Eur Radiol (2015) 25:2898–2904 DOI 10.1007/s00330-015-3702-7
INTERVENTIONAL
Reconciling quality and cost: A case study in interventional radiology Li Zhang 1 & Sascha Domröse 2 & Andreas Mahnken 1
Received: 27 August 2014 / Revised: 16 January 2015 / Accepted: 3 March 2015 / Published online: 24 May 2015 # European Society of Radiology 2015
Abstract Objectives To provide a method to calculate delay cost and examine the relationship between quality and total cost. Methods The total cost including capacity, supply and delay cost for running an interventional radiology suite was calculated. The capacity cost, consisting of labour, lease and overhead costs, was derived based on expenses per unit time. The supply cost was calculated according to actual procedural material use. The delay cost and marginal delay cost derived from queueing models was calculated based on waiting times of inpatients for their procedures. Results Quality improvement increased patient safety and maintained the outcome. The average daily delay costs were reduced from 1275 € to 294 €, and marginal delay costs from approximately 2000 € to 500 €, respectively. The one-time annual cost saved from the transfer of surgical to radiological procedures was approximately 130,500 €. The yearly delay cost saved was approximately 150,000 €. With increased revenue of 10,000 € in project phase 2, the yearly total cost saved was approximately 290,000 €. Optimal daily capacity of 4.2 procedures was determined. Conclusions An approach for calculating delay cost toward optimal capacity allocation was presented. An overall quality improvement was achieved at reduced costs.
* Li Zhang [email protected] 1
Department of Diagnostic and Interventional Radiology, University Hospital Giessen and Marburg, Philipps University of Marburg, Baldinger Strasse 35033, Marburg, Germany
2
Division of Controlling, University Hospital Giessen and Marburg, Philipps University of Marburg, Baldinger Strasse 35033, Marburg, Germany
Key points • Improving quality in terms of safety, outcome, efficiency and timeliness reduces cost. • Mismatch of demand and capacity is detrimental to quality and cost. • Full system utilization with random demand results in long waiting periods and increased cost. Keywords Quality . Cost . Efficiency . Timeliness . Interventional radiology
Introduction Recently, hospitals in several countries have increasingly experienced the financial pressure of lump compensation based on diagnosis related groups (DRG). Cost reduction programmes by negotiating lower prices for materials, firing vulnerable staff, budget cuts by intuition or across-the-board budget cuts have been attempted for financial survival of hospitals [1–3]. Without understanding the relationship between quality of care and cost and without regard to the treatment outcomes achieved, such cost reduction is dangerous and self-defeating, leading to false ‘savings’ [4] and deterioration in quality of care. The challenge currently faced by the healthcare industry revolves around how to maintain or improve the quality of care and simultaneously lower the cost. In this sense, quality and cost obviously become the two most important parameters in healthcare management. The quality of care encompasses safety, effectiveness, patient-centeredness, timeliness, efficiency and equality [5]. Any effort that leads to improvement of one or more of these quality dimensions is regarded as an overall improvement of quality. In recent years, there have been extensive studies on the improvement of quality of care in different areas [6–12].
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While the need for improvement is generally agreed among stakeholders, the question is open whether better quality of care is only possible at increasing resources and costs [13] or whether efforts at improving efficiency come at the expense of patient care and quality [14]. To answer these questions, correct understanding and measurement of the different dimensions of quality of care and cost are crucial. The measurement of quality dimensions, such as outcome, efficiency and timeliness [15–17], and the direct cost involved in patient care including labour cost, depreciation of equipment, supplies or other operating expenses can be easily performed [2, 4]. Since diagnostic and treatment delays are characteristic in the healthcare environment and these delays often require extra resource uses, for example for inpatient care, it is necessary to calculate the cost of delay as well. This is relevant for the measurement of the total cost including both direct costs and delay costs. Without this knowledge it is difficult to relate quality to cost. There have been numerous studies regarding costs [1, 18–20]. There is currently, however, no literature dealing with the calculation of delay costs in health care. Using interventional radiology (IR) procedures, especially placement of vascular devices as an example, we present the results of quality improvement and provide an approach to calculate delay costs for random healthcare processes. The goal is to elucidate the relationship between quality and total cost.
