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Modeling the potential impact on the US blood supply of transfusing critically ill patients with fresher stored red blood cells

Background Although some studies have suggested that transfusion recipients may have better medical outcomes if transfused with red blood cell units stored for a short time, the overall body of evidence shows mixed results. It is important to understand how using fresher stored red blood cell units for certain patient groups may affect blood availability. Methods Based on the Stock-and-Flow simulation model of the US blood supply developed by Simonetti et al. 2014, we evaluated a newly implemented allocation method of preferentially transfusing fresher stored red blood cell units to a subset of high-risk group of critically ill patients and its potential impact on supply. Results Simulation results showed that, depending on the scenario, the US blood total supply might be reduced between 2-42%, when compared to the standard of care in transfusion medicine practice. Among our simulated scenarios, we observed that the number of expired red blood cell units modulated the supply levels. The age threshold of the required red blood cell units was inversely correlated with both the supply levels and the number of transfused units that failed to meet that age threshold. Conclusion To our knowledge, this study represents the first attempt to develop a comprehensive framework to evaluate the impact of preferentially transfusing fresher stored red blood cells to the higher-risk critically ill patients on supply. Model results show the difficulties to identify an optimal scenario.


Results
Simulation results showed that, depending on the scenario, the US blood total supply might be reduced between 2-42%, when compared to the standard of care in transfusion medicine practice. Among our simulated scenarios, we observed that the number of expired red blood cell units modulated the supply levels. The age threshold of the required red blood cell units was inversely correlated with both the supply levels and the number of transfused units that failed to meet that age threshold.

Conclusion
To our knowledge, this study represents the first attempt to develop a comprehensive framework to evaluate the impact of preferentially transfusing fresher stored red blood cells to the higher-risk critically ill patients on supply. Model results show the difficulties to identify an optimal scenario. PLOS

Introduction
Likely Newest (LN). In this study, we implemented a 'Threshold Method' [13] (TM) to distribute RBC units of a certain age to patients in specific high-risk groups. We divided blood recipients into two groups. The High Risk Groups (HRGs) included critically ill patients who were potentially at a higher risk for adverse events if they received a transfusion of older RBCs. The Baseline Blood Recipients (BBRs) are patients not belonging to the HRGs. The newly implemented algorithm affected the distribution of RBC units between the two model stocks of interest: the aggregate collector bank (Collector) and the aggregate blood distributor (Hospital) [10]. The TM algorithm attempted to allocate blood into the system: 1) from the Hospital to the HRGs recipients; and 2) from the Collector to the Hospital (S1 Fig). On each simulated day, the Hospital attempted to allocate blood to the HRGs in order to fulfill the average daily demand of RBCs from the specific group and the 'threshold age' of RBCs to be transfused. Then, for each blood type, the Hospital attempted to distribute RBC units of a specific age by first using an exact match. If no blood was available for cross matching, then the algorithm allocated compatible blood based on availability by age. If no compatible blood of a specific age was available to fulfill the HRGs needs, the algorithm provided the freshest stored RBC unit available using Last-In-First-Out. TM allocated compatible blood using the algorithm for phenotype compatibility rules [10] (S1 Table). The instances in which the Hospital failed to provide any RBC unit with the pre-specified age were recorded as 'unmet RBC units by age.' After allocating blood to the HRGs, the model attempted to allocate blood to the rest of the blood recipients. RBC units were distributed to BBRs using the LO allocation method [10].
The Collector attempted to supply the Hospital with enough young RBC units to meet the HRGs expected demand of blood for the next day. The Hospital received blood from the Collector to fulfill any need of blood demand regardless the RBCs age, while maintaining an inventory of 6 days of supply. Transfers of blood from the Collector to the Hospital occurred by using 'standard' phenotype compatibility rules (S2 Table). We defined the difference between the daily demand (requested RBC units) and the daily transfused as 'unmet demand. ' The daily predictions of supply and demand were derived using aggregated blood donation information from America's Blood Centers (ABC) [14], and updated blood utilization data among the inpatient US elderly (age 65+) billing information from the CMS for the period 2007-2012. We also used national blood collection and utilization estimates from the 2011 National Blood Collection and Utilization Survey [15] to reflect the 2010 US blood supply and estimated demand levels. We then generated quantitative estimates with uncertainty of the daily blood availability in the US for the overall blood and by ABO/Rh type [10]. We enhanced the phenotypic predictions to account for potential variability in the phenotype prevalence by using a Dirichlet-multinomial process (S3 Table,

