with the novel method presented here, as more studies with aggregated statistics emerge outside China.

Creation of a Geospatially Explicit, Agent-based Model of a Regional Healthcare Network with Application to Clostridioides difficile Infection

Agent-based models (ABMs) describe and simulate complex systems comprising unique agents, or individuals, while accounting for geospatial and temporal variability among dynamic processes. ABMs are increasingly used to study healthcare-associated infections (ie, infections acquired during admission to a healthcare facility), including Clostridioides difficile infection, currently the most common healthcare-associated infection in the United States. The overall burden and transmission dynamics of healthcare-associated infections, including C difficile infection, may be influenced by community sources and movement of people among healthcare facilities and communities. These complex dynamics warrant geospatially explicit ABMs that extend beyond single healthcare facilities to include entire systems (eg, hospitals, nursing homes and extended care facilities, the community). The agents in ABMs can be built on a synthetic population, a model-generated representation of the actual population with associated spatial (eg, home residence), temporal (eg, change in location over time), and nonspatial (eg, sociodemographic features) attributes. We describe our methods to create a geospatially explicit ABM of a major regional healthcare network using a synthetic population as microdata input. We illustrate agent movement in the healthcare network and the community, informed by patient-level medical records, aggregate hospital discharge data, healthcare facility licensing data, and published literature. We apply the ABM output to visualize agent movement in the healthcare network and the community served by the network. We provide an application example of the ABM to C difficile infection using a natural history submodel. We discuss the ABM's potential to detect network areas where disease risk is high; simulate and evaluate interventions to protect public health; adapt to other geographic locations and healthcare-associated infections, including emerging pathogens; and meaningfully translate results to public health practitioners, healthcare providers, and policymakers.

Dealing with highly skewed hospital length of stay distributions: The use of Gamma mixture models to study delivery hospitalizations

The increased focus on addressing severe maternal morbidity and maternal mortality has led to studies investigating patient and hospital characteristics associated with longer hospital stays. Length of stay (LOS) for delivery hospitalizations has a strongly skewed distribution with the vast majority of LOS lasting two to three days in the United States. Prior studies typically focused on common LOSs and dealt with the long LOS distribution tail in ways to fit conventional statistical analyses (e.g., log transformation, trimming). This study demonstrates the use of Gamma mixture models to analyze the skewed LOS distribution. Gamma mixture models are flexible and, do not require data transformation or removal of outliers to accommodate many outcome distribution shapes, these models allow for the analysis of patients staying in the hospital for a longer time, which often includes those women experiencing worse outcomes. Random effects are included in the model to account for patients being treated within the same hospitals. Further, the role and influence of differing placements of covariates on the results is discussed in the context of distinct model specifications of the Gamma mixture regression model. The application of these models shows that they are robust to the placement of covariates and random effects. Using New York State data, the models showed that longer LOS for childbirth hospitalizations were more common in hospitals designated to accept more complicated deliveries, across hospital types, and among Black women. Primary insurance also was associated with LOS. Substantial variation between hospitals suggests the need to investigate protocols to standardize evidence-based medical care.

Exploratory data analysis for pre and post 24/7/365 attending radiologist coverage support in an emergency department: fundamentals of data science

OBJECTIVE

To present a detailed exploratory data analysis for critically investigating the patterns in medical doctor (MD) to disposition time, pre and post 24/7/365 attending radiologist coverage, for patients presenting to an emergency department (ED).

MATERIALS AND METHODS

The process involved presenting several modeling techniques. To share an understanding of concepts and techniques, we used proportions, medians, and means, Mann-Whitney U test, Kaplan-Meier's (KM) survival analysis, linear and log-linear regression, log-ranked test, Cox proportional hazards model, Weibull parametric survival models and tertile analysis. Retrospective chart review was conducted to obtain a data set which was used to determine the trends in MD to disposition time. Data comprised of patients who had visited the emergency department (ED) during two distinct time periods and whose imaging studies were read by an attending emergency and trauma radiologist.

RESULTS

Median provided more insight into the data as compared with the mean. The Mann-Whitney U test was appropriate to evaluate MD to disposition time, but provided limited information. The Kaplan-Meier (KM) was able to offer more insight into the data since it did not assume an underlying model and that is the reason why it was appropriate. However, KM had limited ability to handle measured confounders and was unable to describe the magnitude of difference between curves. The Cox proportional hazards semi-parametric model or some other parametric model such as the Weibull could handle multiple measured confounders and described the magnitude of difference between two (survival) groups in the data set. However, both methods assumed underlying models that may not apply to the data set such as the one used in this study. Linear regression was unlikely to be appropriate due to the shape of survival time distributions, but log transforming the outcome could address the distribution issue. Nearly all the results of the KM subgroup analyses were consistent with the results of the log-transformed linear regression subgroup analyses and the interpretation of the results was the same for both.

CONCLUSION

Different statistical procedures may be applied to conduct exploratory subgroup analysis for a data set from a pre and post 24/7/365 attending coverage model. This could guide potential areas of further research to compare trends in MD to disposition time in ED. Pattern analysis provides evidence for various stakeholders to rethink the discourse about trends in MD to disposition time, pre and post 24/7/365 attending coverage. Graphical Illustration: The role of Emergency and Trauma Radiology in an Emergency Department.