Materials and methods One of the IR suites in a large academic medical centre is exclusively used for central venous access management and percutaneous gastrostomy. On workdays a daily uptime of 5 hours is allocated. The patient population is made up of inpatients (61 %) and outpatients (39 %). Some of these procedures, especially venous access ports, are also implanted in the operation room (OR) by a surgical team of the same hospital. A Lean Six Sigma (LSS) quality improvement project was carried out for improving efficiency and reducing delays, and the results are reported separately (Improving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). LSS is a managerial concept [12] that aims at eliminating different kinds of wastes such as delay or waiting, reworking and examination overuse that usually exist in hospitals and have no value to patients. According to the LSS system, the above-mentioned project was divided into phase 1 and phase 2. In phase 1, the need for a referring physician or patient was evaluated and set as the improvement goal. In addition, thorough measurements of IR procedures including workflow, timing and resource use were undertaken. Analysis was then carried out to study the root causes of different wastes. Subsequently, improvement measures were designed and implemented. In phase 2, the results of
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improvement were monitored. The daily demand rate for IR procedures was 3.06 in phase 1: Daily demand and throughput of procedures have been determined from RIS data. ANOVA demonstrated no statistical difference in the monthly demand between two project phases (p=0.42). The daily demand follows a Poisson distribution (p=0.10) with a Poisson mean of 3.06 procedures per day. The quality of care in this study was measured by safety, outcome, efficiency and timeliness. Safety and outcome were measured by adverse events or complication rates, efficiency by the cycle time of procedures, and timeliness by the expected delay time. A delay occurs if the requested procedure cannot be performed because of capacity shortage. In this regard, any improvement in safety, outcome, efficiency and delay time leads to a higher quality of care. From the perspective of the hospital, the total cost for running the IR suite can be divided into capacity costs, supply costs and delay costs. The capacity costs are the costs of maintaining the ability to provide interventional procedures. They include labour costs for staff directly involved in the procedures such as radiologists, technologists and support staff; the lease cost for allocating the room;, and the hospital overhead cost. The average labour expenses per time unit were calculated for each profession by dividing the total labour expenses by the number of units of time and the number of full-time equivalents. The cost per minute for radiologists, technologists or support staff was derived accordingly. An overall hourly labour cost including all professions involved was calculated. Although a radiologist was not continuously present on site during the IR suite uptime, other tasks related to the interventional procedures like obtaining informed consent or reporting have to be processed outside the IR suite. The supply cost was related to materials required for individual procedures, such as catheters, contrast material, surgical instruments and medication. The supply costs for each of the different types of procedure were calculated. The total supply cost equals the accumulation of different supply costs of different procedure types multiplied by their respective numbers. An average supply cost for any procedure is thus obtained by dividing total supply cost by the total number of all procedures. The hospital overhead cost includes all other costs attributed to radiology by the hospital. They are expenses for administration, maintenance, office supplies and others. The hourly hospital overhead costs for the IR suite are arrived at by dividing the total overhead cost by the number of working places per unit of time. The procedures are planned in scheduling slots. The cost of each scheduled time slot is the sum of the labour cost for one procedure, the proportional room lease and overhead costs. The daily capacity cost is the sum of the average labour cost, hospital overhead cost per hour and the daily average lease. The daily supply cost is the average supply cost per procedure multiplied by the number of throughputs. The throughputs were 3.22 and 3.55 in project phases 1
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and 2, respectively (BImproving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). The daily capacity and supply costs equal the sum of the daily capacity cost and daily supply cost. The average unit cost per procedure was calculated by dividing the average daily capacity and supply costs by the number of throughputs. The actual average unit cost per procedure was calculated to be the supply cost per procedure plus timely proportional labour cost and hospital overhead cost. The delay cost refers to the cost of waiting. It is assumed that such delay prolongs the length of hospital stay and thus increases costs. According to the German DRG payment scheme, the median infrastructure cost alone for one regular inpatient day amounts to approximately 108 € without any medical coverage [21]. For convenience, by assuming 100 € for covering expenses for each extra hospital day as a lower bound, the delay cost was calculated (Appendix 1) using a daily demand rate of 3.06 procedures (BImproving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). The revenues of implantation or removal of implantable venous access ports (port) were known. The revenues of percutaneous gastrostomy, peripherally inserted central catheter (PICC) and dialysis catheter were assumed to be identical to that of port implantation. The revenue of port revision was assumed to be equal to that of port removal. The average revenue of any one procedure was calculated by the total revenue divided by the total number of all procedures. The yearly opening days of the IR suite were set to be 250 days.
Results Improvement in quality metrics The following quality improvements have been achieved and reported (BImproving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). The active postoperative monitoring implemented in phase 2 increased patient safety. The medical outcome was maintained. The cycle time was decreased from 75 to 53 minutes, an increase of about 29 % in efficiency. The expected length of delay for a procedure decreased from 6.4 to 2.1 days, a decrease of 67 %. Capacity and supply cost, and delay cost The average hourly labour cost including one radiologist and one technologist in project phase 1 and project phase 2 with an additional support staff member are listed in Table 1.
Eur Radiol (2015) 25:2898–2904 Table 1
Calculation of capacity and supply, and delay cost Phase 1
Phase 2
78
81
Capacity and supply cost Average labour cost (€) / hour Average supply cost (€) /procedure Lease cost of IR suite (€) / hour Hospital overhead (€) /hour Average revenue (€) /procedure Average capacity and supply costs (€) /day* Average unit cost (€) /procedure Actual average unit cost /procedure (€) Cost (€) / time slot Delay cost Average daily delay cost (€) /day
224 2 39.2 365 1,326
1,414
412 426
398 360
201
136
1,275
294
Comparison of surgical and radiological costs Radiological capacity cost (€) /hour
119
122
Surgical capacity cost (€) /hour Radiological capacity cost (€) /procedure Surgical capacity cost (€) /procedure
900 198 450
134
*
The uptime for 1 day equals 5 h
Additional relevant capacity and supply costs were calculated and also listed in Table 1. The average costs per day resulting from delay in phases 1 and 2 were calculated (Table 1) as described previously. The difference in their mean daily delay cost savings was 981 € (−77 %). By multiplying 250 working days and an inpatient proportion of 61 %, yearly savings of nearly 150,000 € from project phase 1 to phase 2 were calculated. The relationship between capacity utilization and different costs is illustrated in Fig. 1 for project phase 1, where the delay cost first increases linearly with increasing utilization level from 0 % to about 75 %. From a 75–100 % utilization level, the delay cost skyrockets exponentially to very high values. There is apparently a trade-off between capacity and supply costs and delay cost. With increasing utilization toward 100 %, the delay cost increases, while the capacity and supply costs decrease. The optimal daily total cost comprised of daily capacity, supply costs and delay cost is at the minimum of the total cost that equals about 837 €, corresponding to a utilization level of 73 % (Fig. 1). In project phase 1, however, the demand rate of 3.06 in relation to the actual throughput of 3.22 representing the actual total capacity corresponds to a utilization level of about 95 %. At this level, the current daily total cost is about 1871 € for the hospital as shown in Fig. 1, which is more than twice the optimal daily total cost. If the demand rate of 3.06 as measured in phase 1 were to represent a utilization level of 73 %, i.e., constitutes 73 % of the total capacity available, an optimal daily total capacity of 4.2 procedures is
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Fig. 1 Optimal daily capacity and optimal total cost derived from capacity, supply and delay costs in project phase 1 with a daily demand rate of 3.06 procedures, showing a trade-off between capacity and supply costs and delay cost. Capacity and supply costs decrease with increasing capacity utilization. The delay cost increases exponentially with capacity utilization, especially at the utilization level, from about 73 % to 100 %. The total cost decreases first at a low utilization level, reaches a minimum at about the capacity utilization level of 73 % and increases further exponentially with increasing utilization level. The optimal daily capacity in this calculation is determined by the lowest total cost, i.e. the optimal daily total cost. It follows that the daily demand should not
exceed 73 % of the available capacity. Once the demand is known, an optimal daily capacity can be calculated. For example, the daily demand is measured to be 3.06 procedures; since it should be equal to 73 % of the optimal daily capacity, it follows that the optimal daily capacity would be then 4.2 procedures. However, the current daily capacity is only about 3.22 procedures as measured by throughput time. This means a 95 % capacity utilization. At this utilization level, the exponentially increased delay cost far outweighs the decrease in capacity and supply cost altogether as shown in figure. The skyrocketed delay cost at high capacity utilization contributes to a very high daily total cost
needed to achieve the minimum total cost. Capacity levels, especially lower than 4.2 procedures per day, in other words capacity utilization higher than 73 %, are thus accompanied by very high delay costs.
