Vox Sanguinis (2014) © 2014 International Society of Blood Transfusion DOI: 10.1111/vox.12224
ORIGINAL PAPER
Feasibility of reducing the maximum shelf life of red blood cells stored in additive solution: a dynamic simulation study involving a large regional blood system A. Grasas,1,a A. Pereira,2 M.-A. Bosch,3 P. Ortiz3 & L. Puig3 1
Department of Economics and Business, Universitat Pompeu Fabra, Barcelona, Spain Service of Hemotherapy and Hemostasis, Hospital Clınic, Barcelona, Spain 3 Banc de Sang I Teixits, Barcelona, Spain a Present address: Department of Marketing, Operations and Supply, EADA Business School, Barcelona, Spain 2
Background and Objective Recent studies suggest that transfusion of old red blood cell (RBC)s, mainly those close to the 42-day maximum shelf life (MSL), is associated with increased morbi-mortality. Although there is no formal proof supporting a causal relationship, the precautionary principle asks for corrective interventions whenever they do not bring about other risks or unjustified costs. Here, we investigated the feasibility of reducing the MSL. Materials and Methods A trace simulation model was used to analyse the repercussions of several MSLs on a large regional blood system. The baseline model was fed with real input and output data from years 2009 to 2010 and validated against real inventory data. Shortage and outdate rates and inventory levels for each blood group were derived assuming 42-, 35-, 28-, 21- and 14-day MSLs, as well as several distribution rules and supply shocks (periods without blood collections). Results The model shows that MSL could be reduced to 28–35 days without major increases in the shortage or outdate rates, even after supply shocks. At the 21-day MSL, the inventory capability to compensate supply shocks was severely reduced and translated into large shortage rates. The later were higher for group O and Rh-negative RBCs as compared to group A and Rh-positive, respectively.
Received: 22 July 2014, revised 17 October 2014, accepted 26 October 2014
Conclusion Reductions of MSL to 28–35 days seem feasible and riskless and do not require major changes in the inventory management policies. Consequently, and giving preponderance to the precautionary principle, the Catalan Blood Agency has decided to reduce the MSL of RBCs from 42 to 35 days. Key words: inventory management, maximal shelf life, red blood cells, simulation, storage.
Introduction Scientific research over the past two decades suggests that length of storage of transfused RBCs is associated with an increased risk of adverse clinical outcomes, probably mediated by the so-called RBC storage lesion [1]. Nevertheless, the causal relationship between transfusion Correspondence: Arturo Pereira, Service of Hemotherapy and Hemostasis, Hospital Clınic, Villarroel 170, 08036 Barcelona, Spain E-mail: [email protected]
of old blood and poor clinical outcomes has not yet been formally proved, and there is much uncertainty about what ‘old blood’ really means in terms of length of storage [1, 2]. Currently, the maximum shelf life (MSL) is 42 days for RBCs suspended in additive solutions although some blood agencies have reduced the MSL to 35 days [1]. Considering the aforementioned uncertainties together with the financial and logistic challenges that a reduced MSL can pose on blood agencies, many authors recommend waiting for the conclusion of ongoing clinical trials
1
2 A. Grasas et al.
aimed at clarifying the issue before making any policy decision [3–5]. The problem is that clinical trials may fail to provide a definitive answer due to lack of potency or other design issues [6], or they may confirm a deleterious effect of prolonged RBC storage but fail to provide any useful policy advice. For instance, a trial showing higher mortality in patients receiving RBCs older than 14 days would not automatically mean that MSL had to be reduced to two weeks. Beside the strictly scientific viewpoint, that is, a hypothesis that has to be verified or rejected, the purported association between transfusion of old blood and poor clinical outcomes has an important public health dimension. Indeed, in a large epidemiological study encompassing nearly 400 000 blood recipients, Edgreen et al. [7] found a significant 5% (95% CI, 2–8%) excess mortality in patients who had received blood stored for 30 to 42 days. Although the authors deemed that figure small enough as to having presumably been due to undetected confounding, it amounted to more than 1000 patients over the 6-year study period, a quantity large enough to constitute a big public health issue if really related to the transfusion of old blood. In Catalonia (Northeast Spain), the region of this study, where nearly 88 000 patients are transfused yearly with RBCs [8], and approximately 10–15% of them receive blood older than 30 days, more than 400 persons could be dying prematurely every year if the 5% increased mortality observed by Edgreen et al. [7] was actually due to stored blood. Faced with such a potential health impact of transfusing old blood, we decided to apply the precautionary principle and evaluate the feasibility of reducing the current 42-day MSL by one, two or more weeks. Note that a bibliography review found only two recent studies specifically aimed at evaluating the impact of reduced MSL. Fontain et al. [9] used a simulation to evaluate several MSL in a single centre, concluding that while a reduction of MSL to 35 or 28 days can be done without a significant increase in shortages and outdates, shorter MSLs would be unassumable without radical changes in how blood inventories are currently managed. On the other hand, Blake et al. [10] simulated the entire HemaQuebec blood system (about 240 000 blood collections per annum) under several assumptions for the MSL. They conclude that a MSL of 21–28 days ‘is feasible without excessive increases to system-wide outdate, shortage or emergency ordering rates’. Nevertheless, none of the above models analysed the effect of supply shocks, that is unexpected periods with reduced or absent blood collections. Since results from published studies can be influenced by the simulation methods and assumptions as well as by local peculiarities in the inventory management policies,
we decided to build a simulation model of the Catalonian RBC inventory dynamics to ascertain the impact of a reduced MSL on our regional blood supply.
Materials and methods Catalonia is a seven million inhabitants, autonomous region in Northeast Spain. Blood services are provided by Banc de Sang i Teixits (BST or ‘Blood and Tissue Bank’), which is the single, government-owned, blood agency in the region. BST collects approximately 280 000 wholeblood donations and distributes approximately 260 000 RBC units per annum. Blood collected all over the region is processed at the BST headquarters’ central laboratory, located in Barcelona, and is then distributed on demand to hospitals across the territory. In addition, BST directly manages the hospital transfusion services of nearly all the major- and medium-size hospitals in Catalonia. Blood inventories held in these later centres are overseen from BST headquarters through a networked, shared information system. The trace-based simulation model used in the study reproduces the inventory at BST, by age and blood group, under different scenarios over the period 2009–2010. The model was populated with real daily supply and demand data from calendar years 2009 and 2010. We did not use more recent data because of decreased surgical activity in 2011–2012, caused by a severe economic crisis, which made these years to be exceptionally unrepresentative.
Data sources and assumptions We retrieved the following data from the electronic information systems of the BST headquarters and the BSTmanaged hospital transfusion services for the 2009–2010 period: (1) Daily number of whole-blood units collected, by ABO/Rh blood group. (2) Daily number of RBC units irradiated, by ABO/Rh blood group. (3) Daily number of RBC units issued to hospitals, by ABO/Rh group. (4) Daily number of RBC units transfused in BST-managed hospitals, by ABO/Rh group. (5) Yearly aggregated number of whole-blood and produced RBC units discarded due to abnormal laboratory results or other causes. (6) Yearly aggregated number of whole-blood and RBC units used for non-transfusional purposes (e.g. antibody identification panels, research projects, etc.). (7) Yearly aggregated number of RBC units outdated. (8) Weekly RBC inventory levels available at BST headquarters, by ABO/Rh group. © 2014 International Society of Blood Transfusion Vox Sanguinis (2014)
Reducing RBCs maximum shelf life 3
Since we could not gather all the data that would have been ideally necessary for a perfect description of the inventory dynamics, we had to make the following assumptions: (1) The inventory level by ABO/Rh group at the beginning of the simulation (morning of 1 January 2009) was estimated using the first available data (January 5th) and the inputs and outputs during the first four days of 2009. The exact age of all RBC units at the beginning of 2009 was unknown, so the initial inventory was assumed to be uniformly distributed along the 42-day shelf life. (2) Irradiated RBC units have a reduced life span (28 days) that would require distinct simulation rules. Since they account for only a small proportion, they were disregarded from the analysis, that is, we assumed they never entered the inventory system. The same assumption was applied to the small number of blood units used for purposes other than transfusion. (3) The exact date of transfusion was known for every RBC unit sent to the BST-managed hospitals and the Hospital Clinic (they together accounting for most transfused blood), but it was unknown for those units sent to other centres. Therefore, we conservatively assumed that these later units were transfused the date they were delivered from BST headquarters. (4) We assumed demand backlogging, that is, if a shortage occurs, pending units are satisfied whenever inventory becomes available. This assumption is consistent with the postponement of non-urgent blood transfusions (e.g. programmed surgery) in periods of blood shortages. (5) We assumed a single inventory system that included the RBC units held in both BST headquarters and hospitals. Hospital inventories were estimated by survey to be 15-fold the average daily demand. Considering a unique ‘warehouse’ simplifies greatly the simulation and makes sense as blood shipments from BST headquarters to hospitals occur daily – or even more frequently for the largest hospitals. (6) According to what really happens in our regional blood systems, the model did not contemplate any kind of transshipments between hospitals.
Model description The simulation was divided into three experiments as follows: (i) baseline scenario, (ii) long-run simulations and (iii) simulations with supply shocks. First, we calibrated the model with a baseline scenario (MSL: 42 days) to ensure the simulation was accurate and resembled reality (see details below in the ‘Model validation’). Then, © 2014 International Society of Blood Transfusion Vox Sanguinis (2014)
simulations were run under different MSL values (42, 35, 28, 21 and 14 days). Outputs from each simulated day consisted in shortage and outdate rates, average age of RBCs held in stock and average length of storage at the time of transfusion, both aggregated and disaggregated by ABO/Rh group. The simulation was written in Visual Basic for Applications and was run on Excel 2007 spreadsheets (Microsoft Spain, Madrid, Spain) [11]. We studied the long-term effects of the different inventory policies by running 100-year simulations that allowed reaching a steady state. Blood input and output data for this 100-year period were made up of repeated bits of calendar years 2009 and 2010, that is, we run 50 consecutive 2-year-long simulations. Finally, in the last experiment, we introduced shocks in the supply, that is, disruptions in blood donations consisting in periods of 2 or 5 consecutive days with no blood collection (beginning the 10th day of the month). For each MSL (except for the 14-day case) and supply shock type, 12 different simulations were run, each one applying the shock in a different month (from February 2009 to January 2010). The simulation routine works as follows. Simulated data are stored in a matrix in which rows represent storage days (up to the corresponding MSL value) and columns represent each of the eight ABO/Rh blood groups. Each number in the matrix cell corresponds to the RBC units with a given storage length by ABO/Rh group. At daily clock cycles, the RBC units in each cell can either be transfused or advance to the next row. The remaining untransfused units in the last row are counted as outdated in the next daily cycle. The daily cycles begin on 1 January 2009 and continue until 31 December 2010. We modelled the following two possible inventory management policies: (i) a strict ‘first-in, first-out’ (FIFO) policy, and (ii) what we denote a Uniform+FIFO policy. Under the strict FIFO rule, daily demand for every ABO/ Rh group is supplied from RBCs in the matrix cell closer to their MSL. If the number of units in such a cell is less than the quantity demanded, the difference is supplied by RBCs in the immediately preceding, younger cell. If RBCs of a given ABO/Rh group are insufficient to cover the daily demand for that blood group, the oldest units from compatible blood groups are used. When total daily demand is not met, unsatisfied RBC units are accounted for as shortage for that day and blood group. For the Uniform+FIFO policy, the idea is to satisfy the demand with blood from all storage dates first (Uniform), and then use FIFO for the remaining unassigned units. These units result from not having availability of all storage dates or due to rounding. With this second policy, we attempt to model the fact that a proportion of units are currently not served according to a strict FIFO rule (e.g. neonates, massive transfusion, phenotyped units, etc.). This
4 A. Grasas et al.
combined rule, though, may be overestimating this proportion.
differences between predicted and real quantities were small enough as to consider that the model was validated by both tests.
Model validation Our simulation model was validated by running a baseline scenario that reproduced the current operating conditions. Two tests were performed to check the accuracy of the model: (i) a weekly inventory evolution, and (ii) the sum of outdated RBC units. Every Monday, a stocktaking of all RBC units stored in the BST and ready to be distributed to hospitals is carried out. These units represent the weekly ‘labelled inventory. The first test compares the weekly inventory predictions by blood group given by the simulation and the ‘labelled inventory’ in the BST. The second test compares the outdated units obtained in the simulation with the actual aggregate values provided by BST. The outcomes of these tests are in ‘Results’.
Results Baseline state and model validation Daily figures for collected whole-blood donations and transfused RBC units over years 2009 and 2010 are shown in Fig. 1. In total, 282 377 and 280 775 wholeblood units were collected, and 262 527 and 266 658 RBC units were transfused in 2009 and 2010, respectively. Donations discarded due to laboratory abnormalities or other reasons accounted for 4%, on average, and yearly expiration rates averaged 15%. Among RBC units distributed from BST headquarters, 57% went to hospitals where date of transfusion was available and 43% to other hospitals. Irradiated RBC units accounted for 33% of those distributed to hospitals. With regard to model validation, weekly inventory evolution (Test 1, see ‘Model validation’ in ‘Material and methods’) is displayed in the supplementary figure, with actual (i.e. ‘labelled inventory’) and predicted quantities for years 2009 and 2010, respectively. Differences were minimal in 2009. In 2010, the inventory predicted by the model reproduced the temporal profile of ‘labelled inventory’, but systematically overestimating the actual weekly stocktaking figures. The average difference, however, accounted for
ORIGINAL PAPER
Feasibility of reducing the maximum shelf life of red blood cells stored in additive solution: a dynamic simulation study involving a large regional blood system A. Grasas,1,a A. Pereira,2 M.-A. Bosch,3 P. Ortiz3 & L. Puig3 1
Department of Economics and Business, Universitat Pompeu Fabra, Barcelona, Spain Service of Hemotherapy and Hemostasis, Hospital Clınic, Barcelona, Spain 3 Banc de Sang I Teixits, Barcelona, Spain a Present address: Department of Marketing, Operations and Supply, EADA Business School, Barcelona, Spain 2
Background and Objective Recent studies suggest that transfusion of old red blood cell (RBC)s, mainly those close to the 42-day maximum shelf life (MSL), is associated with increased morbi-mortality. Although there is no formal proof supporting a causal relationship, the precautionary principle asks for corrective interventions whenever they do not bring about other risks or unjustified costs. Here, we investigated the feasibility of reducing the MSL. Materials and Methods A trace simulation model was used to analyse the repercussions of several MSLs on a large regional blood system. The baseline model was fed with real input and output data from years 2009 to 2010 and validated against real inventory data. Shortage and outdate rates and inventory levels for each blood group were derived assuming 42-, 35-, 28-, 21- and 14-day MSLs, as well as several distribution rules and supply shocks (periods without blood collections). Results The model shows that MSL could be reduced to 28–35 days without major increases in the shortage or outdate rates, even after supply shocks. At the 21-day MSL, the inventory capability to compensate supply shocks was severely reduced and translated into large shortage rates. The later were higher for group O and Rh-negative RBCs as compared to group A and Rh-positive, respectively.
Received: 22 July 2014, revised 17 October 2014, accepted 26 October 2014
Conclusion Reductions of MSL to 28–35 days seem feasible and riskless and do not require major changes in the inventory management policies. Consequently, and giving preponderance to the precautionary principle, the Catalan Blood Agency has decided to reduce the MSL of RBCs from 42 to 35 days. Key words: inventory management, maximal shelf life, red blood cells, simulation, storage.
Introduction Scientific research over the past two decades suggests that length of storage of transfused RBCs is associated with an increased risk of adverse clinical outcomes, probably mediated by the so-called RBC storage lesion [1]. Nevertheless, the causal relationship between transfusion Correspondence: Arturo Pereira, Service of Hemotherapy and Hemostasis, Hospital Clınic, Villarroel 170, 08036 Barcelona, Spain E-mail: [email protected]
of old blood and poor clinical outcomes has not yet been formally proved, and there is much uncertainty about what ‘old blood’ really means in terms of length of storage [1, 2]. Currently, the maximum shelf life (MSL) is 42 days for RBCs suspended in additive solutions although some blood agencies have reduced the MSL to 35 days [1]. Considering the aforementioned uncertainties together with the financial and logistic challenges that a reduced MSL can pose on blood agencies, many authors recommend waiting for the conclusion of ongoing clinical trials
1
2 A. Grasas et al.
aimed at clarifying the issue before making any policy decision [3–5]. The problem is that clinical trials may fail to provide a definitive answer due to lack of potency or other design issues [6], or they may confirm a deleterious effect of prolonged RBC storage but fail to provide any useful policy advice. For instance, a trial showing higher mortality in patients receiving RBCs older than 14 days would not automatically mean that MSL had to be reduced to two weeks. Beside the strictly scientific viewpoint, that is, a hypothesis that has to be verified or rejected, the purported association between transfusion of old blood and poor clinical outcomes has an important public health dimension. Indeed, in a large epidemiological study encompassing nearly 400 000 blood recipients, Edgreen et al. [7] found a significant 5% (95% CI, 2–8%) excess mortality in patients who had received blood stored for 30 to 42 days. Although the authors deemed that figure small enough as to having presumably been due to undetected confounding, it amounted to more than 1000 patients over the 6-year study period, a quantity large enough to constitute a big public health issue if really related to the transfusion of old blood. In Catalonia (Northeast Spain), the region of this study, where nearly 88 000 patients are transfused yearly with RBCs [8], and approximately 10–15% of them receive blood older than 30 days, more than 400 persons could be dying prematurely every year if the 5% increased mortality observed by Edgreen et al. [7] was actually due to stored blood. Faced with such a potential health impact of transfusing old blood, we decided to apply the precautionary principle and evaluate the feasibility of reducing the current 42-day MSL by one, two or more weeks. Note that a bibliography review found only two recent studies specifically aimed at evaluating the impact of reduced MSL. Fontain et al. [9] used a simulation to evaluate several MSL in a single centre, concluding that while a reduction of MSL to 35 or 28 days can be done without a significant increase in shortages and outdates, shorter MSLs would be unassumable without radical changes in how blood inventories are currently managed. On the other hand, Blake et al. [10] simulated the entire HemaQuebec blood system (about 240 000 blood collections per annum) under several assumptions for the MSL. They conclude that a MSL of 21–28 days ‘is feasible without excessive increases to system-wide outdate, shortage or emergency ordering rates’. Nevertheless, none of the above models analysed the effect of supply shocks, that is unexpected periods with reduced or absent blood collections. Since results from published studies can be influenced by the simulation methods and assumptions as well as by local peculiarities in the inventory management policies,
we decided to build a simulation model of the Catalonian RBC inventory dynamics to ascertain the impact of a reduced MSL on our regional blood supply.
Materials and methods Catalonia is a seven million inhabitants, autonomous region in Northeast Spain. Blood services are provided by Banc de Sang i Teixits (BST or ‘Blood and Tissue Bank’), which is the single, government-owned, blood agency in the region. BST collects approximately 280 000 wholeblood donations and distributes approximately 260 000 RBC units per annum. Blood collected all over the region is processed at the BST headquarters’ central laboratory, located in Barcelona, and is then distributed on demand to hospitals across the territory. In addition, BST directly manages the hospital transfusion services of nearly all the major- and medium-size hospitals in Catalonia. Blood inventories held in these later centres are overseen from BST headquarters through a networked, shared information system. The trace-based simulation model used in the study reproduces the inventory at BST, by age and blood group, under different scenarios over the period 2009–2010. The model was populated with real daily supply and demand data from calendar years 2009 and 2010. We did not use more recent data because of decreased surgical activity in 2011–2012, caused by a severe economic crisis, which made these years to be exceptionally unrepresentative.
Data sources and assumptions We retrieved the following data from the electronic information systems of the BST headquarters and the BSTmanaged hospital transfusion services for the 2009–2010 period: (1) Daily number of whole-blood units collected, by ABO/Rh blood group. (2) Daily number of RBC units irradiated, by ABO/Rh blood group. (3) Daily number of RBC units issued to hospitals, by ABO/Rh group. (4) Daily number of RBC units transfused in BST-managed hospitals, by ABO/Rh group. (5) Yearly aggregated number of whole-blood and produced RBC units discarded due to abnormal laboratory results or other causes. (6) Yearly aggregated number of whole-blood and RBC units used for non-transfusional purposes (e.g. antibody identification panels, research projects, etc.). (7) Yearly aggregated number of RBC units outdated. (8) Weekly RBC inventory levels available at BST headquarters, by ABO/Rh group. © 2014 International Society of Blood Transfusion Vox Sanguinis (2014)
Reducing RBCs maximum shelf life 3
Since we could not gather all the data that would have been ideally necessary for a perfect description of the inventory dynamics, we had to make the following assumptions: (1) The inventory level by ABO/Rh group at the beginning of the simulation (morning of 1 January 2009) was estimated using the first available data (January 5th) and the inputs and outputs during the first four days of 2009. The exact age of all RBC units at the beginning of 2009 was unknown, so the initial inventory was assumed to be uniformly distributed along the 42-day shelf life. (2) Irradiated RBC units have a reduced life span (28 days) that would require distinct simulation rules. Since they account for only a small proportion, they were disregarded from the analysis, that is, we assumed they never entered the inventory system. The same assumption was applied to the small number of blood units used for purposes other than transfusion. (3) The exact date of transfusion was known for every RBC unit sent to the BST-managed hospitals and the Hospital Clinic (they together accounting for most transfused blood), but it was unknown for those units sent to other centres. Therefore, we conservatively assumed that these later units were transfused the date they were delivered from BST headquarters. (4) We assumed demand backlogging, that is, if a shortage occurs, pending units are satisfied whenever inventory becomes available. This assumption is consistent with the postponement of non-urgent blood transfusions (e.g. programmed surgery) in periods of blood shortages. (5) We assumed a single inventory system that included the RBC units held in both BST headquarters and hospitals. Hospital inventories were estimated by survey to be 15-fold the average daily demand. Considering a unique ‘warehouse’ simplifies greatly the simulation and makes sense as blood shipments from BST headquarters to hospitals occur daily – or even more frequently for the largest hospitals. (6) According to what really happens in our regional blood systems, the model did not contemplate any kind of transshipments between hospitals.
Model description The simulation was divided into three experiments as follows: (i) baseline scenario, (ii) long-run simulations and (iii) simulations with supply shocks. First, we calibrated the model with a baseline scenario (MSL: 42 days) to ensure the simulation was accurate and resembled reality (see details below in the ‘Model validation’). Then, © 2014 International Society of Blood Transfusion Vox Sanguinis (2014)
simulations were run under different MSL values (42, 35, 28, 21 and 14 days). Outputs from each simulated day consisted in shortage and outdate rates, average age of RBCs held in stock and average length of storage at the time of transfusion, both aggregated and disaggregated by ABO/Rh group. The simulation was written in Visual Basic for Applications and was run on Excel 2007 spreadsheets (Microsoft Spain, Madrid, Spain) [11]. We studied the long-term effects of the different inventory policies by running 100-year simulations that allowed reaching a steady state. Blood input and output data for this 100-year period were made up of repeated bits of calendar years 2009 and 2010, that is, we run 50 consecutive 2-year-long simulations. Finally, in the last experiment, we introduced shocks in the supply, that is, disruptions in blood donations consisting in periods of 2 or 5 consecutive days with no blood collection (beginning the 10th day of the month). For each MSL (except for the 14-day case) and supply shock type, 12 different simulations were run, each one applying the shock in a different month (from February 2009 to January 2010). The simulation routine works as follows. Simulated data are stored in a matrix in which rows represent storage days (up to the corresponding MSL value) and columns represent each of the eight ABO/Rh blood groups. Each number in the matrix cell corresponds to the RBC units with a given storage length by ABO/Rh group. At daily clock cycles, the RBC units in each cell can either be transfused or advance to the next row. The remaining untransfused units in the last row are counted as outdated in the next daily cycle. The daily cycles begin on 1 January 2009 and continue until 31 December 2010. We modelled the following two possible inventory management policies: (i) a strict ‘first-in, first-out’ (FIFO) policy, and (ii) what we denote a Uniform+FIFO policy. Under the strict FIFO rule, daily demand for every ABO/ Rh group is supplied from RBCs in the matrix cell closer to their MSL. If the number of units in such a cell is less than the quantity demanded, the difference is supplied by RBCs in the immediately preceding, younger cell. If RBCs of a given ABO/Rh group are insufficient to cover the daily demand for that blood group, the oldest units from compatible blood groups are used. When total daily demand is not met, unsatisfied RBC units are accounted for as shortage for that day and blood group. For the Uniform+FIFO policy, the idea is to satisfy the demand with blood from all storage dates first (Uniform), and then use FIFO for the remaining unassigned units. These units result from not having availability of all storage dates or due to rounding. With this second policy, we attempt to model the fact that a proportion of units are currently not served according to a strict FIFO rule (e.g. neonates, massive transfusion, phenotyped units, etc.). This
4 A. Grasas et al.
combined rule, though, may be overestimating this proportion.
differences between predicted and real quantities were small enough as to consider that the model was validated by both tests.
Model validation Our simulation model was validated by running a baseline scenario that reproduced the current operating conditions. Two tests were performed to check the accuracy of the model: (i) a weekly inventory evolution, and (ii) the sum of outdated RBC units. Every Monday, a stocktaking of all RBC units stored in the BST and ready to be distributed to hospitals is carried out. These units represent the weekly ‘labelled inventory. The first test compares the weekly inventory predictions by blood group given by the simulation and the ‘labelled inventory’ in the BST. The second test compares the outdated units obtained in the simulation with the actual aggregate values provided by BST. The outcomes of these tests are in ‘Results’.
Results Baseline state and model validation Daily figures for collected whole-blood donations and transfused RBC units over years 2009 and 2010 are shown in Fig. 1. In total, 282 377 and 280 775 wholeblood units were collected, and 262 527 and 266 658 RBC units were transfused in 2009 and 2010, respectively. Donations discarded due to laboratory abnormalities or other reasons accounted for 4%, on average, and yearly expiration rates averaged 15%. Among RBC units distributed from BST headquarters, 57% went to hospitals where date of transfusion was available and 43% to other hospitals. Irradiated RBC units accounted for 33% of those distributed to hospitals. With regard to model validation, weekly inventory evolution (Test 1, see ‘Model validation’ in ‘Material and methods’) is displayed in the supplementary figure, with actual (i.e. ‘labelled inventory’) and predicted quantities for years 2009 and 2010, respectively. Differences were minimal in 2009. In 2010, the inventory predicted by the model reproduced the temporal profile of ‘labelled inventory’, but systematically overestimating the actual weekly stocktaking figures. The average difference, however, accounted for