Probabilistic Modeling of Exam Durations in Radiology Procedures

In this paper, we model the statistical properties of imaging exam durations using parametric probability distributions such as the Gaussian, Gamma, Weibull, lognormal, and log-logistic. We establish that in a majority of radiology procedures, the underlying distribution of exam durations is best modeled by a log-logistic distribution, while the Gaussian has the poorest fit among the candidates. Further, through illustrative examples, we show how business insights and workflow analytics can be significantly impacted by making the correct (log-logistic) versus incorrect (Gaussian) model choices.

A framework to address key issues of neonatal service configuration in England: the NeoNet multimethods study

Background

There is an inherent tension in neonatal services between the efficiency and specialised care that comes with centralisation and the provision of local services with associated ease of access and community benefits. This study builds on previous work in South West England to address these issues at a national scale.

Objectives

(1) To develop an analytical framework to address key issues of neonatal service configuration in England, (2) to investigate visualisation tools to facilitate the communication of findings to stakeholder groups and (3) to assess parental preferences in relation to service configuration alternatives.

Main outcome measures

The ability to meet nurse staffing guidelines, volumes of units, costs, mortality, number and distance of transfers, travel distances and travel times for parents.

Design

Descriptive statistics, location analysis, mathematical modelling, discrete event simulation and economic analysis were used. Qualitative methods were used to interview policy-makers and parents. A parent advisory group supported the study.

Setting

NHS neonatal services across England.

Data

Neonatal care data were sourced from the National Neonatal Research Database. Information on neonatal units was drawn from the National Neonatal Audit Programme. Geographic and demographic data were sourced from the Office for National Statistics. Travel time data were retrieved via a geographic information system. Birth data were sourced from Hospital Episode Statistics. Parental cost data were collected via a survey.

Results

Location analysis shows that to achieve 100% of births in units with ≥ 6000 births per year, the number of birth centres would need to be reduced from 161 to approximately 72, with more parents travelling > 30 minutes. The maximum number of neonatal intensive care units (NICUs) needed to achieve 100% of very low-birthweight infants attending high-volume units is 36 with existing NICUs, or 48 if NICUs are located wherever there is currently a neonatal unit of any level. Simulation modelling further demonstrated the workforce implications of different configurations. Mortality modelling shows that the birth of very preterm infants in high-volume hospitals reduces mortality (a conservative estimate of a 1.2-percentage-point lower risk) relative to these births in other hospitals. It is currently not possible to estimate the impact of mortality for infants transferred into NICUs. Cost modelling shows that the mean length of stay following a birth in a high-volume hospital is 9 days longer and the mean cost is £5715 more than for a birth in another neonatal unit. In addition, the incremental cost per neonatal life saved is £460,887, which is comparable to other similar life-saving interventions. The analysis of parent costs identified unpaid leave entitlement, food, travel, accommodation, baby care and parking as key factors. The qualitative study suggested that central concerns were the health of the baby and mother, communication by medical teams and support for families.

Limitations

The following factors could not be modelled because of a paucity of data – morbidity outcomes, the impact of transfers and the maternity/neonatal service interface.

Conclusions

An evidence-based framework was developed to inform the configuration of neonatal services and model system performance from the perspectives of both service providers and parents.

Future work

To extend the modelling to encompass the interface between maternity and neonatal services.

Funding

The National Institute for Health Research Health Services and Delivery Research programme.

Assessment of length of stay in a general surgical unit using a zero-inflated generalized Poisson regression

Background: The effective use of limited health care resources is of prime importance. Assessing the length of stay (LOS) is especially important in organizing hospital services and health system. This study was conducted to identify predictors of LOS among patients who were admitted to a general surgical unit.

Methods: In this cross-sectional study, the sample included all patients who were admitted to the general surgical unit of Shariati hospital in 2013 (n= 334). To determine the factors affecting LOS, Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated generalized Poisson (ZIGP) regression models were fitted using R software, and then the best model was selected.

Results: Among all 334 patients, the mean (±SD) age of the patients was 45.2 (±16.47) years and 220 (65.9%) of them were male. The results revealed that based on ZIGP model, type of surgery (appendicitis, abdomen and its contents, hemorrhoids, lung, and skin), type of insurance, comorbid diseases (hypertension, heart disease, and hyperlipidemia), place of residence (local and non-local), age, and number of tests had significant effects on the LOS of GS patients.

Conclusion: According to the Akaike information criterion (AIC) in each fitted model, it was found that ZIGP regression model is more appropriate than ZIP and ZINB regression models in assessing LOS in GS patients, especially due to the presence of excess zeros and overdispersion in count data.

Simulation modelling of patient flow and capacity planning for regional long-term care needs: a case study

The need for Long-Term Care (LTC) arises in the elderly population, especially those reaching age 65 each year. This elderly population will grow tremendously in the United States over the next decade, resulting in short- and long-term challenges of matching resource capacity with uncertain demand for hospitals and other healthcare providers. This paper describes research involving the development of a simulation model of patient flow in order to understand the relationship between capacity and demand, and to investigate the impacts on performance measures such as average wait times for LTC patients. We propose an aggregate capacity model to consider patient flow among various types of care providers by integrating hospitals, nursing homes, assisted living facilities, and home health care. Using the data including patient demographics and service provider information, we forecast patient demand for LTC. The computational results demonstrate the efficacy of a simulation-based optimisation solution approach for capacity planning.

