Application of quantitative decision-making tools in planning for seasonal variations of fever cases reporting at the medical emergency of a tertiary care hospital in New Delhi

doi:10.21203/rs.3.rs-1728827/v1

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Application of quantitative decision-making tools in planning for seasonal variations of fever cases reporting at the medical emergency of a tertiary care hospital in New Delhi

https://doi.org/10.21203/rs.3.rs-1728827/v1

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Background

The healthcare industry of today is defined by patient centricity, perishability, intangibility and heterogenicity. Healthcare managers are faced with a challenge to maximize results by utilizing minimum resources. Forecasting is one of the techniques that help them in planning services. However, the accuracy of the forecast depends on multiple factors such as time horizon, the technique that is applied and certain irregular variations, which may be beyond the control of managers.

Methods

A retrospective record analysis was done to analyze trends in the monthly footfall in the emergency. Forecasting techniques were applied to predict the number of fever cases that were expected during a particular time period, based on which, the quantum of supplies needed was calculated using linear programming model. The actual and predicted number of patients that visited the emergency for 4 years was tabulated.

Results

It was observed that the demand for different consumables increased by 33–200% during the peak season. The Mean Absolute Deviation (MAD) was calculated to be 3981.22, Mean Absolute Percentage Error (MAPE) was 30.17% and the Tracking Signal varied between − 1.78 and + 0.86 which indicates that the forecast method was fairly accurate.

Conclusion

The same method may be applied to forecast the number of patients and accordingly the quantum of resources required for their management.

Operations research

quantitative techniques

healthcare planning

seasonal variations

linear programming

emergency care

forecasting in healthcare

The healthcare industry of today is defined by patient centricity, perishability, intangibility and heterogenicity. ¹ Healthcare managers are faced with a challenge to maximize results by utilizing minimum resources. They are responsible for planning services that are to be offered and for determining their volume for optimum output. Healthcare managers are instrumental in the smooth functioning of their organizations through supply chain management, quality improvement and organization of men and material. This requires decision making, starting with the mid-level management which takes operational decisions, to the top management which is responsible for strategic decisions. Decisions must however be informed and supported by quantifiable data. Forecasting is one of the techniques that helps healthcare managers plan services in their organization. Accuracy of the forecast depends on multiple factors such as time horizon, the technique that is applied and certain irregular variations which may be beyond the control of managers.

The Emergency Department (ED) of any hospital is dynamic, and the patterns of utilization of services and supplies are hard to predict. Our hospital caters to huge volume of patients each day and this burden is on the rise with average number of patients visiting the emergency rising gradually each year. Apart from this continuous rise, there have been seasonal variations, especially in the number of fever cases that report to the medical emergency during monsoons because of rise in incidence of vector-borne diseases. During the peak season, this rise has warranted creation of a special ‘fever clinic’ in the emergency where additional arrangements are made for prompt investigation and management of such cases. There has been deployment of additional manpower and allocation of resources to cater to these cases. The resources require space for storage which is one of the major bottlenecks in the already space-constrained, over-burdened facility. On the other hand, these resources should be maintained in adequate quantities to ensure that there are no stock-outs which might compromise patient care. Scientific resource planning and allocation calls for the is of forecasting techniques that require an analysis of past usage patterns. However, the seasonal variation in fever cases reporting to the ED of tropical and subtropical countries has witnessed a substantial flux which calls for quantitative decision-making tools to predict the optimal resource allocation in the emergency department after analysing available historical data. The study was aimed at predicting the number of patients that were likely to visit the emergency and the quantity of consumables that would be needed for management of fever cases in the emergency. The accuracy of the forecasting method used was also measured by statistically comparing the forecast with actual footfall.

This was a retrospective record based study that was conducted in the medical emergency of a tertiary care teaching hospital in North India. The data regarding the monthly footfall of patients in the medical emergency was collected from the Medical Records Department and trends were analysed. The number of hemograms performed was obtained from the records of the emergency laboratory. The trends in the monthly tests were derived from this data and correlated with the number of patients that visited the emergency during the same time. The demand of consumables generated from the Medical Emergency during this period was obtained from the records of the stores department. The data was then entered in MS Excel and sorted. Forecasting techniques were applied to predict the number of fever cases that were expected to arrive at the medical emergency during a particular time period. Based on the predicted footfall, the number of consumables needed for managing these patients was calculated using linear programming.