Measures of performance of the blood system
We used the annual average daily (AAD) age of RBCs as a summary measure for the overall evaluation of the performance of the blood system for each simulated scenario. Specifically, we used the weighted AAD age of RBCs, which represented the distribution of RBC units among different blood ages. Other measures of performance were 'unmet RBC units by age' and 'percentage of unmet RBC units by age' for HGRs and BBRs. 'Unmet RBC units by age' represented the amount of RBC units that failed to meet the age requirement derived from the literature [1][2][3][4][5][6]. 'Percentage of unmet RBC units by age' was defined as the ratio between the number of RBC units that failed to meet the age requirement and the total number of units needed to meet that requirement. We used the percentage of met RBC units (100%-percentage of unmet RBC units) as a measure of the system efficiency. We also estimated the AAD total supply to represent the annual average daily number of RBC units available in the overall US blood supply system (collector + hospital), while the AAD expired RBC units was used to represent the annual average daily number of RBC units expired in the overall blood supply system (collector + hospital).

High-risk groups' identification and age of RBCs
We identified three HRGs-Cardiac Surgery (CS), Trauma (TR) and Intensive Care Unit (ICU) patients [2,5]-from the literature [1][2][3][4][5][6]. Due to the different ward setting among hospitals, we also included Coronary Care Unit (CCU) patients. We used the International Classification of Diseases, 9th revision, Clinical modification (ICD-9-CM) codes [16] to identify patients belonging to the HRGs. We used Diagnosis codes to identify TR patients. We included fractures to the head and injuries of the abdomen, and extremities as trauma conditions that could potentially require blood transfusions [17][18][19][20][21][22][23]. We used the ICD-9-CM Procedure codes to identify CS patients who received RBC transfusion procedures (S4 and S5 Tables, SM). CCU and ICU patients were identified using Revenue codes, respectively. We ascertained blood utilization among the inpatient US elderly overall, annually, and for the identified HRGs for the years 2007-2012 by using the CMS databases. CMS data were used to ascertain average daily number of RBC units transfused, total number of RBC units transfused, and the percentage of total RBC units transfused for each of the mutually exclusive HRGs and their combinations among the inpatient US elderly during 2007-2012. Since a CS patient may also become an ICU patient if prognosis worsens, the same CS patient may be recorded in the database twice. In order to avoid double counting of patients and units transfused, we identified mutually exclusive groups of patients (Table 1). Table 1 illustrates the average percentage of total RBC units transfused and the corresponding 95% Confidence Interval for each of the mutually exclusive HRG and their combinations (S1 Fig). Table 2 details the scenarios simulated in this study; a brief description of the scenario is given in second column; third column shows the percentages of RBC units transfused to each of the HRGs and BBRs and the last columns defines the allocation method used for each group. For example, in Scenario 2, any ICU patient is determined by adding the percentage of any mutually exclusive group from Table 1 that includes ICU patients. We applied the TM to model the effect on US blood supply of transfusing the HRGs with the corresponding 'threshold' age of RBCs we assumed from the literature [1-6] (i.e., age of RBCs 7 days for ICU, 14 days for CS and CCU patients and 28 days for TR patients). For scenarios in which two or more HRGs were combined, the TM attempted to allocate the younger age of RBCs to the overlapping group, i.e., in Scenario 6, Table 2 we applied TM7 to ICU and TM14 to CS, while we assigned TM7 to ICU [ CS.