Hospital Surge Capacity: A Web-Based Simulation Tool for Emergency Planners

The National Center for the Study of Preparedness and Catastrophic Event Response (PACER) has created a publicly available simulation tool called Surge (accessible at http://www.pacerapps.org) to estimate surge capacity for user-defined hospitals. Based on user input, a Monte Carlo simulation algorithm forecasts available hospital bed capacity over a 7-day period and iteratively assesses the ability to accommodate disaster patients. Currently, the tool can simulate bed capacity for acute mass casualty events (such as explosions) only and does not specifically simulate staff and supply inventory. Strategies to expand hospital capacity, such as (1) opening unlicensed beds, (2) canceling elective admissions, and (3) implementing reverse triage, can be interactively evaluated. In the present application of the tool, various response strategies were systematically investigated for 3 nationally representative hospital settings (large urban, midsize community, small rural). The simulation experiments estimated baseline surge capacity between 7% (large hospitals) and 22% (small hospitals) of staffed beds. Combining all response strategies simulated surge capacity between 30% and 40% of staffed beds. Response strategies were more impactful in the large urban hospital simulation owing to higher baseline occupancy and greater proportion of elective admissions. The publicly available Surge tool enables proactive assessment of hospital surge capacity to support improved decision-making for disaster response. (Disaster Med Public Health Preparedness. 2018;12:513–522)

How to Compare the Length of Stay of Two Samples of Inpatients? A Simulation Study to Compare Type I and Type II Errors of 12 Statistical Tests

BACKGROUND

Although many researchers in the field of health economics and quality of care compare the length of stay (LOS) in two inpatient samples, they often fail to check whether the sample meets the assumptions made by their chosen statistical test. In fact, LOS data show a highly right-skewed, discrete distribution in which most of the observations are tied; this violates the assumptions of most statistical tests.

OBJECTIVES

To estimate the type I and type II errors associated with the application of 12 different statistical tests to a series of LOS samples.

METHODS

The LOS distribution was extracted from an exhaustive French national database of inpatient stays. The type I error was estimated using 19 sample sizes and 1,000,000 simulations per sample. The type II error was estimated in three alternative scenarios. For each test, the type I and type II errors were plotted as a function of the sample size.

RESULTS

Gamma regression with log link, the log rank test, median regression, Poisson regression, and Weibull survival analysis presented an unacceptably high type I error. In contrast, the Student standard t test, linear regression with log link, and the Cox models had an acceptable type I error but low power.

CONCLUSIONS

When comparing the LOS for two balanced inpatient samples, the Student t test with logarithmic or rank transformation, the Wilcoxon test, and the Kruskal-Wallis test are the only methods with an acceptable type I error and high power.

Modelling hospital length of stay using convolutive mixtures distributions

Length of hospital stay (LOS) is an important indicator of the hospital activity and management of health care. The skewness in the distribution of LOS poses problems in statistical modelling because it fails to adequately follow the usual traditional distribution of positive variables such as the log-normal distribution. We present in this paper a model using the convolution of two distributions, a technique well known in the signal processing community. The specificity of that model is that the variable of interest is considered to be the resulting sum of two random variables with different distributions. One of the variables features the patient-related factors in terms of their need to recover from their admission condition, while the other models the hospital management process such as the discharging process. Two estimation procedures are proposed. One is the classical maximum likelihood, while the other relates to the expectation-maximization algorithm. We present some results obtained by applying this model to a set of real data from a group of hospitals in Victoria (Australia). Copyright © 2016 John Wiley & Sons, Ltd.

Using Length of Stay to Control for Unobserved Heterogeneity When Estimating Treatment Effect on Hospital Costs with Observational Data: Issues of Reliability, Robustness, and Usefulness

OBJECTIVE

To evaluate the sensitivity of treatment effect estimates when length of stay (LOS) is used to control for unobserved heterogeneity when estimating treatment effect on cost of hospital admission with observational data.

DATA SOURCES/STUDY SETTING

We used data from a prospective cohort study on the impact of palliative care consultation teams (PCCTs) on direct cost of hospital care. Adult patients with an advanced cancer diagnosis admitted to five large medical and cancer centers in the United States between 2007 and 2011 were eligible for this study.

STUDY DESIGN

Costs were modeled using generalized linear models with a gamma distribution and a log link. We compared variability in estimates of PCCT impact on hospitalization costs when LOS was used as a covariate, as a sample parameter, and as an outcome denominator. We used propensity scores to account for patient characteristics associated with both PCCT use and total direct hospitalization costs.

DATA COLLECTION/EXTRACTION METHODS

We analyzed data from hospital cost databases, medical records, and questionnaires. Our propensity score weighted sample included 969 patients who were discharged alive.

