Characterizing Red Blood Cell Age Exposure in Massive Transfusion Therapy: The Scalar Age of Blood Index (SBI)

Abstract

Background:

The mortality of trauma patients requiring massive transfusion to treat hemorrhagic shock approaches 17% at 24-hours and 26% at 30-days. The use of stored packed red blood cells (PRBCs) is limited to less than 42 days, so older PRBCs are delivered first to rapidly bleeding trauma patients. Patients who receive a greater quantity of older PRBCs may have a higher risk for mortality.

Methods and Materials:

Characterizing blood age exposure requires accounting for the age of each PRBC unit and the quantity of transfused units. To address this challenge, a novel Scalar Age of Blood Index (SBI), that represents the relative distribution of PRBCs received, is introduced and applied to a secondary analysis of the Pragmatic, Randomized Optimal Platelet and Plasma Ratios (PROPPR) randomized controlled trial (NCT01545232, https://clinicaltrials.gov/ct2/show/NCT01545232). The effect of the SBI is assessed on the primary PROPPR outcome, 24-hour and 30-day mortality.

Results:

The distributions of blood storage ages successfully maps to a parameter (SBI) that fully defines the blood age curve for each patient. SBI was a significant predictor of 24-hour and 30-day mortality in an adjusted model that had strong predictive ability (OR = 1.15 [1.01–1.29], p=0.029, C-statistic= 0.81; OR = 1.14 [1.02–1.28], p= 0.019, C-statistic =0.88, respectively).

CONCLUSION:

SBI is a simple scalar metric of blood age that accounts for the relative distribution of PRBCs among age categories. Transfusion of older PRBCs is associated with 24-hour and 30-day mortality, after adjustment for total units and clinical covariates.

INTRODUCTION

Trauma is a leading cause of death and disability in younger adults.¹ Critically ill trauma patients may present with multi-system injury, severe blood loss, and hemorrhagic shock (THS) requiring emergent blood transfusions, often totaling 10 or more units of packed red blood cells (PRBCs). The mortality of THS is high, approaching 17% at 24-hours and 26% at 30-days.²

As PRBCs age, they undergo biochemical and metabolic changes resulting in hemolysis.^3–5 In animal hemorrhage models, transfusion with older PRBCs exacerbates impaired coagulation and organ perfusion, increasing susceptibility to infections, inflammation, oxidative stress, organ damage and death.^6,7 Current practices limit PRBC transfusion to units less than 42 days old. However, because of their large blood transfusion requirements, there is strong potential for THS patients to receive older PRBC units, heightening exposure to stored blood toxicity. While prior randomized controlled trials suggest no harm from transfusion of small quantities (2–4 units) of stored PRBCs in stable patients, these findings are likely not applicable to THS patients who are very unstable and frequently receive massive quantities of PRBCs (10+ units) in short periods of time.^4,8–10 In fact, using data from the Pragmatic, Randomized Optimal Platelet and Plasma Ratios (PROPPR) trial, we found that exposure to PRBCs over 21 days old was independently associated with increased 24-hour mortality.¹¹

Characterizing blood age exposure poses important quantitative challenges, accounting for both 1) the age of each PRBC unit and 2) the quantity of transfused units from each PRBC age group. Prior analyses have used simple methods to characterize PRBC age, including dichotomization (old vs new PRBCs dichotomized by a clinically determined cutpoint),^4,9,12 dichotomization via median split, and ordinal blood age categories.⁸ While certainly reasonable, these ad hoc approaches result in loss of information, further compounded by the understanding that storage age, per se, is only one factor predicting storage hemolysis; donor demographics also affect how PRBCS change during cold-storage.^13,14 Further, interpretation of regression model coefficients in risk analysis is confusing as the number of independent predictors (i.e., multiple blood age groups on the right-hand side of a regression model) increases. Therefore, in this paper, we describe the derivation and application of a novel scalar metric, the Scalar Age of Blood Index (SBI) to characterize the relative distribution of PRBCs administered to trauma patients requiring massive blood transfusion, and subsequently use it to assess risk of mortality.