Results
To evaluate the impact on supply of transfusing a subset of HRGs with fresher stored RBCs, we compared the baseline blood recipients to several selected scenarios (Scenario1 vs. 2-8, Table 2). In Scenario 1 we assumed all patients would receive older RBC units using the LO allocation method [10], while in Scenarios 2 to 8 high-risk patients were given RBCs of a certain younger age (TM). In Table 2, we presented only a subset of the scenarios we simulated (for more details, see additional simulated scenarios, S6 Table and S4-S7 Figs). We set the same initial conditions, i.e., the collector bank, the hospital bank, the daily-predicted donations and transfusions, for each independent simulated scenarios. For each scenario, we estimated the total AAD number of RBC units available in the US blood system (Collector + Hospital) either for all blood types or by blood type. Fig 1(A) illustrates the changes in the percent reduction of the AAD number of RBC units available for each scenario with respect to baseline scenario (BBRs-LO). We sorted scenarios in descending order according to the total blood supply levels. We observed 2.5% and 7.8% reduction in total supply levels for TR (representing 5.2% of total RBC units transfused, TM28) and CCU patients (14.6% of total RBC transfused, TM14), respectively. We observed a reduction in supply of 18.6% and 23.3% for ICU (43.2%, TM7) and CS patients (33.2%, TM14), respectively. The most extreme scenarios, All-HRGs TM7 and TM14, reduced the total available supply levels by up to 42% compared to baseline. Fig 1(B) shows the percent reduction in the AAD number of expired RBC units corresponding to each scenario of Fig 1(A). We observed the fewest expired RBC units in BBRs-LO scenario (AAD of 1,725 units, 95% CI: 1,466-1,985); while the highest expiration occurred in All HRGs-TM14 scenario (AAD of 3,585 units, 95% CI: 3,191-3,979) showing a 52% increase in the number of expired units compared to baseline. Fig 1(C) shows for each scenario the AAD number of unmet RBC units by age at the hospital level, the percentage of unmet RBC units by age; and the AAD age of transfused RBCs at the hospital level. We observed a wide range of unmet RBC units by age from a daily average of 60 unmet units (3%) for TR scenario, to approximately a daily average of 20,000 unmet units (81%) for the All HRGs-TM7 scenario. Fig 1(C) shows also the AAD age of the overall transfused blood (BBRs+HRGs) at the hospital, which measured the effect of the allocation method on the AAD age among the different scenarios. The AAD age of the overall transfused RBCs ranged from 26.4 days for the baseline (BBRs-LO) scenario to 15.7 days for the All-HRGs TM7 scenario.
In Fig 2, we designed a half-pie chart for each scenario reported in Table 2 (Scenarios 1-8). In those scenarios in which we applied TM7 only to the HRGs, the AAD age of RBCs transfused to the BBRs was higher-ICU (27.6 days) and All HRGs-TM7 (27.7 days)-compared to  Fig 2 that the actual AAD age of the overall transfused RBCs allowed by the system was about 8.8 days when we applied TM7, i.e., ICU and All HRGs-TM7 scenarios. However, the actual AAD age of the overall transfused RBCs allowed by the system when we applied TM14 ranged from 11.1 to 11.5, i.e., CS and CCU scenarios. Results on the performance of the blood system in meeting the desired 'threshold' age of transfused RBCs suggest an overall higher performance of TM14 compared to TM7, although the system likely expires more RBC units. For each scenario, in order to assess the efficiency of the system, we explored the percentage of met RBC units by age (i.e., 100%percentage of unmet RBC units by age) to the HRGs, and the average age of RBC transfused to the HRG (numbers shown in bold red, Fig 2). If the percentage of met RBC units by age was greater than 50%, then the age of the transfused RBC units would be below the considered age threshold. This holds true only for those scenarios where a single age threshold was applied. For example, the scenarios that implemented TM7 only, i.e., ICU and All HRGs TM7, we found that the efficiency of the system was only 25% and 19%, respectively. In both scenarios, the system failed to provide the RBC units stored for 7 days or less, in fact, the average age of transfused RBC units was 8.9 days for ICU and 8.8 days for All HRGs TM7. On the other side, those scenarios that implemented TM14 only, i.e., CS and All HRGs-TM14, the efficiency of the system was 74% and 63%, respectively, with the average age of the RBC units 11.1 days and 11.2 days. In the case where two or more TMs were implemented, the average age of transfused RBC units to the HRGs is less clear. The percentage of met units by age could still be used to assess the system efficiency without giving details about a specific HRG.