the calculation, the daily demand rate λ=3.06 was used. Cycle times were used to calculate the reciprocal of service time μ for phases 1 and 2. The marginal delay cost was estimated based on two different queueing models M/G/1 and M/M/1 in order to obtain an indication of the orders of magnitude that may be involved. The external marginal delay cost is significantly higher than the internal marginal delay cost. While the cost of the external part is about fourfold of the internal part at a cycle time of 75 min, it reduces to about twofold with a cycle time of 53 min. The marginal delay cost estimated by two queueing models, though at the same order of magnitude, differ from each other. In phase 1, the marginal delay cost with model M/M/1 is higher than with model M/G/1. In phase 2 it is the opposite. It is generally noted that the D/D/1 model determines the lower bound and M/M/1 the upper bound of delays [22]. The magnitude of delay given by model M/G/1 depends on the magnitude of coefficient of variation (CV), which is a measure of the dispersion of cycle times. If a CV of 9.3 for phase 2 is assumed, a marginal delay cost of 274 € is calculated, which is lower than the 360 € calculated using the model M/M/1, as shown in Table 2. At a constant demand rate, the marginal delay cost decreases dramatically from four- to three-digit numbers, with a moderate decrease of cycle time (−30 %) from phase 1 to phase 2.
Marginal delay cost Marginal delay cost per procedure was estimated (Table 2) based on the approach described earlier (Appendix 1). For
Table 2 Estimates of marginal delay costs for one additional intervention in the queue Cycle time CV (min)
Congestion Marginal delay cost (€) M/G/1 M/M/1
Phase 1
75
9.3
95 %
Phase 2
53
17.0
86 %
CV coefficient of variation
Internal External Total Internal External Total
409 1,733 2,142 165 359 524
561 2,378 2,939 114 247 360
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Saving from transfer from surgical to radiological procedure The number of venous access and gastrostomy procedures carried out in radiology increased from 523 to 832 between 2012 and 2013, an increase of 59 %. Since the total patient populations treated in the hospital in these 2 years remained constant and there was no organizational change in the referring clinics regarding their demand behaviour, the difference in the numbers of procedures can be approximately attributed to the transfer from surgery to radiology, because the increase of gastrostomy procedures contributes only about 5 % to the increase of all procedures. The hourly capacity costs of the IR room including hourly labour cost and hospital overhead cost in phases 1 and 2, respectively, were calculated (Table 1). As a comparison, the hourly capacity cost of the OR room is listed as well. Based on the average throughput time of 30 min for one surgical procedure, 100 min in phase 1 and 66 min in phase 2 for one radiological procedure, the average capacity costs of the surgical and radiological procedures were calculated (Table 1). It is clear that the surgical procedure is more than twice as expensive as the radiological procedure. Assuming the costs of a surgical procedure are twice the costs of the radiological procedure cost of 426 €, the savings resulting from the transfer from surgery to radiology amount to 131, 500 € per year. Savings from efficiency improvement The increase in average number of daily performed procedures from 3.22 to 3.55 increases the yearly revenue by about 30,000 €. There is simultaneously a reduction in delay cost of nearly 150,000 €. Subtracting the increased supply cost needed in phase 2 of about 20,000 €, there is an annual net saving of about 160,000 € from the quality improvement initiative.