MATERIALS AND METHODS

Design, Study Setting and Patients

We performed a secondary analysis of the PROPPR randomized controlled trial (RCT), which compared the effects of different plasma, platelets, and red blood cells ratios (1:1:1 vs 1:1:2, respectively) on mortality after traumatic hemorrhagic shock.^15,16 The study was previously approved by the Committee for the Protection of Human Subjects of the University of Texas Health Science Center at Houston. PROPPR was a randomized controlled trial involving 12 Level I trauma centers in North America.¹⁶ From August 2012 to December 2013 the trial enrolled severely injured adults aged $\ge$ 15 years who presented to receiving trauma centers with shock, received at least one unit of PRBCs in the first hour of hospitalization, and who were predicted to require massive transfusion ($\ge$10 PRBC unit in the first 24 hours) as indicated by an Assessment of Blood Consumption (ABC) score of ≥2 or physician intuition. The primary paper found no difference in mortality but decreased incidence of exsanguination in the 1:1:1 vs 1:1:2 group (9.2% vs 14.6%, p=0.03). The current analysis includes all patients enrolled in the PROPPR trial with available mortality data (N=678 at 24-hours and N=674 at 30-days).

Measures – Development of the Scalar Blood Age Index (SBI)

Study personnel recorded the age (in days) of all transfused PRBC units from labels affixed to each PRBC unit. Following our prior study, we divided PRBC age into four storage age categories: 0–7 days, 8–14 days, 15–21 days and 22+ days.¹¹

We defined the SBI to characterize the distribution of ages of PRBCs received by each patient. First, the proportion of blood received within each PRBC age category was defined by calculating a cumulative distribution function (CDF) for each patient. For example, if a patient received 4, 2, 1, and 3 PRBC units for PRBC age categories 0–7 days, 8–14 days, 15–21 days, and 22+ days, respectively, they received a total of 10 PRBC units, and the proportions of blood the patient received within each PRBC age category were (0.4, 0.2, 0.1, 0.3). Summing in order of increasing PRBC age category leads to the CDF vector (0.4, 0.6, 0.7, 1.0). We then fit a curve to the CDF using mathematical techniques adapted from well-characterized phase I dose finding trials, which we briefly describe below.^17,18

Within the dose finding literature for phase I trials, the probability of a dose limiting toxicity increases as standardized dose, “d,” increases. This increasing dose-toxicity curve is modeled using a one parameter power function in order to estimate a maximum tolerable dose.¹⁸ For blood product proportions, one may find a direct analogy from this literature. Specifically, the CDF of PRBC proportions is also an increasing curve, and thus a one parameter power function can similarly be used to model PRBC units within age category.¹⁸ The one parameter power function for patient$i$, is given by:

$$P\left(K_i\le k\right)=F_K\left(k\right)\approx f\left(a\right)=d_k^{\text{exp}\left(a\right)}fork=1,2,\dots ,n$$ (1)

where the left side of the equation represents the true CDF for blood product age,$d_k$ is a standardized dose which lies between 0 and 1, $k$is the indicator of $n$ blood product age categories, and a is the scalar value that dictates the shape of the mapped one parameter power function (i.e., the SBI). In the current setting where there are 4 blood product age categories, then $k$=1, 2, 3, 4 for the 4 clinically chosen groupings of 0–7 days, 8–14 days, 15–21 days, and 22+ days, respectively, where, in absence of prior information,$d_k$ = 0.25, 0.5, 0.75, 1 for the standardized “dose.” In equation (1),$k=1,2,\dots ,n$ refers to the probabilities in the vector; the $n^{th}$ probability is fully defined by the first $n-1$, since probabilities must sum to 1. Of course, the cutoffs can easily be changed while the SBI modeling process remains exactly the same. The value for “a” is called the SBI, and encapsulates the relative distribution of PRBC a person received.