The monthly average attendance was calculated using the following formula:

A_m= (C1_m + C2_m + C3_m)/3

Where,

A_m= Average attendance for the month m

C1_m = Actual monthly attendance for the month m in 1st year

C2_m = Actual monthly attendance for the month m in 2nd year

C3_m = Actual monthly attendance for the month m in 3rd year

The multiplicative seasonality was derived in the form of monthly indices using the following formula:

Monthly Index_m= A_m/A_o

Where,

Monthly Index_m= Monthly index for the month m

A_m= Average attendance for the month m

A_o= Overall average monthly attendance

The number of patients visiting the Emergency during any particular month in future was calculated using linear regression technique and applying the monthly indices to account for the seasonal variations. The following formula was used to predict the Emergency attendance during a month based on linear regression after de-seasonalizing the data:

y = a + b*t

Where,

y= predicted (dependent) variable, ie number of people visiting the emergency in a month

b= slope of the data line =

a = value of y when t = 0 which is given by the formula =

t= predictor time variable

After applying liner regression, the seasonal variations were accounted for by applying the monthly indices using the following formula:

ya_m= y* Monthly Index_m

Where,

ya_m= Monthly adjusted forecast for month m

y= predicted variable arrived through linear regression

Monthly Index_m= Monthly index for the month m

The data regarding average monthly consumption of various consumables was obtained from the Hospital Stores and the Medical Emergency Sub-store. The consumables were selected based on Pareto’s principle; 80% of the fever patients are managed in the emergency using 20% of the items available in the Stores inventory. Hence, the most common items used in management of majority of the patients, which included Ethylenediaminetetraacetic acid (EDTA) hemogram vials, injection paracetamol (PCM) 1 gm and disposable Syringe 5 cc, were considered in the study. The quantity of consumables required for managing fever patients in the emergency during any month was the dependent variable while the number of patients visiting the Emergency was the independent variable. Hence, the consumables were calculated using linear regression based on the predicted number of patients that would attend the emergency. The following formula was used to predict the resources required during a month, based on linear regression:

y_m= a + b*x_m

Where,

y_m = predicted (dependent) variable, ie quantity of consumables needed for management of patients in the month m

b= slope of the data line =

a= value of y when t=0 =

x_m= Emergency attendance predicted for the month m

The accuracy of the forecasting techniques used was determined by calculating the following parameters:

Mean Absolute Deviation (MAD) = ∑ǀActual - Forecastǀ/n

Mean Absolute Percentage Error (MAPE) = ∑ǀActual-Forecastǀ/ ∑ Actual

Tracking Signal = ∑ Errors/MAD

The actual and predicted average monthly footfall in the ED, number of hemograms, consumption of EDTA vials, 5cc syringes and injection PCM has been depicted in Table 1.

Table 1

Actual and predicted monthly figures
Parameter	Monthly average
Parameter	Predicted Value	Actual Value
ED Footfall*	12985	12919
Hemograms**	6322	6276
EDTA vials**	6394	6303
Syringe 5 cc**	20932	21208
Inj PCM**	1573	1614
*- Based on data over a period of 48 months
**- Based on data over a period of 18 months

The average monthly footfall predicted was 12985 as against 12919 which was the actual footfall observed during the study period. The month-wise comparison has been depicted in Fig. 1.

Figure 2 compares the predicted and actual number of hemograms done each month during the period of the study.

The average number of EDTA vials required in a month, based on the past data was observed to be 6047. During the peak season for fevers, the monthly consumption shall increase to nearly 8500, which is an increase of 33.33%. The forecast regarding the monthly consumption of EDTA vials indicated that more than 33% rise was expected between July and October each year. The actual consumption and the forecast regarding the requirement of EDTA vials has been depicted in the Fig. 3.