PRINCIPAL FINDINGS

In analyses of hospitalization costs, treatment effect estimates are highly sensitive to methods that control for LOS, complicating interpretation. Both the magnitude and significance of results varied widely with the method of controlling for LOS. When we incorporated intervention timing into our analyses, results were robust to LOS-controls.

CONCLUSIONS

Treatment effect estimates using LOS-controls are not only suboptimal in terms of reliability (given concerns over endogeneity and bias) and usefulness (given the need to validate the cost-effectiveness of an intervention using overall resource use for a sample defined at baseline) but also in terms of robustness (results depend on the approach taken, and there is little evidence to guide this choice). To derive results that minimize endogeneity concerns and maximize external validity, investigators should match and analyze treatment and comparison arms on baseline factors only. Incorporating intervention timing may deliver results that are more reliable, more robust, and more useful than those derived using LOS-controls.

Using the M/G/∞ queueing model to predict inpatient family medicine service census and resident workload

The number and timing of unplanned admissions to inpatient teaching services vary. Recent changes to resident duty hours make it essential to maximize learning experiences and balance workload on these services. Queueing theory provides a mechanism for understanding and planning for the variations in admissions and daily census. Daily admissions, length of stay, and daily census were modeled for a teaching inpatient family medicine service over 46 months using an M/G/∞ queueing model. Q–Q plots and a Kolmogorov–Smirnov test were used to check the fit of actual data to the model. Admissions and daily census followed a Poisson distribution (λ = 3.28 and λ = 8.28, respectively), while length-of-stay followed a lognormal distribution (µ = 0.49, σ2 = 0.83). The M/G/∞ queueing model proved useful for predicting overflow admission frequency, defining expected resident workload in terms of patient-days, and determining hospital unit size requirements.

Evaluation of the Performance of Diagnosis-Related Groups and Similar Casemix Systems: Methodological Issues

With the increasing recognition and application of casemix for managing and financing healthcare resources, the evaluation of alternative versions of systems such as diagnosis-related groups (DRGs) has been afforded high priority by governments and researchers in many countries. Outside the United States, an important issue has been the perceived need to produce local versions, and to establish whether or not these perform more effectively than the US-based classifications. A discussion of casemix evaluation criteria highlights the large number of measures that may be used, the rationale and assumptions underlying each measure, and the problems in interpreting the results. A review of recent evaluation studies from a number of countries indicates that considerable emphasis has been placed on the predictive validity criterion, as measured by the R2 statistic. However, the interpretation of the findings has been affected greatly by the methods used, especially the treatment and definition of outlier cases. Furthermore, the extent to which other evaluation criteria have been addressed has varied widely. In the absence of minimum evaluation standards, it is not possible to draw clear-cut conclusions about the superiority of one version of a casemix system over another, the need for a local adaptation, or the further development of an existing version. Without the evidence provided by properly designed studies, policy-makers and managers may place undue reliance on subjective judgements and the views of the most influential, but not necessarily best informed, healthcare interest groups.

Has variation in length of stay in acute hospitals decreased? Analysing trends in the variation in LOS between and within Dutch hospitals

Background

We aimed to get better insight into the development of the variation in length of stay (LOS) between and within hospitals over time, in order to assess the room for efficiency improvement in hospital care.

Methods

Using Dutch national individual patient-level hospital admission data, we studied LOS for patients in nine groups of diagnoses and procedures between 1995 and 2010. We fitted linear mixed effects models to the log-transformed LOS to disentangle within and between hospital variation and to evaluate trends, adjusted for case-mix.

Results

We found substantial differences between diagnoses and procedures in LOS variation and development over time, supporting our disease-specific approach. For none of the diagnoses, relative variance decreased on the log scale, suggesting room for further LOS reduction. Except for two procedures in the same specialty, LOS of individual hospitals did not correlate between diagnoses/procedures, indicating the absence of a hospital wide policy. We found within-hospital variance to be many times greater than between-hospital variance. This resulted in overlapping confidence intervals across most hospitals for individual hospitals’ performances in terms of LOS.

Conclusions

The results suggest room for efficiency improvement implying lower costs per patient treated. It further implies a possibility to raise the number of patients treated using the same capacity or to downsize the capacity. Furthermore, policymakers and health care purchasers should take into account statistical uncertainty when benchmarking LOS between hospitals and identifying inefficient hospitals.

Electronic supplementary material

The online version of this article (doi:10.1186/s12913-015-1087-6) contains supplementary material, which is available to authorized users.

Prospective Cohort Study of Hospital Palliative Care Teams for Inpatients With Advanced Cancer: Earlier Consultation Is Associated With Larger Cost-Saving Effect

PURPOSE

Previous studies report that early palliative care is associated with clinical benefits, but there is limited evidence on economic impact. This article addresses the research question: Does timing of palliative care have an impact on its effect on cost?

PATIENTS AND METHODS

Using a prospective, observational design, clinical and cost data were collected for adult patients with an advanced cancer diagnosis admitted to five US hospitals from 2007 to 2011. The sample for economic evaluation was 969 patients; 256 were seen by a palliative care consultation team, and 713 received usual care only. Subsamples were created according to time to consult after admission. Propensity score weights were calculated, matching the treatment and comparison arms specific to each subsample on observed confounders. Generalized linear models with a γ distribution and a log link were applied to estimate the mean treatment effect on cost within subsamples.