For each patient, we fit the CDF for blood product age and the power function using a non-linear least squares (NLS) algorithm¹⁹ to determine optimal SBI (variable “a”). The NLS algorithm minimizes the residual distance between the CDF data and the fitted function by iteratively fitting values for the SBI. That is, NLS estimation minimizes the following quadratic form over all a and selects the value of a that minimizes it, i.e.,

$$\underset{a}{min}\sum _{k=1}^n{({d_k^{exp\left(a\right)}}_{}-F_K\left(k\right))}^{2}fork=1,2,\dots ,n.$$ (2)

Once the SBI metric has been calculated, it can be easily transformed back into estimated proportions of blood received within each PRBC age category. For example, using a SBI value of −1 derived from 4 blood age categories, the estimated proportion of blood received within each PRBC age category is calculated below.

1. The proportion received within the first blood age category:

   $$d_1^{\exp (a)}={(0.25)}^{\exp (-1)}=\mathrm{0.601.}$$
2. The proportion received within the second blood age category:

   $$d_2^{\text{exp}\left(a\right)}-d_1^{\exp \left(a\right)}={\left(0.50\right)}^{\exp \left(-1\right)}-0.601=0.775-0.601=\mathrm{0.174.}$$
3. The proportion received within the third blood age category:

   $$d_3^{\text{exp}\left(a\right)}-d_2^{\exp \left(a\right)}-d_1^{\exp \left(a\right)}={\left(0.75\right)}^{\exp \left(-1\right)}-0.775=0.900-0.775=\mathrm{0.125.}$$
4. The proportion received within the fourth blood age category:

   $$d_4^{\text{exp}\left(a\right)}-d_3^{\exp \left(a\right)}-d_2^{\exp \left(a\right)}-d_1^{\exp \left(a\right)}={\left(1\right)}^{\exp \left(-1\right)}-0.900=1-0.900=\mathrm{0.100.}$$

Therefore, the estimated proportion of blood received within each PRBC age category for a patient with SBI equal to −1 is given by (0.601, 0.174, 0.125, 0.100). The same procedure detailed above may additionally show that a SBI value greater than 2 translates to more than 88% of transfused units being older than 21 days.

Outcomes and Statistical Methods

We modeled association between the SBI and the two outcomes, 24-hour and 30-day mortality. We used a generalized linear mixed model with a logit link for a binomial outcome, accounting for clustering by each of the 12 trial sites, and adjusting for age, sex, race, mechanism of injury (penetrating, blunt, both), Injury Severity Score (ISS), Revised Trauma Score (RTS), total number of PRBC units transfused in the first 24 hours after hospital admission, and treatment group (1:1:1 vs 1:1:2). The NLS algorithm was fit in Rx64 3.4.3 and after retrieving the SBI values, all regression modeling was conducted in Stata v.14.2 (Stata, Inc., College Station, Texas).

RESULTS

Of 680 patients enrolled in the PROPPR trial, 2 patients were missing PRBC age data, and 4 were missing 30-day mortality data. Trial patients were primarily male and white, with a median age of 34 years (IQR 24–51) (Table 1). The trial cohort received a total of 8,830 units PRBCs in the first 24 hours of treatment, with patients receiving a median of 9 PRBC units (interquartile range, IQR [5, 15]). Patients received PRBCs encompassing a range of storage ages and in varying total units, as shown in Table 2.

TABLE 1:

Characteristics of patients in the PROPPR Trial. N=678 subjects.

Characteristic	N (% or IQR)
Age (years), median (IQR)	34 (24,51)
Male sex, No. (%)	544 (80.2)
Race, No. (%)
White	432 (63.7)
Black	186 (27.4)
Other	60 (8.9)
Mechanism of injury, No. (%)
Blunt	350 (51.6)
Penetrating	320 (47.2)
Both	8 (1.2)
Injury Severity Score, median (IQR)	26 (17,41)
Revised Trauma Score, median (IQR) (n=605)	6.8 (4.1,7.8)
Glasgow Coma Scale score, median (IQR)	14 (3,15)
Systolic blood pressure (mm Hg), median (IQR) (n=656)	102 (80,126)
Diastolic blood pressure (mm Hg), median (IQR) (n=561)	70 (51,91)
Heart rate (beats per minute), median (IQR) (n=675)	114 (94,133)
Respiratory rate (breaths per minute), median (IQR) (n=619)	20 (17,26)
PRBC unit age (days), median (IQR)	19 (13,27)

TABLE 2:

Distribution (mean, median, interquartile range, IQR) of the number of packed red blood cells administered to each patient (N=678).