An average of 15469 disposable syringes of capacity 5 ml were consumed each month. This consumption varied between 7200 and 23400 which means during the peak season, the monthly demand increased by as much as 50%. The forecast indicated that during the peak season in Year 2019, the demand may be double that of the present monthly average. The actual consumption and the forecast regarding the requirement of Disposable Syringe 5cc has been depicted in the Fig. 4.

The average monthly consumption of Injection Paracetamol (PCM) was 1283. During the study, it was observed that in the peak season, at one instance, the demand increased by 200%. The forecast also indicated that due to seasonal variations in the number of fever cases, the demand may increase or decrease by as much as 100%. The actual consumption and the forecast regarding the requirement of Injection PCM has been depicted in Fig. 5.

These items were routinely indented by the emergency department and were provided by the hospital stores where the inventory of these items was maintained. The internal lead time was 2–3 days for these items as they were routinely indented and utilized for patient care. These items were readily available with the vendor and were regularly supplied to the hospital.

The following parameters were calculated to assess the accuracy of the forecasting method applied during the study.

The Mean Mean Absolute Deviation (MAD) was calculated to be 3981.22

Mean Absolute Percentage Error (MAPE) was 30.17%.

Tracking Signal varied between − 1.78 and + 0.86 (Fig. 6)

The monthly index for the footfall in ED varied between 0.88 and 1.17 with the minimum and maximum being for the months of December and September, respectively. September is the tail end of the monsoon season with great humidity but benign temperatures, when most tropical vectors and insects come out of their larval stages into adulthood. There is a steep rise in the incidence of vector borne diseases, especially Dengue, Malaria and Chikungunya. The monthly index was greater than 1 throughout the monsoon season (July to October) indicating that there is a seasonal variation, as expected.

Implications for the management of the stores to ensure continuous supply:

The number of Hemograms and the consumables required for the management of the increased number of fever cases during the peak season can also be calculated dynamically on a monthly basis to achieve a more accurate result. Since the internal lead time was low (2–3 days), the need for maintenance of inventory at the sub-store level (emergency department Stores) was minimal. Inventory in hand for a week may be sufficient and the indents should be placed every week considering the space constraint. At the hospital stores level, the supply orders should be placed 45 days in advance to cater to the substantial increase in monthly requirement of these items during the peak fever season. The predicted monthly consumption may help the managers in adequate planning of resources.

Application of forecasting techniques for emergency services:

Zeev Rotstein et al formulated a statistical model based on the emergency visits between 1992 and 1994 and concluded that in a setting that is so uncertain, their model could serve to streamline the staff and resource allocation in the emergency department. ² Just like our model, their model also yielded very similar results that were close to the actual footfall.

Yan Sun et al conducted a study in the ED of an acute care regional general hospital in Singapore between July 2005 and March 2008. They categorized patients visiting the emergency into 3 categories namely P1 (most acute), P2 (moderate) and P3 (least acute).³ During their study, the approximate daily ED attendance was 400 patients which was very similar to our hospital. Their model yielded a MAPE of 16.9%, 6.7%, 8.6% and 4.8% for P1, P2, P3 and overall patients, respectively. The MAPE calculated for our model was 28.38% which was higher. The authors also observed higher monthly attendances during the months of May to July which they attributed to outbreaks of dengue and influenza. A similar rise in monthly footfall in our emergency was also noted which was predominantly due to rise in vector-borne diseases.

Spencer S. Jones et al conducted a study to predict daily ED attendance in three hospitals where data was collected between 2005 and 2007. ⁴ The authors evaluated the use of various models for forecasting daily patient visits at each of the three hospitals. They compared the accuracy of these models with that of a benchmark forecasting method already available in literature. The benchmark model yielded an MAPE of 14.4%, 9.41% and 9.13% for the three hospitals, while MAPE of their models ranged between 13.89–14.35%, 8.91–9.04% and 8.54–9.06%, respectively. The MAPE for the model that we used for forecasting the ED attendance was 8.8%.