Fig 1. The Annual Average Daily (AAD) numberof RBC units available in the system for: (A) Total Supply (collector + hospital, light blue bars), AAD estimated number of RBC units (red), and percent reduction in total supply with respect to baseline scenario (BBRs-LO) (above bars forscenarios 2 to 8); (B) Expired RBC Units, (collector + hospital, green bars) and AAD number of expired units at collectoronly are shown on bars; (C) AAD Unmet RBC Units by Age at the hospital (dark blue bars), the percentage of unmet units by age (above bars), and AAD age of the transfused blood at the hospital (above bars, red on grey background).
The scenarios are sorted in a descending order according to their total supply. Error bars represent 95% confidence intervals. AAD = annual average daily.
https://doi.org/10.1371/journal.pone.0174033.g001 Table 2. We provide a description of each element of the half-pie chart from the inner to the outer layer, as follows: 1) percentage of total RBC units transfused among elderly for the overall HRGs (blue) versus BBRs (tan); 2) percentage of total RBC units transfused partitioned by HRGs (purple, orange and pink); 3) allocation method used foreach recipient group (HRGs -different shades of light blue; BBRs in teal); 4) AAD age of the blood transfused to each recipient group and the percentage of 'met' (green) and 'unmet' (red) RBC units by age forHRGs only (in parenthesis); and 5) AAD age of the overall transfused blood given to HRGs (bold red).

Fig 2. The annual average daily (AAD) age of transfused blood units for each simulated scenario listed in
https://doi.org/10.1371/journal.pone.0174033.g002 Effect of fresher stored red blood cells on US blood supply