Variable	Mean	Median	IQR
PRBC Age Category
0–7 days	1.1	0	(0, 1)
8–14 days	3.2	1	(0, 4)
15–21 days	3.4	1	(0, 4)
22+ days	5.3	2	(0, 7)
Overall #PRBCs	13.0	9	(5, 15)
Scalar Blood Index (SBI)	0.95	0.57	(−0.11, 1.31)

The median [IQR] SBI value was 0.57 [−0.11, 1.31] (Table 2). Figure 1 depicts the SBI for 5 representative patients in PROPPR in order to illustrate the simple interpretation of the metric. The red curve represents an individual who received mostly the youngest category of RBCs (89% youngest, a= −2.75) while the blue curve represents an individual who received mostly the oldest category of RBCs (90% oldest, a= 2.04); other colors show gradations between these two extreme cases. Figure 1 therefore demonstrates how the SBI single scalar value encapsulates the range and quantities of different PRBC ages received by a patient. Importantly, identical SBI values for two patients who received identical total number of PRBCs means that the two patients received the same exact PRBC age distribution and quantity. Thus there is a 1 to 1 mapping of SBI to PRBC age distribution. The associated color-coded table in Figure 1 directly shows how the SBI value maps to the precise quantity of PRBCs received in each age group.

FIGURE 1.

Graph of the cumulative scalar blood age index (SBI) for 5 representative patients from the PROPPR trial. The table shows these patients’ exact PRBC units and their predicted 24 hour and 30 day mortality from the model. For example, patient 1 received a total of 9 PRBC units: 8 were aged 0–7 days old and 1 was 8–14 days old. The inlaid table maps SBI to age categories and predicted mortality at 24 hours and 30-days.

Note: The predicted mortality is calculated at the sample mean or median for the following adjusters in the model: patient age, sex, race, mechanism of injury, Injury Severity Score, Revised Trauma Score, total PRBC units transfused in the first 24 hours after admission, and PROPPR trial treatment group.

In the unique situation where a patient receives only fresh (0–7 day old) PRBC units, the CDF vector would be a straight line with value at 1 (i.e., CDF vector = (1,1,1,1), precluding fitting the curve to this specific vector form. To accommodate this situation, we simulated CDF vectors close to horizontal, and determined that a value of a=−7.49 best represent vectors of this form. Thus, for the 11 patients in PROPPR receiving only fresh (0–7 days) blood, we imputed the SBI as −7.5. A sensitivity analysis to a range of reasonable negative values resulted in no substantial inferential differences. Given this, the range of the SBI was [−7.5 to 6.3] (Figure 2).

FIGURE 2:

Distribution of SBI among all PROPPR trial patients. Patients transfused with predominately younger RBCs have increasingly more negative SBI values; whereas, patients transfused with predominately older RBCs have increasingly higher positive SBI values.

Outcome Analysis

The SBI was independently associated with 24-hour and 30-day mortality in adjusted models (Table 3). For a 1-unit increase in the SBI, the OR for 24-hour and 30-day mortality were 1.15 [1.01, 1.29], p=0.029 and 1.14 [1.02, 1.28], p=0.019, respectively. The C-statistics indicated the models had very good discrimination for 24-hour and 30-day mortality (0.81 and 0.88, respectively).

TABLE 3:

Association of SBI with 24-hour and 30-day mortality.