RESULTS

Earlier consultation is associated with a larger effect on total direct cost. Intervention within 6 days is estimated to reduce costs by -$1,312 (95% CI, -$2,568 to -$56; P = .04) compared with no intervention and intervention within 2 days by -$2,280 (95% CI, -$3,438 to -$1,122; P < .001); these reductions are equivalent to a 14% and a 24% reduction, respectively, in cost of hospital stay.

CONCLUSION

Earlier palliative care consultation during hospital admission is associated with lower cost of hospital stay for patients admitted with an advanced cancer diagnosis. These findings are consistent with a growing body of research on quality and survival suggesting that early palliative care should be more widely implemented.

Predictive modelling of survival and length of stay in critically ill patients using sequential organ failure scores

INTRODUCTION

The length of stay of critically ill patients in the intensive care unit (ICU) is an indication of patient ICU resource usage and varies considerably. Planning of postoperative ICU admissions is important as ICUs often have no nonoccupied beds available.

PROBLEM STATEMENT

Estimation of the ICU bed availability for the next coming days is entirely based on clinical judgement by intensivists and therefore too inaccurate. For this reason, predictive models have much potential for improving planning for ICU patient admission.

OBJECTIVE

Our goal is to develop and optimize models for patient survival and ICU length of stay (LOS) based on monitored ICU patient data. Furthermore, these models are compared on their use of sequential organ failure (SOFA) scores as well as underlying raw data as input features.

METHODOLOGY

Different machine learning techniques are trained, using a 14,480 patient dataset, both on SOFA scores as well as their underlying raw data values from the first five days after admission, in order to predict (i) the patient LOS, and (ii) the patient mortality. Furthermore, to help physicians in assessing the prediction credibility, a probabilistic model is tailored to the output of our best-performing model, assigning a belief to each patient status prediction. A two-by-two grid is built, using the classification outputs of the mortality and prolonged stay predictors to improve the patient LOS regression models.

RESULTS

For predicting patient mortality and a prolonged stay, the best performing model is a support vector machine (SVM) with GA,D=65.9% (area under the curve (AUC) of 0.77) and GS,L=73.2% (AUC of 0.82). In terms of LOS regression, the best performing model is support vector regression, achieving a mean absolute error of 1.79 days and a median absolute error of 1.22 days for those patients surviving a nonprolonged stay.

CONCLUSION

Using a classification grid based on the predicted patient mortality and prolonged stay, allows more accurate modeling of the patient LOS. The detailed models allow to support the decisions made by physicians in an ICU setting.

A cost sensitive inpatient bed reservation approach to reduce emergency department boarding times

Emergency departments (ED) in hospitals are experiencing severe crowding and prolonged patient waiting times. A significant contributing factor is boarding delays where admitted patients are held in ED (occupying critical resources) until an inpatient bed is identified and readied in the admit wards. Recent research has suggested that if the hospital admissions of ED patients can be predicted during triage or soon after, then bed requests and preparations can be triggered early on to reduce patient boarding time. We propose a cost sensitive bed reservation policy that recommends optimal bed reservation times for patients. The policy relies on a classifier that estimates the probability that the ED patient will be admitted using the patient information collected and readily available at triage or right after. The policy is cost sensitive in that it accounts for costs associated with patient admission prediction misclassification as well as costs associated with incorrectly selecting the reservation time. Results from testing the proposed bed reservation policy using data from a VA Medical Center are very promising and suggest significant cost saving opportunities and reduced patient boarding times.

Estimating oxygen needs for childhood pneumonia in developing country health systems: a new model for expecting the unexpected

BACKGROUND

Planning for the reliable and cost-effective supply of a health service commodity such as medical oxygen requires an understanding of the dynamic need or 'demand' for the commodity over time. In developing country health systems, however, collecting longitudinal clinical data for forecasting purposes is very difficult. Furthermore, approaches to estimating demand for supplies based on annual averages can underestimate demand some of the time by missing temporal variability.

METHODS

A discrete event simulation model was developed to estimate variable demand for a health service commodity using the important example of medical oxygen for childhood pneumonia. The model is based on five key factors affecting oxygen demand: annual pneumonia admission rate, hypoxaemia prevalence, degree of seasonality, treatment duration, and oxygen flow rate. These parameters were varied over a wide range of values to generate simulation results for different settings. Total oxygen volume, peak patient load, and hours spent above average-based demand estimates were computed for both low and high seasons.

FINDINGS

Oxygen demand estimates based on annual average values of demand factors can often severely underestimate actual demand. For scenarios with high hypoxaemia prevalence and degree of seasonality, demand can exceed average levels up to 68% of the time. Even for typical scenarios, demand may exceed three times the average level for several hours per day. Peak patient load is sensitive to hypoxaemia prevalence, whereas time spent at such peak loads is strongly influenced by degree of seasonality.

CONCLUSION

A theoretical study is presented whereby a simulation approach to estimating oxygen demand is used to better capture temporal variability compared to standard average-based approaches. This approach provides better grounds for health service planning, including decision-making around technologies for oxygen delivery. Beyond oxygen, this approach is widely applicable to other areas of resource and technology planning in developing country health systems.