Discussion Quality of care is one unique area where the divergent interests of stakeholders may converge [4]. It has been realized that better quality of care often goes hand in hand with lower total care costs [2, 14]. However, a widespread and persistent perception exists which claims that high quality equals high costs [13]. This is partly because there is a complete lack of understanding of how much it costs to deliver patient care [2]. An accurate measurement of total cost as made in this study is still a challenge for many healthcare institutions. In addition, numerous quality improvement studies provide no data on financial outcome [12, 23–25]. The micromanagement of costs at the individual organizational level [2] as observed in most hospitals is not helpful at maintaining quality of care or reducing total costs. This was
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observed in this study as well. It is well known that a central venous port system performed surgically or radiologically has a similar medical outcome [26]. Likewise, the cost of surgical procedures is known to be much higher than the costs of radiological procedures, since the former requires many more resources. Our calculations agree with the previous study, which showed that it is about twice as costly to perform the procedure surgically than radiologically [27]. Although there is no justification for using scarcer, more expensive OR rooms for achieving the same medical outcome, such financial inefficiency and waste exists if costs are managed at the individual organizational level without taking the costs along the entire clinical pathway into account. In addition, extra demand was artificially generated to compete for OR rooms, which in turn generates further delay costs. By shifting procedures from the OR room to an IR suite, substantial cost savings were realized, showing again that quality can be maintained or improved while reducing costs. The delays increase patient suffering and anxiety and are relevant to the length of hospital stay for inpatients. Although there is no intrinsic reason why delays in health care should be more tolerable than those in air travel [14], they are widely accepted as a characteristic of the system. Reducing delay or increasing timeliness has become the focus of many studies [28]. To date there has been no publication in health care that deals with savings from delay cost through quality improvement. It is therefore impossible to link cost to quality improvement. The calculation of delay cost is admittedly challenging because of the random distribution of the demand rate and the general distribution of service time. Queueing theory from operations management has to be applied to estimate delay cost, and the knowledge of this theory is usually absent in hospitals. This explains why there is currently little published data, and in practice the impact of delay on cost structure is rarely evaluated. As shown in this study, savings from the delay cost (150,000 €) weigh even more than the extra revenue generated by the increase in productivity (30,000 €). Compared to the total yearly revenue of about 300,000 € acquired by this IR suite, the delay cost savings of 150,000 € were indeed substantial. But this significant amount, although somehow implied in the length of hospital stay, was hidden and has not been financially quantified in most cases. This highlights the inevitable need to incorporate delay costs in cost calculation. The reason for the high delay cost originates from the mismatch between demand and capacity. Often, the 1:1 match between demand and capacity is intuitively used for our current environment. This is applicable in a deterministic setting where both daily demand rate and service time of each procedure can be predicted. In such a setting, full capacity utilization is desirably pursued to reach maximum efficiency. However, our current environment represents not a deterministic
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but rather a random setting where daily demand for procedures and service time cannot be predicted. In this setting, full utilization of a system will counterintuitively increase the total cost and generate long waiting lists, negatively impacting both quality of care and cost. Here it is important to determine the proper level of capacity utilization and to match capacity and demand appropriately. In other words, the capacity allocation at a given demand rate should be determined by the optimal total cost as demonstrated in this study. As indicated previously in Fig. 1, the lowest total cost is at about 73 % of the capacity utilization that corresponds to an expected optimal daily capacity of 4.2 procedures. A deviation from 73 % of capacity utilization in this case, especially towards 100 % utilization, will cause severe waiting periods, excessive procedure delays and increased costs with regard to inpatients. After quality improvement, the daily potential capacity available based on the improved throughput time is 4.5 procedures. The improvement effort consequently enabled the match between demand and capacity. The marginal delay cost has been used to determine an equilibrium congestion toll in transport industries [29]. In a congested system each additional user pays for all the additional costs that this user imposes on all other users [30, 31]. Thereby additional costs are externalized to the parties causing it [29]. Understanding of the impact of the marginal delay cost is essential for referring physicians, radiology staff and the hospital management. Firstly, seriously congested systems should be avoided by management. Secondly, if unavoidable, the extra costs should be determined and externalized. The excessive marginal delay cost as shown in this study in a 95 % congested system (Table 2) helps with decision making. On the other hand, health systems are different from transport industries. In health care the capacity can be briefly built up, for example in the form of overtime, to accommodate the demand and to avoid a high delay cost or a high marginal delay cost. The current study was performed in the specific area of IR. Nonetheless, the method and the implication of the results are applicable to the majority of other healthcare processes that have random demand and variable service time. This is particularly relevant in inpatient-related processes such as capacity allocation for OR rooms, diagnostic tests [15] and bed deployment in wards. This study suffers several limitations. Firstly, not all delays due to waiting times for an IR procedure will induce delay costs in the sense of more hospital stays. Nevertheless, any delay in service provision generally induces more process costs and lower care quality. Secondly, revenues are likely to be somewhat overestimated because it was assumed that the revenues of some analysed procedures are equivalent. In conclusion, this study provides an approach for calculating delay cost and marginal delay cost for random
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healthcare processes. It is now possible to examine the relationship between quality and cost. We show that while improving or maintaining safety and medical outcome, an increase in efficiency and timeliness through an LSS initiative improved the quality of care and reduced the total cost. Acknowledgements The scientific guarantor of this publication is Li Zhang. The authors of this manuscript declare no relationships with any companies whose products or services may be related to the subject matter of the article. The authors state that this work has not received any funding. One of the authors has significant statistical expertise. Institutional Review Board approval was not required. Written informed consent was waived by the Institutional Review Board. No study subjects or cohorts have been previously reported. Methodology: performed at one institution.
Appendix The delay cost can be calculated by C ¼ cλW q ; where C is the total delay cost, c delay cost per day per patient, λ the demand rate and Wq the expected waiting time in the queue. In a highly congested facility where congestion arises because the capacity available cannot satisfy the demand and a queue builds up, any additional (marginal) request incurs both costs to itself and costs to all other patients and to the facility [21, 22]. One additional procedure accumulated in the beginning or middle of a scheduling queue will impose incremental delay on all other procedures waiting to be processed in the queue. Such incremental delay is defined as marginal delay [22, 23]. Marginal delay cost (MC) as imposed by an additional request is calculated by MC ¼
dC dW q ¼ cW q þ cλ ; dλ dλ
where cWq is the internal cost of marginal delay experienced by q that additional procedure itself and cλ dW dλ is the external cost of marginal delay experienced by all other procedure requests caused by that additional procedure. Wq can be calculated using a queueing model. Kendall’s notation of A/S/c is used for describing the applied queueing models, where A describes arrival process, S denotes service time distribution and c is the number of servers. M/M/1 means random arrivals to queue, exponentially distributed service time and one server. M/G/1 means random arrivals to queue, general distribution of service time and one server. By adapting the M/M/1 model, Wq ¼
λ ; μðμ λÞ
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and dW q 1 ¼ ; dλ ðμ λÞ2 where μ is the reciprocal of the service time. The equivalent of service time is the cycle time. By adapting the M/G/1 model, λ E 2 ½S þ σ2S ; Wq ¼ 2ð1−ρÞ and dW q E2 ½S þ σ2S λ E2 ½S þ σ2S 1 ¼ þ ; dλ 2ð 1 ρ Þ 2ð 1 ρ Þ 2 μ where E(S) is the service time, σs is the standard deviation of E(S) and ρ=λ/μ the utilization level.