	24-hour (N=605)		30-day (N=601)
	OR[95%CI]	p-value	OR[95%CI]	p-value
SBI	1.15 [1.01–1.29]	0.03	1.14 [1.02–1.28]	0.02
Age	1.02 [1.00–1.03]	0.02	1.04 [1.02–1.05]	<0.001
Sex	0.89 [0.45–1.77]	0.75	0.95 [0.51–1.76]	0.88
Race
Black:White	1.03 [0.51–2.06]	0.94	0.90 [0.46–1.76]	0.76
Other:White	0.33 [0.09–1.21]	0.09	0.78 [0.31–1.94]	0.59
Injury Mechanism
Penetrating:Blunt	1.50 [0.76–2.98]	0.24	1.00 [0.54–1.87]	1.00
Both:Blunt	5.38 [0.83–35.02]	0.08	1.55 [0.19–12.72]	0.69
ISS	1.61 [1.19–2.17]	0.002	1.84 [1.38–2.46]	<0.001
RTS	0.47 [0.35–0.62]	<0.001	0.33 [0.25–0.44]	<0.001
Total PRBC	1.03 [1.02–1.05]	<0.001	1.07 [1.04–1.09]	<0.001
Treatment
1:1:2 vs 1:1:1	1.50 [0.88–2.59]	0.14	1.29 [0.79–2.12]	0.31

^†Adjusted generalized linear mixed effects model with logit link accounts for clustering by study site. The model is adjusted for fixed covariates patient age, sex, race, mechanism of injury, Injury Severity Score, Revised Trauma Score, total PRBC units transfused in the first 24 hours after admission, and PROPPR trial treatment group.

Figure 1 also shows the predicted mortality for the 5 representative patients, calculated at the mean or median of the covariates included in the regression models. Predicted mortality increases as a function of both SBI and number of PRBC units received.

To determine whether there was a “dose-response” relationship between PRBC age and mortality, Figure 3 shows a 3-D graphic of proportion mortality by SBI tertile, and total PRBC units a person received. Tertiles were chosen so that the 9 resultant groups would have a reasonable number of patients in them. Figure 3 depicts an association between mortality on both the SBI and total units; this is especially true for 30-day mortality where predicted mortality increases as one increases both SBI and total PRBC units. In both 24-hour and 30-day adjusted regression models, there was no significant interaction between SBI and total number of PRBC units received, thus the contribution of SBI and total PRBC units to mortality is an additive one.

FIGURE 3:

The (unadjusted) proportion of 24-hour and 30-day patient mortality by SBI tertile and total PRBC units received. Mortality proportions are given on the y-axis by both SBI tertile on the first x-axis, and total PRBC blood unit category on the second x- axis. This 3-dimensional plot shows how mortality in PROPPR changes as a function of both SBI and total number of blood units received.

Sensitivity Analysis

For sensitivity analysis, we used age cutoffs of 0–5 days, 6–10 days, 11–15 days, 16–20 days, 21–25 days, and 26+ days. While these do not necessarily have clinical significance, results from this grouping are demonstrative. Using this $K=6$ grouping, we estimated SBI as described in equations (1) and (2). In adjusted mortality analyses, SBI was still found to be a significant predictor of 30-day mortality (OR = 1.19 [1.04–1.37], p=0.013), though did not quite reach alpha=0.05 level of significance for 24-hour mortality (OR = 1.15 [1.00–1.33], p=0.053). This sensitivity analysis shows that when using these broader blood age categories, we still find that transfusion with older PRBCs is associated with mortality.

While other methods may be used to optimize the power parameter for each patient, we find that the ‘nls’ function (as detailed in Appendix A) performs well. Applying the ‘nls’ function using a dual-core Intel Core i3–3110M laptop with 4 GB RAM, the SBI parameter estimates for 1,000 patients are returned in 5 seconds. The calculations can be easily performed in parallel if data sets are very large. An alternative estimation procedure to NLS is to run a constrained regression without an intercept of the form $\log \left({\widehat{f}}_{ik}\right)=b\log (d_k)$ subject to the constraint b ≥0, and extract the slope coefficient ($b$) which is equivalent to extracting $a$ , where i denotes the individual patient. This speeds computation time if there is a very large number of patients, and the programmer cannot run in parallel.