Decision support for hospital bed management using adaptable individual length of stay estimations and shared resources

Background

Elective patient admission and assignment planning is an important task of the strategic and operational management of a hospital and early on became a central topic of clinical operations research. The management of hospital beds is an important subtask. Various approaches have been proposed, involving the computation of efficient assignments with regard to the patients’ condition, the necessity of the treatment, and the patients’ preferences. However, these approaches are mostly based on static, unadaptable estimates of the length of stay and, thus, do not take into account the uncertainty of the patient’s recovery. Furthermore, the effect of aggregated bed capacities have not been investigated in this context. Computer supported bed management, combining an adaptable length of stay estimation with the treatment of shared resources (aggregated bed capacities) has not yet been sufficiently investigated. The aim of our work is: 1) to define a cost function for patient admission taking into account adaptable length of stay estimations and aggregated resources, 2) to define a mathematical program formally modeling the assignment problem and an architecture for decision support, 3) to investigate four algorithmic methodologies addressing the assignment problem and one base-line approach, and 4) to evaluate these methodologies w.r.t. cost outcome, performance, and dismissal ratio.

Methods

The expected free ward capacity is calculated based on individual length of stay estimates, introducing Bernoulli distributed random variables for the ward occupation states and approximating the probability densities. The assignment problem is represented as a binary integer program. Four strategies for solving the problem are applied and compared: an exact approach, using the mixed integer programming solver SCIP; and three heuristic strategies, namely the longest expected processing time, the shortest expected processing time, and random choice. A baseline approach serves to compare these optimization strategies with a simple model of the status quo. All the approaches are evaluated by a realistic discrete event simulation: the outcomes are the ratio of successful assignments and dismissals, the computation time, and the model’s cost factors.

Results

A discrete event simulation of 226,000 cases shows a reduction of the dismissal rate compared to the baseline by more than 30 percentage points (from a mean dismissal ratio of 74.7% to 40.06% comparing the status quo with the optimization strategies). Each of the optimization strategies leads to an improved assignment. The exact approach has only a marginal advantage over the heuristic strategies in the model’s cost factors (≤3%). Moreover,this marginal advantage was only achieved at the price of a computational time fifty times that of the heuristic models (an average computing time of 141 s using the exact method, vs. 2.6 s for the heuristic strategy).

Conclusions

In terms of its performance and the quality of its solution, the heuristic strategy RAND is the preferred method for bed assignment in the case of shared resources. Future research is needed to investigate whether an equally marked improvement can be achieved in a large scale clinical application study, ideally one comprising all the departments involved in admission and assignment planning.

Improving hospital bed utilisation through simulation and optimisation: with application to a 40% increase in patient volume in a Norwegian General Hospital

PURPOSE

This paper analyses the problem of allocating beds among hospital wards in order to minimise crowding.

METHOD

We present a generic discrete event simulation model of patient flow through the wards of a hospital. In the generic model, each ward can have separate probability distributions for arrival times and length of stay, which may be time dependent. Output of the model is a matrix, with statistics on the utilisation of different hypothetical numbers of beds for each ward. This matrix is fed into an allocation algorithm, which distributes the available beds among the wards in an optimal way. We define bed utilisation either in terms of how often it is in use (prevalence), or in terms of how often a newly arriving patient is placed in it (incidence). For these classes of utilisation measures we develop efficient allocation algorithms, which we prove to be optimal.

APPLICATION

The model was applied to Akershus University Hospital in Norway. In 2011, some of the wards of this hospital experienced a high occupancy rate, while others had a lower utilisation. Our model was applied in order to reallocate the hospital beds among the wards. For each ward, acute arrivals were modelled with Poisson-distributions with time-varying intensity, while elective arrivals were programmed to arrive in specific numbers at specific times. The arrival rates were based on empirical data for 2010, scaled up by an expected increase of 40% due to a restructuring of the hospital districts in Oslo and the greater metropolitan area in 2011. Length of stay was modelled as beta-distributions, using a combination of subject matter experts' evaluations and empirical data from 2010. The model has been verified and validated.

RESULTS

Intuitively, both prevalence (average number of crowding beds in use) and incidence (number of patients placed in crowding beds) might seem like relevant optimisation criteria. However, our experiments show that prevalence optimisation gives more sensible solutions than incidence optimisation, as the latter tends to sacrifice entire wards where length of stay is long and patient turnover is slow. Prevalence optimisation was therefore used. The main results show that when the bed distribution is optimised, the share of crowding patient nights is reduced from 6.5% to 4.2%.

CONCLUSION

This model provides a powerful tool for optimising hospital bed utilisation, and the application showed an important reduction in crowding bed usage. The generic model is flexible, as the level of detail in the modelling of arrivals and length of stay can vary according to the data available and accuracy required.

A two-compartment mixed-effects gamma regression model for quantifying between-unit variability in length of stay among children admitted to intensive care

OBJECTIVE

To quantify between-unit variability in mean length of stay (LoS) between intensive care units (ICUs) after adjusting for differences in case mix using a method that does not require arbitrary trimming of data.