Discussion
We developed the 'Threshold Method' to investigate the impact on the US blood supply levels of preferentially transfusing fresher stored RBCs to the higher risk critically ill patients. The selected scenarios represented plausible examples of the high-risk blood recipients who might benefit from receiving fresher stored RBC units. We expected to see a proportional relationship between the age of RBCs required for transfusion and the total blood supply levels available in the system, i.e., the younger the age of RBCs required, the lower the supply levels. However, we observed a counterintuitive finding when we compared the two scenarios All HRGs-TM7 and All HRGs-TM14 both representing 62% of total RBC units transfused. The estimated AAD total supply for scenario All HRGs-TM14 was 11.5% lower than that of All HRGs-TM7. By comparing Fig 1(A) to Fig 1(B), we observed a nearly inversely proportional relationship between the total supply level for each scenario and the corresponding number of expired units. Because each scenario satisfied the same initial conditions for the daily supply and demand, the reduction we observed in the total supply of scenario All HRGs-TM14 could not be attributed to a higher demand, instead, to a higher number of expired units (Fig 1(B)).
For the non steady-state simulation presented in this paper, we selected the average final banks from among 100 steady-state simulations to be the initial banks for the collector and hospital.
Using the same initial banks, for each scenario presented, we ran 500 independent one-year (365 days) simulations. These findings are in contrast with previous results reported by Simonetti et al. 2014 [10] where no statistically significant difference was found in the number of expired RBCs among the different allocation methods (i.e., FIFO, LO and LN). Moreover, if changes in the transfusion practices take place, a higher demand for fresher stored RBC units will follow to accommodate the HRGs needs. However, in our simulation we observed that the system, due to the scarce availability of RBC units with required age 7 days when implementing TM7, tended to allocate more frequently RBC units that were older than the required age. Conversely, in the relatively relaxed situation of TM14 (required age 14 days), the system was able to supply the demand for fresher stored RBC units for a longer time; while leaving older RBC units to expire more. The new TM allocation method in preferentially transferring fresher stored RBC units from the collector to the hospital and then to the HRG recipient in a not-FIFO way, no longer satisfy previous modeling [10] conditions of a traditional queuing system. The current model is a non-adaptive model where we stochastically sampled daily supply and demand from historic data to illustrate any potential deviation the system would face from the status-quo. In future work, we may consider implementing an adaptive framework to respond to changes in the inventory, and thus mimic practical inventory management techniques.
Model findings suggest that the behavior of the blood supply system may depend on both the amount of blood needed for transfusion to a HRG, i.e., the percentage of blood utilized to the HRG, and on the blood requirement, i.e., the age of RBC units. Both factors play an important role in predicting the transient impact on the blood supply levels during the first year following any potential changes in transfusion practice.
However, the estimated number of units available and those expired cannot provide a sufficient evaluation on the impact on the blood supply if fresher stored RBC units are preferentially transfused to a specific subset of critically ill patients. In order to provide a more accurate measure of the performance of the US blood supply system, it is important to understand the capability of the system in delivering the required RBC units with respect to the specified age, or 'unmet RBC units by age. ' We found no clear trend between the total supply (Fig 1(B)) and the number of unmet RBC units by age (Fig 1(C)). However, we observed a negative correlation between the ratio of TM7 to TM14 and the percentage of unmet RBC units by age. For example, when comparing scenarios ICU with ICU S CS (Table 2 and Fig 1(C)), we estimated 43% of unmet RBC units by age for ICU S CS compared to the 75% estimated in ICU, despite the higher total amount of units transfused to the HRGs (54.9%). In general, despite a larger amount of units transfused to HRGs, we estimated less unmet RBC units by age, when the proportion of the HRGs assigned to TM14 were larger compared to that assigned to TM7, i.e., the performance of the system declines when fresher stored RBCs is constantly required.
All the scenarios in our study were based on data extracted from the CMS database, which is limited to the blood utilization among the US elderly inpatients. The elderly population, in addition to utilizing~58% of the total blood utilized in the US [24], is more vulnerable to infections, hospitalizations, higher prevalence of chronic diseases [25]. Therefore, ascertainment of blood utilization for HRGs, especially for trauma patients [26], in the general US population might be useful to more accurately model the HRGs blood recipients and further predict their impact on the blood supply.
To conclude, we learned from this study how difficult it may be to identify an ideal scenario where the age-specific demand of RBCs is met, while the reduction in the US blood supply is acceptable. Only considering the three measures of performance (i.e., total supply, expired RBC units and unmet RBC units by age) in context, we may help understanding the effect on the US blood supply if transfusing fresher storedRBC units is proven beneficial to improve recipient outcomes. However, under current assumptions, we demonstrated how the newly developed allocation method allows a relatively efficient distribution of blood while preferentially providing fresher stored RBCs to the high-risk blood recipient except for some disruptions in the US blood supply observed in certain simulated scenarios. Most importantly, implementing 'ad-hoc' models can help assist stakeholders and the blood community to make informed decisions that may impact the availability of blood in the US blood supply.  Table 2. Description of each element of the half-pie chart from inner to the outer layer as follows: 1) percentage of total RBC units transfused among elderly for the overall HRGs (blue) versus BBR (tan); 2) percentage of total RBC units transfused decomposed by HRGs (purple, orange and pink); 3) allocation method used for each recipient group (HRGs -different shades of light blue; BBR in teal); 4) mean age of the blood transfused to each recipient group and the percentage of 'met' (green) and 'unmet' (red) RBC units by age for HRGs only (in parenthesis); and 5) mean age of the overall transfused blood given to HRGs (bold red). (DOCX)