Furthermore, although other one parameter functions, e.g., the exponential, logistic, and logarithmic, might initially seem plausible to summarize CDFs, they do not share the advantages of the power function. The Appendix B Figure shows the power function very accurately fits both concave and convex CDFs. Further, the shapes of the resultant curves are symmetric around a=0. This is similar in spirit to the functional uniform prior proposed by Bornkamp and Ickstadt (2009); that the function’s “shape” is evenly distributed across the parameter space makes the choice of $d{}^{\exp (a)}$ superior to alternatives for modeling the CDF in the form of $d^a$ .²³ Under alternatives, we have observed awkward resultant CDFs, and the “jump” from $a=0$ to $a=1$ is large, making it a not useful estimate.

DISCUSSION

Severely injured patients with traumatic hemorrhagic shock often require massive quantities of RBC transfusions. It is of immediate clinical interest to determine whether use of older or nearly-expired blood in hemorrhaging patients results in poorer outcomes, including a greater risk of mortality. To address this, we demonstrated the calculation and utility of the novel SBI metric for characterizing the blood age distribution received by patients in traumatic hemorrhagic shock, and applied it to the PROPPR study.

The SBI offers many scientific and clinical advantages over current tools. First, the new metric is superior to ad hoc dichotomous or ordinal categorizations of numbers of PRBCs that then serve as predictors in a model for mortality. For example, unlike the recent nested analysis in the Age of Blood Evaluation randomized controlled trial that showed no difference in ninety-day mortality risk using dichotomous blood age groups (patients receiving fresh blood (no more than 7 days old) versus patients with standard-issue blood),²⁰ analyses involving SBI do not need to be dichotomized, thus we can use more information about the blood age distribution than these previous authors. Additionally, because it is a scalar, the SBI makes statistical modeling simpler, its interpretation easier, and has properties that facilitate ROC analysis. Furthermore, the SBI easily maps directly to a unique blood product distribution. Thus, ROC analysis could be performed to determine the value that produces optimal ROC characteristics for mortality, and the corresponding optimal blood age categories and quantities can be directly and uniquely determined from the SBI. Current simplistic approaches for modeling blood product age as a regressor in a regression model cannot claim to have these benefits. The SBI value can be easily directly back-transformed to indicate the precise number of units of PRBCs a patient received in each blood age category.

This secondary analysis of the PROPPR data using the SBI to predict mortality, both confirms and augments prior findings that transfusion of older PRBCs increases the risk of mortality.¹¹ Prior findings obtained from fitting a random effects logistic regression model with 4 blood age categories as predictors of mortality showed that just the number of ≥22 day old PRBCs was associated with increased 24-hour mortality; i.e., ≥22 days OR = 1.05[1.01,1.08] per PRBC unit, irrespective of mixing with younger RBCs.⁷ The number of ≥22 day old PRBC units was also associated with 30-day mortality. The current findings are consistent with those findings, but provide a more nuanced picture of those presented in Jones et al (in press; 2018) by utilizing the entire cumulative vector of blood product age. ¹¹ The current analysis demonstrates a significant effect of SBI, which is indicative of the cumulative blood storage age, on mortality with greater magnitude than those previously published.^7,11 Other covariates that significantly predict mortality are age, ISS, RTS, and total PRBCs transfused, which is consistent with prior findings.² Furthermore, as detailed in Figure 1, patient mortality increases both as a function of SBI and as a function of number of PRBC units received; however, comparisons among patients with varying SBI should really not be made without holding PRBC units constant.