SETTING

An analysis of registry data from pediatric ICUs (PICUs) in Australia and New Zealand.

STUDY DESIGN

The relationships between patient LoS and associated patient factors were modeled as a log-linear function of the covariates using two gamma distributions. The predicted distribution is estimated as a weighted average of the two distributions where the relative weighting is conditional on the patient's elective status.

DATA COLLECTION

Data for 12,763 admissions submitted to the Australian and New Zealand Paediatric Intensive Care Registry from the eight dedicated PICUs in Australia and New Zealand in 2007 and 2008.

PRINCIPAL FINDINGS

The two distributions of the mixture model accurately described the distribution of short- and long-stay patients in ICUs. After adjusting for patient case mix, several sites had a statistically significant effect on patient LoS.

CONCLUSION

The two-compartment model characterizes ICU LoS for short- and long-stay patients more effectively than a single-compartment model. There is significant site-level variation in the LoS among children admitted to ICUs in Australia and New Zealand. Differences in the site-level variation between short- and long-stay patients indicate differences in discharge practice.

A review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and new Zealand Intensive Care Adult Patient Data-Base, 2008-2009

BACKGROUND

For the analysis of length-of-stay (LOS) data, which is characteristically right-skewed, a number of statistical estimators have been proposed as alternatives to the traditional ordinary least squares (OLS) regression with log dependent variable.

METHODS

Using a cohort of patients identified in the Australian and New Zealand Intensive Care Society Adult Patient Database, 2008-2009, 12 different methods were used for estimation of intensive care (ICU) length of stay. These encompassed risk-adjusted regression analysis of firstly: log LOS using OLS, linear mixed model [LMM], treatment effects, skew-normal and skew-t models; and secondly: unmodified (raw) LOS via OLS, generalised linear models [GLMs] with log-link and 4 different distributions [Poisson, gamma, negative binomial and inverse-Gaussian], extended estimating equations [EEE] and a finite mixture model including a gamma distribution. A fixed covariate list and ICU-site clustering with robust variance were utilised for model fitting with split-sample determination (80%) and validation (20%) data sets, and model simulation was undertaken to establish over-fitting (Copas test). Indices of model specification using Bayesian information criterion [BIC: lower values preferred] and residual analysis as well as predictive performance (R2, concordance correlation coefficient (CCC), mean absolute error [MAE]) were established for each estimator.

RESULTS

The data-set consisted of 111663 patients from 131 ICUs; with mean(SD) age 60.6(18.8) years, 43.0% were female, 40.7% were mechanically ventilated and ICU mortality was 7.8%. ICU length-of-stay was 3.4(5.1) (median 1.8, range (0.17-60)) days and demonstrated marked kurtosis and right skew (29.4 and 4.4 respectively). BIC showed considerable spread, from a maximum of 509801 (OLS-raw scale) to a minimum of 210286 (LMM). R2 ranged from 0.22 (LMM) to 0.17 and the CCC from 0.334 (LMM) to 0.149, with MAE 2.2-2.4. Superior residual behaviour was established for the log-scale estimators. There was a general tendency for over-prediction (negative residuals) and for over-fitting, the exception being the GLM negative binomial estimator. The mean-variance function was best approximated by a quadratic function, consistent with log-scale estimation; the link function was estimated (EEE) as 0.152(0.019, 0.285), consistent with a fractional-root function.

CONCLUSIONS

For ICU length of stay, log-scale estimation, in particular the LMM, appeared to be the most consistently performing estimator(s). Neither the GLM variants nor the skew-regression estimators dominated.

Contemporary pediatric splenectomy: continuing controversies

PURPOSE

We undertook the current study to update the literature on pediatric splenectomy in the age of minimally invasive proficiency among pediatric surgeons. The study is designed to address specific concerns among surgeons about the suitability of the laparoscopic approach in specific situations and among hematologists about the relative benefits and risks of splenectomy in children.

METHODS

Retrospective analysis of clinicopathologic data for 118 children who underwent open (OS) or laparoscopic (LS) splenectomy at an urban tertiary children's hospital from January 2000 to July 2008.

RESULTS

One hundred and three cases (87%) were started as LS. Operative times were equivalent for LS and OS (P = 0.8). In the LS group, there were four conversions (3.9%) from LS to OS and five early post-operative complications (4.9%). Median length of stay was 2 days for LS and 4 days for both OS and LS converted to OS (P < 0.0001). The ten largest spleens removed by LS had greater mass (P = 0.02) and tended to have greater volume (P = 0.1) than those removed by OS. Children with hereditary spherocytosis, ITP, and hemoglobinopathy had favorable clinical outcomes, regardless of operative approach. There were no cases of overwhelming post-splenectomy sepsis in this series.

CONCLUSIONS

Laparoscopic splenectomy is the preferred approach for splenectomy in children with hematological diseases, with or without splenomegaly. Compared to open splenectomy, laparoscopic splenectomy has equivalent operative time and improved length of stay. Both approaches have excellent therapeutic outcomes for appropriate indications.

Review of statistical methods for analysing healthcare resources and costs

We review statistical methods for analysing healthcare resource use and costs, their ability to address skewness, excess zeros, multimodality and heavy right tails, and their ease for general use. We aim to provide guidance on analysing resource use and costs focusing on randomised trials, although methods often have wider applicability. Twelve broad categories of methods were identified: (I) methods based on the normal distribution, (II) methods following transformation of data, (III) single-distribution generalized linear models (GLMs), (IV) parametric models based on skewed distributions outside the GLM family, (V) models based on mixtures of parametric distributions, (VI) two (or multi)-part and Tobit models, (VII) survival methods, (VIII) non-parametric methods, (IX) methods based on truncation or trimming of data, (X) data components models, (XI) methods based on averaging across models, and (XII) Markov chain methods. Based on this review, our recommendations are that, first, simple methods are preferred in large samples where the near-normality of sample means is assured. Second, in somewhat smaller samples, relatively simple methods, able to deal with one or two of above data characteristics, may be preferable but checking sensitivity to assumptions is necessary. Finally, some more complex methods hold promise, but are relatively untried; their implementation requires substantial expertise and they are not currently recommended for wider applied work.

Length of stay and imminent discharge probability distributions from multistage models: variation by diagnosis, severity of illness, and hospital

Multistage models have been effective at describing length of stay (LOS) distributions for diverse patient groups. Our study objective was to determine whether such models could be used for patient groups restricted by diagnosis, severity of illness, or hospital in order to facilitate comparisons conditioned on these factors. We performed a retrospective cohort study using data from 317,876 hospitalizations occurring over 2 years in 17 hospitals in a large, integrated health care delivery system. We estimated model parameters using data from the first year and validated them by comparing the predicted LOS distribution to the second year of data. We found that 3- and 4-stage models fit LOS data for either the entire hospital cohort or for subsets of patients with specific conditions (e.g. community-acquired pneumonia). Probability distributions were strongly influenced by the degree of physiologic derangement on admission, pre-existing comorbidities, or a summary mortality risk combining these with age, sex, and diagnosis. The distributions for groups with greater severity of illness were shifted slightly to the right, but even more notable was the increase in the dispersion, indicating the LOS is harder to predict with greater severity of illness. Multistage models facilitate computation of the hazard function, which shows the probability of imminent discharge given the elapsed LOS, and provide a unified method of fitting, summarizing, and studying the effects of factors affecting LOS distributions. Future work should not be restricted to expected LOS comparisons, but should incorporate examination of LOS probability distributions.

Adjusting case mix payment amounts for inaccurately reported comorbidity data

Case mix methods such as diagnosis related groups have become a basis of payment for inpatient hospitalizations in many countries. Specifying cost weight values for case mix system payment has important consequences; recent evidence suggests case mix cost weight inaccuracies influence the supply of some hospital-based services. To begin to address the question of case mix cost weight accuracy, this paper is motivated by the objective of improving the accuracy of cost weight values due to inaccurate or incomplete comorbidity data. The methods are suitable to case mix methods that incorporate disease severity or comorbidity adjustments. The methods are based on the availability of detailed clinical and cost information linked at the patient level and leverage recent results from clinical data audits. A Bayesian framework is used to synthesize clinical data audit information regarding misclassification probabilities into cost weight value calculations. The models are implemented through Markov chain Monte Carlo methods. An example used to demonstrate the methods finds that inaccurate comorbidity data affects cost weight values by biasing cost weight values (and payments) downward. The implications for hospital payments are discussed and the generalizability of the approach is explored.

Major elective joint replacement surgery: socioeconomic variations in surgical risk, postoperative morbidity and length of stay

BACKGROUND

Patient deprivation is associated with greater need for total hip and knee replacement surgery (THR/TKR) and a higher prevalence of risk factors for surgical complications. Our aim was to examine associations between deprivation and aspects of the inpatient episode for patients undergoing these procedures.

METHODS

We analysed socioeconomic variations in preoperative surgical risk, postoperative morbidity and length of stay for 655 patients undergoing elective THR/TKR at a large metropolitan hospital. Surgical risk was assessed using the orthopaedic version of the POSSUM scoring system, postoperative morbidity was assessed using the postoperative morbidity survey, and socioeconomic status was measured using the Index of Multiple Deprivation. We adjusted for age, sex, surgical site and primary vs. revision surgery.

RESULTS

We found only a modest, clinically insignificant socioeconomic gradient in preoperative surgical risk and no socioeconomic gradient in postoperative morbidity. There was a strong socioeconomic gradient in length of stay, but only for patients undergoing TKR. This was due to deprived patients being more likely to remain in hospital without morbidity following TKR.

CONCLUSIONS

Our findings suggest differential selection of healthier patients for surgery. Hospitals serving deprived communities may have excess, unfunded costs because of the increased length of stay of socioeconomically disadvantaged patients.

Inpatient length of stay: a finite mixture modeling analysis

Length of stay (LOS) in hospital for inpatient treatment is a measure of crucial recovery time. Using nationwide data on inpatient healthcare in India, a three-component finite mixture negative binomial model was found to provide a reasonable fit to the heterogeneous LOS distribution. Associated risk factors for short-stay, medium-stay and long-stay subgroups were identified from the respective negative binomial components. In addition, significant heterogeneities within each group were also found.