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INTERVENTIONAL
Reconciling quality and cost: A case study in interventional radiology Li Zhang 1 & Sascha Domröse 2 & Andreas Mahnken 1
Received: 27 August 2014 / Revised: 16 January 2015 / Accepted: 3 March 2015 / Published online: 24 May 2015 # European Society of Radiology 2015
Abstract Objectives To provide a method to calculate delay cost and examine the relationship between quality and total cost. Methods The total cost including capacity, supply and delay cost for running an interventional radiology suite was calculated. The capacity cost, consisting of labour, lease and overhead costs, was derived based on expenses per unit time. The supply cost was calculated according to actual procedural material use. The delay cost and marginal delay cost derived from queueing models was calculated based on waiting times of inpatients for their procedures. Results Quality improvement increased patient safety and maintained the outcome. The average daily delay costs were reduced from 1275 € to 294 €, and marginal delay costs from approximately 2000 € to 500 €, respectively. The one-time annual cost saved from the transfer of surgical to radiological procedures was approximately 130,500 €. The yearly delay cost saved was approximately 150,000 €. With increased revenue of 10,000 € in project phase 2, the yearly total cost saved was approximately 290,000 €. Optimal daily capacity of 4.2 procedures was determined. Conclusions An approach for calculating delay cost toward optimal capacity allocation was presented. An overall quality improvement was achieved at reduced costs.
* Li Zhang [email protected] 1
Department of Diagnostic and Interventional Radiology, University Hospital Giessen and Marburg, Philipps University of Marburg, Baldinger Strasse 35033, Marburg, Germany
2
Division of Controlling, University Hospital Giessen and Marburg, Philipps University of Marburg, Baldinger Strasse 35033, Marburg, Germany
Key points • Improving quality in terms of safety, outcome, efficiency and timeliness reduces cost. • Mismatch of demand and capacity is detrimental to quality and cost. • Full system utilization with random demand results in long waiting periods and increased cost. Keywords Quality . Cost . Efficiency . Timeliness . Interventional radiology
Introduction Recently, hospitals in several countries have increasingly experienced the financial pressure of lump compensation based on diagnosis related groups (DRG). Cost reduction programmes by negotiating lower prices for materials, firing vulnerable staff, budget cuts by intuition or across-the-board budget cuts have been attempted for financial survival of hospitals [1–3]. Without understanding the relationship between quality of care and cost and without regard to the treatment outcomes achieved, such cost reduction is dangerous and self-defeating, leading to false ‘savings’ [4] and deterioration in quality of care. The challenge currently faced by the healthcare industry revolves around how to maintain or improve the quality of care and simultaneously lower the cost. In this sense, quality and cost obviously become the two most important parameters in healthcare management. The quality of care encompasses safety, effectiveness, patient-centeredness, timeliness, efficiency and equality [5]. Any effort that leads to improvement of one or more of these quality dimensions is regarded as an overall improvement of quality. In recent years, there have been extensive studies on the improvement of quality of care in different areas [6–12].
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While the need for improvement is generally agreed among stakeholders, the question is open whether better quality of care is only possible at increasing resources and costs [13] or whether efforts at improving efficiency come at the expense of patient care and quality [14]. To answer these questions, correct understanding and measurement of the different dimensions of quality of care and cost are crucial. The measurement of quality dimensions, such as outcome, efficiency and timeliness [15–17], and the direct cost involved in patient care including labour cost, depreciation of equipment, supplies or other operating expenses can be easily performed [2, 4]. Since diagnostic and treatment delays are characteristic in the healthcare environment and these delays often require extra resource uses, for example for inpatient care, it is necessary to calculate the cost of delay as well. This is relevant for the measurement of the total cost including both direct costs and delay costs. Without this knowledge it is difficult to relate quality to cost. There have been numerous studies regarding costs [1, 18–20]. There is currently, however, no literature dealing with the calculation of delay costs in health care. Using interventional radiology (IR) procedures, especially placement of vascular devices as an example, we present the results of quality improvement and provide an approach to calculate delay costs for random healthcare processes. The goal is to elucidate the relationship between quality and total cost.
Materials and methods One of the IR suites in a large academic medical centre is exclusively used for central venous access management and percutaneous gastrostomy. On workdays a daily uptime of 5 hours is allocated. The patient population is made up of inpatients (61 %) and outpatients (39 %). Some of these procedures, especially venous access ports, are also implanted in the operation room (OR) by a surgical team of the same hospital. A Lean Six Sigma (LSS) quality improvement project was carried out for improving efficiency and reducing delays, and the results are reported separately (Improving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). LSS is a managerial concept [12] that aims at eliminating different kinds of wastes such as delay or waiting, reworking and examination overuse that usually exist in hospitals and have no value to patients. According to the LSS system, the above-mentioned project was divided into phase 1 and phase 2. In phase 1, the need for a referring physician or patient was evaluated and set as the improvement goal. In addition, thorough measurements of IR procedures including workflow, timing and resource use were undertaken. Analysis was then carried out to study the root causes of different wastes. Subsequently, improvement measures were designed and implemented. In phase 2, the results of
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improvement were monitored. The daily demand rate for IR procedures was 3.06 in phase 1: Daily demand and throughput of procedures have been determined from RIS data. ANOVA demonstrated no statistical difference in the monthly demand between two project phases (p=0.42). The daily demand follows a Poisson distribution (p=0.10) with a Poisson mean of 3.06 procedures per day. The quality of care in this study was measured by safety, outcome, efficiency and timeliness. Safety and outcome were measured by adverse events or complication rates, efficiency by the cycle time of procedures, and timeliness by the expected delay time. A delay occurs if the requested procedure cannot be performed because of capacity shortage. In this regard, any improvement in safety, outcome, efficiency and delay time leads to a higher quality of care. From the perspective of the hospital, the total cost for running the IR suite can be divided into capacity costs, supply costs and delay costs. The capacity costs are the costs of maintaining the ability to provide interventional procedures. They include labour costs for staff directly involved in the procedures such as radiologists, technologists and support staff; the lease cost for allocating the room;, and the hospital overhead cost. The average labour expenses per time unit were calculated for each profession by dividing the total labour expenses by the number of units of time and the number of full-time equivalents. The cost per minute for radiologists, technologists or support staff was derived accordingly. An overall hourly labour cost including all professions involved was calculated. Although a radiologist was not continuously present on site during the IR suite uptime, other tasks related to the interventional procedures like obtaining informed consent or reporting have to be processed outside the IR suite. The supply cost was related to materials required for individual procedures, such as catheters, contrast material, surgical instruments and medication. The supply costs for each of the different types of procedure were calculated. The total supply cost equals the accumulation of different supply costs of different procedure types multiplied by their respective numbers. An average supply cost for any procedure is thus obtained by dividing total supply cost by the total number of all procedures. The hospital overhead cost includes all other costs attributed to radiology by the hospital. They are expenses for administration, maintenance, office supplies and others. The hourly hospital overhead costs for the IR suite are arrived at by dividing the total overhead cost by the number of working places per unit of time. The procedures are planned in scheduling slots. The cost of each scheduled time slot is the sum of the labour cost for one procedure, the proportional room lease and overhead costs. The daily capacity cost is the sum of the average labour cost, hospital overhead cost per hour and the daily average lease. The daily supply cost is the average supply cost per procedure multiplied by the number of throughputs. The throughputs were 3.22 and 3.55 in project phases 1
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and 2, respectively (BImproving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). The daily capacity and supply costs equal the sum of the daily capacity cost and daily supply cost. The average unit cost per procedure was calculated by dividing the average daily capacity and supply costs by the number of throughputs. The actual average unit cost per procedure was calculated to be the supply cost per procedure plus timely proportional labour cost and hospital overhead cost. The delay cost refers to the cost of waiting. It is assumed that such delay prolongs the length of hospital stay and thus increases costs. According to the German DRG payment scheme, the median infrastructure cost alone for one regular inpatient day amounts to approximately 108 € without any medical coverage [21]. For convenience, by assuming 100 € for covering expenses for each extra hospital day as a lower bound, the delay cost was calculated (Appendix 1) using a daily demand rate of 3.06 procedures (BImproving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). The revenues of implantation or removal of implantable venous access ports (port) were known. The revenues of percutaneous gastrostomy, peripherally inserted central catheter (PICC) and dialysis catheter were assumed to be identical to that of port implantation. The revenue of port revision was assumed to be equal to that of port removal. The average revenue of any one procedure was calculated by the total revenue divided by the total number of all procedures. The yearly opening days of the IR suite were set to be 250 days.
Results Improvement in quality metrics The following quality improvements have been achieved and reported (BImproving efficiency of interventional service by Lean Six Sigma. Zhang L, Runzheimer K et al. accepted by Journal of the American College of Radiology). The active postoperative monitoring implemented in phase 2 increased patient safety. The medical outcome was maintained. The cycle time was decreased from 75 to 53 minutes, an increase of about 29 % in efficiency. The expected length of delay for a procedure decreased from 6.4 to 2.1 days, a decrease of 67 %. Capacity and supply cost, and delay cost The average hourly labour cost including one radiologist and one technologist in project phase 1 and project phase 2 with an additional support staff member are listed in Table 1.
Eur Radiol (2015) 25:2898–2904 Table 1
Calculation of capacity and supply, and delay cost Phase 1
Phase 2
78
81
Capacity and supply cost Average labour cost (€) / hour Average supply cost (€) /procedure Lease cost of IR suite (€) / hour Hospital overhead (€) /hour Average revenue (€) /procedure Average capacity and supply costs (€) /day* Average unit cost (€) /procedure Actual average unit cost /procedure (€) Cost (€) / time slot Delay cost Average daily delay cost (€) /day
224 2 39.2 365 1,326
1,414
412 426
398 360
201
136
1,275
294
Comparison of surgical and radiological costs Radiological capacity cost (€) /hour
119
122
Surgical capacity cost (€) /hour Radiological capacity cost (€) /procedure Surgical capacity cost (€) /procedure
900 198 450
134
*
The uptime for 1 day equals 5 h
Additional relevant capacity and supply costs were calculated and also listed in Table 1. The average costs per day resulting from delay in phases 1 and 2 were calculated (Table 1) as described previously. The difference in their mean daily delay cost savings was 981 € (−77 %). By multiplying 250 working days and an inpatient proportion of 61 %, yearly savings of nearly 150,000 € from project phase 1 to phase 2 were calculated. The relationship between capacity utilization and different costs is illustrated in Fig. 1 for project phase 1, where the delay cost first increases linearly with increasing utilization level from 0 % to about 75 %. From a 75–100 % utilization level, the delay cost skyrockets exponentially to very high values. There is apparently a trade-off between capacity and supply costs and delay cost. With increasing utilization toward 100 %, the delay cost increases, while the capacity and supply costs decrease. The optimal daily total cost comprised of daily capacity, supply costs and delay cost is at the minimum of the total cost that equals about 837 €, corresponding to a utilization level of 73 % (Fig. 1). In project phase 1, however, the demand rate of 3.06 in relation to the actual throughput of 3.22 representing the actual total capacity corresponds to a utilization level of about 95 %. At this level, the current daily total cost is about 1871 € for the hospital as shown in Fig. 1, which is more than twice the optimal daily total cost. If the demand rate of 3.06 as measured in phase 1 were to represent a utilization level of 73 %, i.e., constitutes 73 % of the total capacity available, an optimal daily total capacity of 4.2 procedures is
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Fig. 1 Optimal daily capacity and optimal total cost derived from capacity, supply and delay costs in project phase 1 with a daily demand rate of 3.06 procedures, showing a trade-off between capacity and supply costs and delay cost. Capacity and supply costs decrease with increasing capacity utilization. The delay cost increases exponentially with capacity utilization, especially at the utilization level, from about 73 % to 100 %. The total cost decreases first at a low utilization level, reaches a minimum at about the capacity utilization level of 73 % and increases further exponentially with increasing utilization level. The optimal daily capacity in this calculation is determined by the lowest total cost, i.e. the optimal daily total cost. It follows that the daily demand should not
exceed 73 % of the available capacity. Once the demand is known, an optimal daily capacity can be calculated. For example, the daily demand is measured to be 3.06 procedures; since it should be equal to 73 % of the optimal daily capacity, it follows that the optimal daily capacity would be then 4.2 procedures. However, the current daily capacity is only about 3.22 procedures as measured by throughput time. This means a 95 % capacity utilization. At this utilization level, the exponentially increased delay cost far outweighs the decrease in capacity and supply cost altogether as shown in figure. The skyrocketed delay cost at high capacity utilization contributes to a very high daily total cost
needed to achieve the minimum total cost. Capacity levels, especially lower than 4.2 procedures per day, in other words capacity utilization higher than 73 %, are thus accompanied by very high delay costs.
the calculation, the daily demand rate λ=3.06 was used. Cycle times were used to calculate the reciprocal of service time μ for phases 1 and 2. The marginal delay cost was estimated based on two different queueing models M/G/1 and M/M/1 in order to obtain an indication of the orders of magnitude that may be involved. The external marginal delay cost is significantly higher than the internal marginal delay cost. While the cost of the external part is about fourfold of the internal part at a cycle time of 75 min, it reduces to about twofold with a cycle time of 53 min. The marginal delay cost estimated by two queueing models, though at the same order of magnitude, differ from each other. In phase 1, the marginal delay cost with model M/M/1 is higher than with model M/G/1. In phase 2 it is the opposite. It is generally noted that the D/D/1 model determines the lower bound and M/M/1 the upper bound of delays [22]. The magnitude of delay given by model M/G/1 depends on the magnitude of coefficient of variation (CV), which is a measure of the dispersion of cycle times. If a CV of 9.3 for phase 2 is assumed, a marginal delay cost of 274 € is calculated, which is lower than the 360 € calculated using the model M/M/1, as shown in Table 2. At a constant demand rate, the marginal delay cost decreases dramatically from four- to three-digit numbers, with a moderate decrease of cycle time (−30 %) from phase 1 to phase 2.
Marginal delay cost Marginal delay cost per procedure was estimated (Table 2) based on the approach described earlier (Appendix 1). For
Table 2 Estimates of marginal delay costs for one additional intervention in the queue Cycle time CV (min)
Congestion Marginal delay cost (€) M/G/1 M/M/1
Phase 1
75
9.3
95 %
Phase 2
53
17.0
86 %
CV coefficient of variation
Internal External Total Internal External Total
409 1,733 2,142 165 359 524
561 2,378 2,939 114 247 360
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Saving from transfer from surgical to radiological procedure The number of venous access and gastrostomy procedures carried out in radiology increased from 523 to 832 between 2012 and 2013, an increase of 59 %. Since the total patient populations treated in the hospital in these 2 years remained constant and there was no organizational change in the referring clinics regarding their demand behaviour, the difference in the numbers of procedures can be approximately attributed to the transfer from surgery to radiology, because the increase of gastrostomy procedures contributes only about 5 % to the increase of all procedures. The hourly capacity costs of the IR room including hourly labour cost and hospital overhead cost in phases 1 and 2, respectively, were calculated (Table 1). As a comparison, the hourly capacity cost of the OR room is listed as well. Based on the average throughput time of 30 min for one surgical procedure, 100 min in phase 1 and 66 min in phase 2 for one radiological procedure, the average capacity costs of the surgical and radiological procedures were calculated (Table 1). It is clear that the surgical procedure is more than twice as expensive as the radiological procedure. Assuming the costs of a surgical procedure are twice the costs of the radiological procedure cost of 426 €, the savings resulting from the transfer from surgery to radiology amount to 131, 500 € per year. Savings from efficiency improvement The increase in average number of daily performed procedures from 3.22 to 3.55 increases the yearly revenue by about 30,000 €. There is simultaneously a reduction in delay cost of nearly 150,000 €. Subtracting the increased supply cost needed in phase 2 of about 20,000 €, there is an annual net saving of about 160,000 € from the quality improvement initiative.
Discussion Quality of care is one unique area where the divergent interests of stakeholders may converge [4]. It has been realized that better quality of care often goes hand in hand with lower total care costs [2, 14]. However, a widespread and persistent perception exists which claims that high quality equals high costs [13]. This is partly because there is a complete lack of understanding of how much it costs to deliver patient care [2]. An accurate measurement of total cost as made in this study is still a challenge for many healthcare institutions. In addition, numerous quality improvement studies provide no data on financial outcome [12, 23–25]. The micromanagement of costs at the individual organizational level [2] as observed in most hospitals is not helpful at maintaining quality of care or reducing total costs. This was
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observed in this study as well. It is well known that a central venous port system performed surgically or radiologically has a similar medical outcome [26]. Likewise, the cost of surgical procedures is known to be much higher than the costs of radiological procedures, since the former requires many more resources. Our calculations agree with the previous study, which showed that it is about twice as costly to perform the procedure surgically than radiologically [27]. Although there is no justification for using scarcer, more expensive OR rooms for achieving the same medical outcome, such financial inefficiency and waste exists if costs are managed at the individual organizational level without taking the costs along the entire clinical pathway into account. In addition, extra demand was artificially generated to compete for OR rooms, which in turn generates further delay costs. By shifting procedures from the OR room to an IR suite, substantial cost savings were realized, showing again that quality can be maintained or improved while reducing costs. The delays increase patient suffering and anxiety and are relevant to the length of hospital stay for inpatients. Although there is no intrinsic reason why delays in health care should be more tolerable than those in air travel [14], they are widely accepted as a characteristic of the system. Reducing delay or increasing timeliness has become the focus of many studies [28]. To date there has been no publication in health care that deals with savings from delay cost through quality improvement. It is therefore impossible to link cost to quality improvement. The calculation of delay cost is admittedly challenging because of the random distribution of the demand rate and the general distribution of service time. Queueing theory from operations management has to be applied to estimate delay cost, and the knowledge of this theory is usually absent in hospitals. This explains why there is currently little published data, and in practice the impact of delay on cost structure is rarely evaluated. As shown in this study, savings from the delay cost (150,000 €) weigh even more than the extra revenue generated by the increase in productivity (30,000 €). Compared to the total yearly revenue of about 300,000 € acquired by this IR suite, the delay cost savings of 150,000 € were indeed substantial. But this significant amount, although somehow implied in the length of hospital stay, was hidden and has not been financially quantified in most cases. This highlights the inevitable need to incorporate delay costs in cost calculation. The reason for the high delay cost originates from the mismatch between demand and capacity. Often, the 1:1 match between demand and capacity is intuitively used for our current environment. This is applicable in a deterministic setting where both daily demand rate and service time of each procedure can be predicted. In such a setting, full capacity utilization is desirably pursued to reach maximum efficiency. However, our current environment represents not a deterministic
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but rather a random setting where daily demand for procedures and service time cannot be predicted. In this setting, full utilization of a system will counterintuitively increase the total cost and generate long waiting lists, negatively impacting both quality of care and cost. Here it is important to determine the proper level of capacity utilization and to match capacity and demand appropriately. In other words, the capacity allocation at a given demand rate should be determined by the optimal total cost as demonstrated in this study. As indicated previously in Fig. 1, the lowest total cost is at about 73 % of the capacity utilization that corresponds to an expected optimal daily capacity of 4.2 procedures. A deviation from 73 % of capacity utilization in this case, especially towards 100 % utilization, will cause severe waiting periods, excessive procedure delays and increased costs with regard to inpatients. After quality improvement, the daily potential capacity available based on the improved throughput time is 4.5 procedures. The improvement effort consequently enabled the match between demand and capacity. The marginal delay cost has been used to determine an equilibrium congestion toll in transport industries [29]. In a congested system each additional user pays for all the additional costs that this user imposes on all other users [30, 31]. Thereby additional costs are externalized to the parties causing it [29]. Understanding of the impact of the marginal delay cost is essential for referring physicians, radiology staff and the hospital management. Firstly, seriously congested systems should be avoided by management. Secondly, if unavoidable, the extra costs should be determined and externalized. The excessive marginal delay cost as shown in this study in a 95 % congested system (Table 2) helps with decision making. On the other hand, health systems are different from transport industries. In health care the capacity can be briefly built up, for example in the form of overtime, to accommodate the demand and to avoid a high delay cost or a high marginal delay cost. The current study was performed in the specific area of IR. Nonetheless, the method and the implication of the results are applicable to the majority of other healthcare processes that have random demand and variable service time. This is particularly relevant in inpatient-related processes such as capacity allocation for OR rooms, diagnostic tests [15] and bed deployment in wards. This study suffers several limitations. Firstly, not all delays due to waiting times for an IR procedure will induce delay costs in the sense of more hospital stays. Nevertheless, any delay in service provision generally induces more process costs and lower care quality. Secondly, revenues are likely to be somewhat overestimated because it was assumed that the revenues of some analysed procedures are equivalent. In conclusion, this study provides an approach for calculating delay cost and marginal delay cost for random
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healthcare processes. It is now possible to examine the relationship between quality and cost. We show that while improving or maintaining safety and medical outcome, an increase in efficiency and timeliness through an LSS initiative improved the quality of care and reduced the total cost. Acknowledgements The scientific guarantor of this publication is Li Zhang. The authors of this manuscript declare no relationships with any companies whose products or services may be related to the subject matter of the article. The authors state that this work has not received any funding. One of the authors has significant statistical expertise. Institutional Review Board approval was not required. Written informed consent was waived by the Institutional Review Board. No study subjects or cohorts have been previously reported. Methodology: performed at one institution.
Appendix The delay cost can be calculated by C ¼ cλW q ; where C is the total delay cost, c delay cost per day per patient, λ the demand rate and Wq the expected waiting time in the queue. In a highly congested facility where congestion arises because the capacity available cannot satisfy the demand and a queue builds up, any additional (marginal) request incurs both costs to itself and costs to all other patients and to the facility [21, 22]. One additional procedure accumulated in the beginning or middle of a scheduling queue will impose incremental delay on all other procedures waiting to be processed in the queue. Such incremental delay is defined as marginal delay [22, 23]. Marginal delay cost (MC) as imposed by an additional request is calculated by MC ¼
dC dW q ¼ cW q þ cλ ; dλ dλ
where cWq is the internal cost of marginal delay experienced by q that additional procedure itself and cλ dW dλ is the external cost of marginal delay experienced by all other procedure requests caused by that additional procedure. Wq can be calculated using a queueing model. Kendall’s notation of A/S/c is used for describing the applied queueing models, where A describes arrival process, S denotes service time distribution and c is the number of servers. M/M/1 means random arrivals to queue, exponentially distributed service time and one server. M/G/1 means random arrivals to queue, general distribution of service time and one server. By adapting the M/M/1 model, Wq ¼
λ ; μðμ λÞ
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and dW q 1 ¼ ; dλ ðμ λÞ2 where μ is the reciprocal of the service time. The equivalent of service time is the cycle time. By adapting the M/G/1 model, λ E 2 ½S þ σ2S ; Wq ¼ 2ð1−ρÞ and dW q E2 ½S þ σ2S λ E2 ½S þ σ2S 1 ¼ þ ; dλ 2ð 1 ρ Þ 2ð 1 ρ Þ 2 μ where E(S) is the service time, σs is the standard deviation of E(S) and ρ=λ/μ the utilization level.
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