We note that Jones et al (in press; 2018) used 4 pre-defined blood age groups as 4 predictors on the right-hand side of a regression model predicting mortality to show that receipt of PRBCs greater than 21 days old is predictive of mortality.¹¹ This analysis involved the interpretation of 4 different regressor effects on mortality (one for each blood age category). In this paper, we avoided the difficulty in interpreting 4 different coefficients by a priori specifying the SBI to summarize PRBC age and quantity, using the same pre-defined clinically meaningful age groups as Jones et al.¹¹ It is notable that our approach allows one to easily re-define blood age groups (if needed) to obtain a different SBI. This could allow researchers, for example, to agnostically examine other meaningful cutoffs of blood age.

It is also notable that any number of pre-specified blood age categories with any pre-specified cutoffs can be used, and the SBI would be similarly constructed. Thus, one could perform a sensitivity analysis for any regression model by altering age cutoffs and constructing multiple SBIs. The scalar summary measure potentially applied to other conditions where the primary exposure entails a range of values; for example, Glasgow Coma Score, the ISS and the RTS.

LIMITATIONS

This analysis also has important limitations; prospective validation of our results is mandatory prior to changes in clinical practice. For example, total transfused PRBC units may serve as a proxy of the degree of physiologic damage or injury, even though these potential confounders were controlled for in the model. Although we accounted for site clustering by incorporating a random effect for site, there is variation in the median PRBC age across the study sites suggesting that practice variation may influence these results. In terms of allocating PRBC units based on age, this aspect of care was not incorporated as part of the treatment protocol for patients enrolled in the PROPPR trial. Furthermore, no standard protocols exist to guide blood banks or emergency medical services in the choice of PRBC units based on storage age. Thus, these factors may have also influenced outcomes on both the patient and study site level.

The purpose of the PROPPR trial was to compare blood product ratios, not PRBC age. While the trial applied strict inclusion and exclusion criteria and employed standardized protocols at all study sites, variations in patient-mix and clinical protocols used over the course of hospitalization may have influenced the results. Other factors of influence to consider include: time from injury to initiation of care, diagnosed and undiagnosed comorbidities, and variation in care outside of transfusion protocols, both within and among study sites; however, most of these would be mitigated by a randomized design. While we used panel regression techniques to account for clustering by study center, we limited further inference to protect site confidentiality. Finally, we must acknowledge the limitations associated with a secondary analysis of a randomized trial. Our findings suggest a possible risk of adverse outcomes related to the transfusion of older PRBCs in the trauma population, but require validation with a Level I prospective study specifically designed to address the issue of blood age in the trauma setting. An important limitation of our analysis is the absence of PRBC age randomization.

Although this study focused on the effect of transfused PRBCs, platelets and plasma are also associated with cellular and/or protein degradation during storage and increased risk of complications after trauma.²¹ In addition, practitioners and blood banks may have selected specific-aged PRBCs for massive transfusion. However, given the tempo of PRBC transfusions in PROPPR, we do not expect systematic bias. Finally, the nature of the PROPPR trial did not allow for definitive diagnosis of all injuries prior to study enrollment. As such, patients with traumatic brain injury associated with coagulopathy and complications after trauma were included in the study sample.²²

In summary, multiple factors may influence the patterns of RBC age given to a patient, including confounding by indication and the PRBC storage practices of an institution. An alternate strategy to an RCT on this topic may entail defining the harmful mechanisms of stored blood toxicity, potentially leading to pharmacologic interventions to block the adverse effects of older stored PRBCs.

CONCLUSIONS

The proposed scalar blood index is an easy-to-calculate proxy for blood age that accounts for the relative distribution of PRBC received within each age group. This paper demonstrates that meaningful information about blood age can be encapsulated into an easily analyzable scalar metric. To demonstrate its utility, this research found that transfusion of older PRBCs is associated with higher 24-hour and 30-day mortality, after adjusting for total number of PRBC units received, and clinical covariates. Future works should apply SBI to new data sets to reproduce/validate results from the current study and further investigate the use of the SBI when conducting studies with stored PRBCs in relation to patient morbidity and mortality.