Multiple studies that have been conducted to predict ED visits have observed season variation similar to ours. Holly Batal et al observed a peak in patient visit in their acute care clinic between November and February. ⁵ A K Diehl et al in their study observed a rise in patient visits between May and August.⁶ Another study conducted by D R Holleman Jr et al to predict the daily visits using calendar and weather data and they also observed a seasonal variation with the emergency visits rising between November and February. ⁷

The forecasting was done based on historical data and analysing trends over a period of 48 months. Various parameters were calculated to assess the accuracy of the forecasting technique in an emergency department which witnesses seasonal variations in fever cases. The Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE) were calculated to be 3981.22 and 30.17%, respectively. The tracking signal varied between − 1.78 and + 0.86, the acceptable limits being between + and − 4. The tracking signal remained well within the acceptable limit, indicating that the forecasting technique applied has provided accurate results. Hence, it may be used in future to forecast the number of patients and accordingly the quantum of resources required for their management.

ED	Emergency Department
EDTA	Ethylenediaminetetraacetic acid
MAD	Mean Absolute Deviation
MAPE	Mean Absolute Percentage Error
PCM	Paracetamol

Ethics approval and consent to participate – No human subject/ sample was involved. The study was based on retrospective data regarding the total number of patients received in the emergency department and the consumption of various hospital supplies. The permission for obtaining the data was taken from the competent authority. All methods were carried out in accordance with relevant guidelines and regulations. No experiment was done on any patient or their sample. Since the study was based on the total number of patients and consumption of medical and surgical consumables and did not involve any patient information, no consent was needed.

The National Regulations do not require ethics committee approval since the work does not involve any human subjects and the study did not include any patient data.

The data was accessed after obtaining due permission from the Competent Authority viz. the Medical Superintendent in this case.

Consent for publication - Not applicable

Availability of data and materials - The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests - The authors declare that they have no competing interests.

Funding - The authors declare that they did not receive any funding for this research work.

Authors' contributions – NS conceptualized the study, collected, analyzed and interpreted the data regarding the footfall in ED and the consumption of various hospital supplies and was a major contributor in writing the manuscript. NM conceptualized the study and was a major contributor in writing the manuscript. AG analyzed and interpreted the data regarding the footfall in ED and the consumption of various hospital supplies and was a major contributor in writing the manuscript. All authors read and approved the final manuscript.

Acknowledgements - Not applicable

Nadowska A. Services Marketing in the Health Care Industry- Elekta in Sweden Agnieszka Nadowska.
Rotstein Z, Wilf-Miron R, Lavi B, Shahar A, Gabbay U, Noy S. The dynamics of patient visits to a public hospital ED: A statistical model. Am J Emerg Med. 1997;15(6):596–9. doi:10.1016/S0735-6757(97)90166-2.
Sun Y, Heng BH, Seow YT, Seow E. Forecasting daily attendances at an emergency department to aid resource planning. BMC Emerg Med. 2009;9. doi:10.1186/1471-227X-9-1.
Jones SS, Thomas A, Evans RS, Welch SJ, Haug PJ, Snow GL. Forecasting daily patient volumes in the emergency department. Acad Emerg Med. 2008;15(2):159–70. doi:10.1111/j.1553-2712.2007.00032.x.
Batal H, Tench J, McMillan S, Adams J, Mehler PS. Predicting patient visits to an urgent care clinic using calendar variables. Acad Emerg Med. 2001;8(1):48–53. doi:10.1111/j.1553-2712.2001.tb00550.x.
Diehl AK, Morris MD, Mannis SA. Use of calendar and weather data to predict walk-in attendance. South Med J. 1981 Jun;74(6):709 – 12. doi: 10.1097/00007611-198106000-00020. PMID: 7244751.
Holleman DR Jr, Bowling RL, Gathy C. Predicting daily visits to a walk-in clinic and emergency department using calendar and weather data. J Gen Intern Med. 1996 Apr;11(4):237-9. doi: 10.1007/BF02642481. PMID: 8744882.

No competing interests reported.

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Application of quantitative decision-making tools in planning for seasonal variations of fever cases reporting at the medical emergency of a tertiary care hospital in New Delhi

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Abstract

Background

Methods

Results

Conclusion

Figures

Background

Methods

Results

Discussion

Implications for the management of the stores to ensure continuous supply:

Application of forecasting techniques for emergency services:

Conclusion

LIST OF ABBREVIATIONS

Declarations

References

Additional Declarations

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