Appendix A:

R Code for implementation of SBI using statistical software R (R Foundation, Vienna, Austria)

########################################################
# R Function to create Scalar Age of Blood Index (SBI) #
########################################################

###################
# Function Inputs #
###################
# proportion= A user defined object containing the ordered proportions of
# blood the patient received within each PRBC age category.
#
# data= An optional data frame to attach the calculated SBI value.

####################
# Function Outputs #
####################
# SBI= The calculated Scalar Age of Blood Index variable.
# data= The data frame with attached SBI value.

SBI<-function(proportion=NULL, data=NULL){

# Number of subjects
N<-dim(proportion)[1]

# Number of categories
size<-dim(proportion)[2]

#Non-Linear Least Squares Coding
cdf<-t(apply(proportion[,], 1,cumsum))
Z<- seq(1, dim(proportion)[2], by=1)

#Create SBI Variable
Znorm<-sort(unique(Z))/max(unique(Z))
SBI<-rep(0,N)

for( i in 1:N){
y<-cdf[i,]
mod<-nls(y~I(Znormêxp(power)), control = nls.control(maxiter = 150, tol = 1e-05, minFactor = 1/1024,printEval = FALSE, warnOnly = TRUE), start = list(power = 0),trace = F)

parm<-summary(mod)$coefficients[1]

SBI[i] <- parm #SBI=Scalar Age of Blood Index

}

#Attach SBI to user defined dataframe
if (!is.null(data)){
data$SBI<- SBI
}

returnlist<-list(SBI=SBI, data=data, NULL=NULL)
returnlistfinal<- returnlist[-which(sapply(returnlist, is.null))]
return(returnlistfinal)

}

####################
# END SBI Function #
####################

#Example Dataframe
#mortality is an indicator variable for vital status (1=dead, 0=alive)
#total_0_7 - total_22plus are numeric variables for the quantity of PRBC
#received in each age category


set.seed(20)

mortality <- rbinom(n = 100, 1, .3)
total_0_7 <- round(runif(n=100, min=0, max=20), digits=0)
total_8_14 <- round(runif(n=100, min=0, max=20), digits=0)
total_15_21 <- round(runif(n=100, min=0, max=20), digits=0)
total_22plus <- round(runif(n=100, min=0, max=20), digits=0)

analysis <- as.data.frame(cbind(mortality, total_0_7, total_8_14, total_15_21, total_22plus))

analysis$total_PRBC <- rowSums(analysis[,2:5])

head(analysis)

#Create Blood Proportion Variables
p1<- analysis$total_0_7/analysis$total_PRBC
p2<- analysis$total_8_14/analysis$total_PRBC
p3<- analysis$total_15_21/analysis$total_PRBC
p4<- analysis$total_22plus/analysis$total_PRBC

#Create Proportion Object
pdf<-cbind(p1, p2, p3, p4)

#Run SBI Function with example data
scalar<-SBI(proportion=pdf, data=analysis)

#Example Outcome Analysis (logistic regression)
model<-glm(mortality~ SBI, data=scalar$data, family=binomial(link='logiť))
summary(model)

Appendix B:

Numerical simulation study to assess the mapping of “a” to varying PRBC distributions with 4, 5, 8, and 10 blood age categories.

To demonstrate the accuracy of mapping with the SBI metric, the following presents a numerical simulation study of varying PRBC distributions, with 4, 5, 8, and 10 different blood age categories. For each distribution, 1,000 observations were simulated (similar to the method used in Appendix A). Furthermore, the true blood distribution CDF was calculated for each observation, as well as the SBI metric. The Appendix C Figure below shows the true blood distribution CDF and mapped power function, based on SBI, for 5 simulated observations, for each PRBC distribution. Overall, there is excellent mapping of the power function to the PRBC distribution, based on the SBI metric. On average, across all 1,000 observations, the mean of the absolute values of the difference between the true CDF and the mapped power function were 0.051, 0.049, 0.042, and 0.038 for 4, 5, 8, and 10 blood age categories, respectively. Thus the approach can be used for any number of clinically determined age categories.

Appendix C: