Author + information
- Received August 10, 2015
- Revision received April 11, 2016
- Accepted April 14, 2016
- Published online September 1, 2016.
- Natasha A. Loghmanpour, PhDa,
- Robert L. Kormos, MDb,
- Manreet K. Kanwar, MDc,
- Jeffrey J. Teuteberg, MDb,
- Srinivas Murali, MDc and
- James F. Antaki, PhDa,∗ ()
- aDepartment of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania
- bHeart and Vascular Institute, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania
- cCardiovascular Institute, Allegheny Health Network, Pittsburgh, Pennsylvania
- ↵∗Reprint requests and correspondence:
Dr. James F. Antaki, Department of Biomedical Engineering, Carnegie Mellon University, Scott Hall 4N203, Pittsburgh, Pennsylvania 15213.
Objectives This study investigates the use of a Bayesian statistical model to address the limited predictive capacity of existing risk scores derived from multivariate analyses. This is based on the hypothesis that it is necessary to consider the interrelationships and conditional probabilities among independent variables to achieve sufficient statistical accuracy.
Background Right ventricular failure (RVF) continues to be a major adverse event following left ventricular assist device (LVAD) implantation.
Methods Data used for this study were derived from 10,909 adult patients from the Inter-Agency Registry for Mechanically Assisted Circulatory Support (INTERMACS) who had a primary LVAD implanted between December 2006 and March 2014. An initial set of 176 pre-implantation variables were considered. RVF post-implant was categorized as acute (<48 h), early (48 h to 14 daysays), and late (>14 days) in onset. For each of these endpoints, a separate tree-augmented naïve Bayes model was constructed using the most predictive variables employing an open source Bayesian inference engine.
Results The acute RVF model consisted of 33 variables including systolic pulmonary artery pressure (PAP), white blood cell count, left ventricular ejection fraction, cardiac index, sodium levels, and lymphocyte percentage. The early RVF model consisted of 34 variables, including systolic PAP, pre-albumin, lactate dehydrogenase level, INTERMACS profile, right ventricular ejection fraction, pro-B-type natriuretic peptide, age, heart rate, tricuspid regurgitation, and body mass index. The late RVF model included 33 variables and was predicted mostly by peripheral vascular resistance, model for end-stage liver disease score, albumin level, lymphocyte percentage, and mean and diastolic PAP. The accuracy of all Bayesian models was between 91% and 97%, with an area under the receiver operator characteristics curve between 0.83 and 0.90, sensitivity of 90%, and specificity between 98% and 99%, significantly outperforming previously published risk scores.
Conclusions A Bayesian prognostic model of RVF based on the large, multicenter INTERMACS registry provided highly accurate predictions of acute, early, and late RVF on the basis of pre-operative variables. These models may facilitate clinical decision making while screening candidates for LVAD therapy.
- Bayesian networks
- Bayesian statistics
- left ventricular assist device
- right ventricular failure
- risk stratification
Left ventricular assist devices (LVADs) are increasingly used for management of patients with end-stage heart failure, both as a bridge to cardiac transplantation and as a destination therapy. Post-operative right ventricular failure (RVF) is known to contribute significantly to post-LVAD morbidity and mortality. The risk of developing RVF after LVAD implantation is multifactorial and dependent on hemodynamic variables such as RV preload and afterload as well as clinical variables such as hepatic and renal function, among others. There have been numerous publications examining risk factors associated with RVF over the past decade that have led to the development of several risk scores for RVF (1–13). These scores consist of weighted sums of 4 to 7 risk factors which do not contribute much sensitivity or specificity. Furthermore, accurate prediction of patients at risk to develop RVF after implantation of a continuous flow LVAD depends on the complex and dynamic interplay of multiple pre-operative variables which cannot be adequately captured by traditional multivariate modeling. In contradistinction, Bayesian network (BN) algorithms can account for nonlinear interactions between variables by identifying groups of risk factors and their conditional interdependency.
We sought to develop a Bayesian-based prognostic model of RVF following implantation of a continuous flow LVAD, using the Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS).
This study was approved by the INTERMACS Data, Access, Analysis, and Publication Committee. The Data Coordinating Center at University of Alabama at Birmingham provided deidentified patient data for implantations undertaken between December 2006 and June 2014 (n = 10,909) (Online Table 1). The inclusion criteria for this study was the use of a continuous flow LVAD as the primary implant and age ≥18 years. Patients who received a right ventricular assist device (RVAD) were included as long as the initial implant was an LVAD. Total artificial heart recipients were excluded from this study.
The definition for RVF was based on the INTERMACS definition prior to 2014 (see INTERMACS Appendix A ). We studied 3 RVF endpoints: <48 h (acute onset), 48 h to 14 days (early onset), and >14 days (late onset). These endpoints were chosen to stress the fact that different clinical variables affect the risk of RVF at different time points. Therefore, we considered how the model might be used in clinical practice to highlight differences in the associated set of risk factors, which in turn might provide insights into the mitigation of risk. The first endpoint (acute) refers to the immediate intraoperative and post-operative period (<48 h) in which the surgical team might use the information to consider whether or not to implant a temporary or permanent RVAD. The next period (early, i.e., 48 h to 14 days) generally considers the duration from intensive care unit to initial discharge from hospital. The clinical response to this risk might involve pharmacological management of RV function or peripheral vascular resistance (PVR); or possibly the use of a temporary RVAD. Late endpoint (>14 days) would be used to alert the follow-up care provider to be vigilant about the risk of RVF and to be prepared to intervene if necessary. Also, chronic or late RVF (>14 days) is being increasingly recognized as an adverse event that may occur in patients who do not develop acute or early RVF.
Data entries in the INTERMACS registry exhibited varying degrees of “missing-ness” (Online Table 2). Data elements with excessive missing data (>90%) were excluded from analysis. Of the pre-implantation variables remaining, both numerical and categorical missing data elements were imputed (5 iterations) using the random forest multiple imputation by chained equation (rfMICE) method, using open source R statistical software (15). The average of all 5 iterations was used for the final imputed value.
Bayesian methodology requires discretization of continuous variables (Online Table 3). This was performed by assuming a normal, Gaussian distribution and defining breakpoints at 1 standard deviation (SD) above and below the mean, thereby creating 3 ranges, or classes (below average, average, and above average). Lower boundaries were truncated if the breakpoint was <0. In some cases, a fourth range was defined (well above average: if the distribution had a negative, left-sided skew). Examples of discretized intervals include body mass index BMI (≤22.0, 22.0 to 28.7, 28.7 to 35.3, and ≥35.3 kg/m2), international normalized ratio (INR) (≤0.89, 0.90 to 1.34, 1.35 to 1.80, and ≥1.81), and central venous pressure (≤7.6, 7.7 to 11.4, 11.5 to 15.2, and ≥15.3). The above discretization was performed using commercially available statistical software (SPSS version 22.0, IBM, Armonk, New York).
Bayesian networks (16) incorporate informational relationships and process individual patient data to predict probable outcomes for survival and adverse events. These networks can encode both qualitative and quantitative knowledge and provides a rigorous framework to perform inferences from predictive variables that are readily interpreted. These inferences are often represented diagrammatically, in which nodes represent independent variables and directed edges (arrows between nodes) represent influences between those variables. Absence of an arrow between a pair of nodes implies independence between those variables. This adds to the practicality of BNs for this application. BNs are equipped with conditional probability tables associated with each node that describe both the direction and the magnitude of influence between variables. The methods used for the present study evolved from our prior experience with machine learning for decision support applied to various VAD cohorts (6–8,17–23). For this study, we used tree-augmented naïve Bayesian architecture, which adds 1 level of complexity to the naïve Bayes network. Tree-augmented naïve architecture allows independent variables to both directly and indirectly impact the outcome through their influences on other variables. All Bayesian models were graphed using GeNIe version 2.0 software developed at the University of Pittsburgh School of Information Science (24).
Selection of variables
After we eliminated sparse variables with excessive missing data, redundancies by the clinical authors (e.g., age and contraindication for VAD due to age), and irrelevant variables (e.g., educational level), further variables were eliminated that would cause over-fitting the model to the data. In the present study, this was measured by information gain (25), which is based on the same principle as decision trees. This process provides ranking of variables based on their influence on outcome.
Derivation of model structure
All BN classifiers were derived from an independent dataset consisting of a training set of approximately 90% of the data records and a testing set from the remaining approximate 10%, also known as 10-fold cross-validation. This same process was repeated for evaluating the performance of models. The reduced datasets for each of the 3 RVF time points were reviewed by the clinical authors to further refine the variables to be included and remove redundancies that might have been included in the registry data (e.g., representing hemoglobin and hematocrit as separate variables). The interested reader is referred to our previously published study (18) for further details of the procedure.
RVF score comparison
We compared the performance of our models with that of the RVF risk score (RVFRS) published by Matthews et al. (5) and the score by Drakos et al. (3) as these were the 2 most cited and widely used scores for RVF in an LVAD population. The RVFRS was calculated by summing points awarded for the presence of a vasopressor (4 points) and concentrations of aspartate aminotransferase (AST) of ≥80 IU/l (2 points), bilirubin ≥2.0 mg/dl (2.5 points), and creatinine ≥2.3 mg/dl (3 points). The resulting score was stratified as low risk (RVFRS of ≤3.0, and an RVF likelihood ratio of 0.49), medium risk (RVFRS 4.0 to 5.0, 2.8 likelihood ratio), and high risk (RVFRS ≥5.5, 7.6 likelihood ratio). The Drakos score was calculated as the sum of points assigned for the existence of each of 8 perioperative variables: destination therapy patients (3.5 points), intra-aortic balloon pump (4 points); pulmonary vascular resistance (PVR) of ≤1.7 Woods units (WU) (1 point), a PVR of 1.8 to 2.7 (2 points), a PVR of 2.8 to 4.2 (3 points), and a PVR of ≥4.3 (4 points); inotrope dependency (2.5 points); obesity, defined as a BMI of ≥30 kg/m3 (2 points); angiotensin-converting enzyme inhibitor and/or angiotensin II receptor blocker (−2.5 points), and β-blocker (2 points). The resulting risk scores are stratified as low-risk: score of ≤5.0, 11% risk RVF; medium-risk: score of 5.5 to 8.0, 37% risk RVF; high-risk: score of 8.5 to 12, 56% risk RVF, and very–high-risk: score of ≥12.5, 83% risk RVF. When they were applied to INTERMACS data, missing values for either score were imputed using the same rfMICE methods described previously (Table 1).
To compare the performance and results of the Bayesian models, RVFRS, and Drakos score, we used the area under the receiver operator characteristics curve (AUC). ROC curves were plotted using SPSS version 22.0 software (IBM Corporation, Armonk, New York). For the Bayesian models, we also report accuracy, sensitivity, and specificity computed using GeNIe software (24). These metrics cannot be calculated for the risk scores, as they do not provide an actual prediction of RVF, but instead stratify patients into risk levels associated with certain percentages of RVF prevalence.
There were a total of 10,909 patients who met the inclusion criteria. The majority were between 50 and 69 years of age (n = 6,568; 60%); 78% (n = 8,606) were male; 3,811 patients (35%) received the LVAD as destination therapy, and 6,901 patients (63%) were listed as bridging to transplantation. Ischemia was listed as the cause for cardiomyopathy in 4,466 patients (41%). At the time of implantation, 17% (n = 1,900) were categorized as INTERMACS profile 1, 38% (n = 4,169) as INTERMACS profile 2, and 26% (n = 2,875) as INTERMACS profile 3. Overall, RVF was diagnosed in 18.5% of the patients (n = 2,024), acute RVF in 2.7% of patients (n = 293), early RVF in 9.5% of patients (n = 1,036), and late onset RVF in 6.4% of patients (n = 695).
Accuracy, AUC, sensitivity, and specificity are summarized in Figure 1 and Table 2, respectively. Accuracy levels of all 3 models ranged between 91% and 97%, and their AUC ranged between 0.83 and 0.90, significantly outperforming all previously published risk scores. Bayesian models for acute (<48 h), early (between 48 h and 14 days), and late (>14 days) RVF are illustrated in Figures 2, 3, and 4. Variables are color-coded according to 4 categories: hemodynamics, medications, laboratory test results, and demographics.
Acute RVF model (<48 h)
The acute RVF model contains 33 variables directly connected to the outcome, each of which being related to one other independent variable (Figure 2). Although the order of influence changes as variables are observed or specified (i.e., while calculating the risk for a specific patient), the variables most predictive of RVF, given the population distribution, included systolic pulmonary artery pressure (PAP), white blood cell (WBC) count, left ventricular ejection fraction, cardiac index, sodium levels, lymphocyte percentage, hemoglobin, and heart rate.
Early RVF model (48 h to 14 days)
The early RVF model contains 34 variables with 67 direct relationships (Figure 3). The top 10 variables most predictive of RVF, given the population distribution, were systolic PAP, pre-albumin level, lactate dehydrogenase level, INTERMACS profile, right ventricular ejection fraction, pro-B-type natriuretic peptide, age, heart rate, tricuspid regurgitation, and BMI.
Late RVF model (>14 days)
The late RVF model also contains a different subset of 34 variables with 67 direct relationships. (Figure 4). Variables most predictive of RVF, given the population distribution, include PVR, a model for end-stage liver disease (MELD) score, device strategy (destination therapy versus bridge to transplantation), use of inotropes, primary diagnosis (cause of HF), albumin, lymphocyte percentage, mean PAP, and diastolic PAP.
Drakos risk score and RVFRS
For benchmark comparison, we computed the RVFRS as well as Drakos risk score using the same INTERMACS registry data set. Corresponding AUCs were 54.7% and 49.8% for the RVFRS and Drakos scores, respectively. It can be seen in Figure 1 that these curves closely approximate the line of unity, with the Drakos risk score performing worse than random chance. These were considerably lower than reported in their originally published studies (74% and 73%, respectively) (3,5).
When the Drakos score was first introduced, it stratified survival among 4 different categories (<5.0, 5.5 to 8, 8.5 to 12, and >12.5 points). The corresponding 30-day survival rates after LVAD were reported as 97%, 92%, 85%, and 83% (log-rank for linear trend, p < 0.029) and the 180-day survival rates were reported as 94%, 85%, 75%, and 72% (p < 0.009). When the Drakos score was applied to the INTERMACS data, it did not significantly differentiate survival rates among the 4 categories. However, it is important to notice the relatively even distribution of RV failure across the different groups: low: n = 2,573, 16% RVF; medium: n = 3,670, 17% RVF; high: n = 3,737, 20% RVF; and very high: n = 929, 24% RVF; in the INTERMACS data compared to the original derivation cohort (Online Table 4).
When it was first published, RVFRS was shown to significantly stratify survival at 180 days: 66 ± 9%, 80 ± 8%, and 90 ± 3% for the high, medium, and low RVFRS strata, respectively, and a log rank for linear trend of p < 0.0045, showing an increased risk of mortality with greater RVFRS. Although the risk strata of the RVFRS had significantly different survival when applied to the INTERMACS cohort, it did so to a lesser degree. The high-risk stratum had a distinctly lower survival rate, but the medium and low-risk strata overlay each other by approximately 9 months. Unlike the Drakos score, the RVFRS was highly skewed toward the low-risk stratum (n = 9,623, 19% RVF), with relatively few patients identified as medium risk (n = 856, 15.8% RVF) and high risk (n = 430, 17.2% RVF).
Despite improving VAD technology and increasing focus on pre-emptive strategies to medically optimize the patient’s physiology pre-operatively, adverse events are common and significantly impact survival and quality of life after LVAD implantation. This is partly due to the heterogeneous and complex nature of these patients, rendering generalized recommendations for patient selection or those derived from small patient cohorts only partly helpful. Specifically, for RVF, it is critical to identify the patients who will successfully tolerate isolated LVAD implantation without RV failure at the time of surgical decision making. Recent studies using the INTERMACS registry have been performed to identify individual clinical variables such as INTERMACS profile and elevated PVR that might be predictive of RVF (26).
These analyses revealed a variety of risk factors from disparate categories (e.g., nutrition, hemodynamics, laboratory test results, history, and others). These data, in turn, can inform clinical decision making. However, in clinical practice, evaluation for risk for RVF is a dynamic process that incorporates many pathways of information, including physical examination findings, laboratory results, imaging, and hemodynamic data. Existing risk scores attempt to combine a multiplicity of factors by using a weighted summation, but in reality, some (most) risk factors are interrelated, that is, they will affect dissimilar patients differently. Depending on prevailing conditions, some factors may increase the risk in one patient yet reduce the risk in another. For example, the AST concentration of ≥80 IU/liter allows for 2 points in the RVFRS, which may elevate an otherwise medium-risk patient to a high-risk category. Elevated AST is usually a reflection of liver congestion and aggressive optimization within days preceding an LVAD could result in lowering this value to <80 IU/l transiently. This would then recategorize the patient from a higher to lower risk group, but in clinical practice, we all realize the dynamic interplay between cardiac output, RV failure, elevated transaminases, and renal dysfunction. Even though a lower AST level implies a lower pre-operative risk, the fact that it was achieved using inotropes, aggressive diuresis, and possibly temporary balloon pump support days before LVAD placement may only imply a more subtle improvement in the risk of RVF in this patient than represented by RVFRS. In the current study we found that the accuracy of both the RVFRS and Drakos score in predicting RVF in the INTERMACS registry was virtually equivalent to the flip of a coin. We acknowledge that these scores might have performed better if calibrated to the same training set as used for our Bayesian models, but it would be mathematically impossible to outperform the Bayesian models when using a weighted summation of variables with fixed coefficients.
We previously endeavored to model the complexity of determining the risk of RVF (based on the need for an RVAD) using a decision tree classifier (6–8). This provided promising results but was limited to a single center and a combination of pulsatile and continuous flow LVADs. The Bayesian models reported here are particularly suited for combining large sets of risk factors because they are based on conditional probabilities of the likelihood of RVF for a given combination of interrelated variables. In this way, these algorithms better reflect human logic in prioritizing dynamic clinical information, while benefiting from the corpus of evidence provided by the INTERMACS registry. To our best knowledge, this is the first report of a prognostic model of RVF following continuous flow LVAD, using the INTERMACS database and adopting machine learning methods for statistical analysis.
In the current study, each of 3 independent models for RVF consisted of 33 to 34 pre-operative variables from several categories: demographics, laboratory values, medications, and hemodynamics. This allowed for inclusion of variables such as measures of nutrition (pre-albumin, cholesterol, lymphocyte count), functional class (6-min walk distance), rehospitalizations (recent cardiac hospitalization) in addition to the more apparent hemodynamic (PAP), laboratory (BNP, sodium), and imaging (LV end diastolic diameter) factors in the calculation of risk assessment. Because the selection of variables and their interdependence were determined automatically by computer algorithm, not all variables appear to be intuitive, and some of the interrelationships are difficult to interpret biologically. Although biological plausibility is not always necessary for an accurate predictive model, it does lend credibility to the associations. Fortunately, the structure of the Bayesian tree is relatively “flexible” inasmuch as interconnections can be changed, removed, or added manually without necessarily impairing the accuracy of the model. Therefore, the clinician has the freedom to modify the structure (within bounds) to correspond more logically with his/her reasoning and understanding of the underlying physiology/pathology.
Limitations of this study include missing data, skewedness toward absence of RVF (which reduces the sensitivity), and a variety of aberrations that are intrinsic to a retrospective study using a registry data set. Multiple imputation methods were investigated to address missing data entries. The choice to exclude data with >90% was determined by trial and error but, we acknowledge, was somewhat arbitrary. However most of the variables included in the 3 models had fewer than 5% missing data, and only a few variables had missing data exceeding 50%. Choosing a lower cutoff would have reduced the errors associated with imputation but at the cost of eliminating potentially important variables. An unfortunate consequence of lack of data was our inability to include the severity of RVF in the model. Also, we acknowledge that patients who were deemed to be at too great a risk for RVF and who therefore never received an LVAD were excluded from the registry. Additional variables that may impact the risk of RVF in clinical practice, such as bypass time, blood products used, and dose of inotropes were not available in the INTERMACS registry and thereby for our analysis. We also recognize errors due to the variability of timing of data entry into the registry, particularly those variables that are most dynamically changing in practice. Finally we acknowledge that the criteria for diagnosing RVF in the INTERMACS dataset is heterogeneous. Not all patients who were declared to have RVF received an RVAD. (Surprisingly, there are cases in the INTERMACS registry of patients who did receive and RVAD who were NOT identified as having RVF.) Many of the aforementioned limitations will be addressed in an ongoing multi-site prospective study.
This is the first application of Bayesian analysis to predict the risk of RVF in a large, multicenter LVAD cohort. Three separate Bayesian models for acute, early, and late RVF substantially outperformed the existing risk scores in their ability to predict the risk of RV failure. These models show great promise as a reliable and accurate risk stratification tool for clinical decision making (Figure 5). (The reader is invited to contact the corresponding author for access to the beta version of the Web-based application.)
COMPETENCY IN MEDICAL KNOWLEDGE: When the Bayesian network model is implemented with a particular patient, it can accept numerous combinations of input variables to compute risk of RVF. In other words, the model can predict the likelihood of RVF even with a limited, incomplete set of data. However, if additional data points are added (as they become available), the predictive ability of the algorithm improves incrementally. To illustrate, we consider a VAD patient for whom, initially, no additional data are available. Based on the current INTERMACS registry report, the baseline probability for late RVF is 21%. The addition of high systolic PAP (e.g., 65 mm Hg) increases this risk to 62%. Inclusion of CI, for example, of 2.5 increases the risk of RVF to 77%, and then to 92.4% if the patient has an elevated WBC count of 10 × 109/l. In a second hypothetical high-risk patient scenario with the same baseline risk and systolic PAP, entering a condition of hypotension with a systolic blood pressure ranging from 86 to 102 mm Hg increases the calculated risk of RVF to 66%. If the patient has moderately reduced pre-operative right ventricular ejection fraction, the model now calculates the risk to be 83%. In a third scenario, addition of high lymphocyte count increases the 21% baseline risk to 27%, and further addition of mean PAP of ≥36 mm Hg increases the risk to 49%. These scenarios exemplify the dynamic interdependency of various risk factors on the final clinical outcome, which is unique to Bayesian analysis. This provides the possibility to examine the changes in risk over time, as well as explore hypothetical scenarios by manually entering variables. One could even envision entering variables interoperatively, thereby acknowledging recent reports of the importance of intraoperative events to the occurrence of post-operative RV failure.
TRANSLATIONAL OUTLOOK: We recognize that the utility of these Bayesian models, containing over 30 variables, will depend greatly on the ease/difficulty with which they can be calculated. For this reason, ongoing work aims to provide accessible and easy-to-use decision support tools for physicians and patients engaged in LVAD discussion. Entitled Cardiac Outcomes Risk Assessment (CORA), this application will be provided in the form of an interactive, graphic interface accessible on smartphones and other devices that would be integrated with commonly available electronic medical records (such as Epic). It will provide the user access to all the Bayesian models derived for predicting adverse events (including RVF) and mortality in a patient being evaluated for an LVAD.
The authors thank the Data Access, Analysis, and Publications Committee of INTERMACS for allowing us to use their registry for the study, and we specifically thank Dr. James Kirklin, Dr. Francis Pagani, and Dr. David Naftel. The authors also thank Susan Meyers and Grant Studdard for administrative, database, and statistical assistance with INTERMACS, and they are grateful for contributions from Dr. Marek Druzdzel and Decision Systems Laboratory, University of Pittsburgh.
For supplemental tables, please see the online version of this article.
Funding for this work was provided by National Institutes of Health, Division of National Heart, Lung, and Blood Institute grants R41 HL120428 STTR Phase I Cardiac Health Risk Stratification System, R01 HL122639, CORA: a Personalized Cardiac Counselor for Optimal Therapy, and R01 HL086918, Identification and Optimization of Ventricular Recovery of Patients on Ventricular Assistance. Data for this study was provided by the International Registry for Mechanical Circulatory Support (INTERMACS), funded from the National Heart, Lung, and Blood Institute, National Institutes of Health, under Contract No. HHSN268201100025C. Dr. Kanwar has received a research grant through her institution from Thoratec. Dr. Teuteberg has industry and financial relationships with HeartWare, Abiomed, CareDx, Thoratec, and Sunshine Heart. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.
- Abbreviations and Acronyms
- body mass index
- Inter-Agency Registry for Mechanically Assisted Circulatory Support
- left ventricular assist device
- pulmonary artery pressure
- peripheral vascular resistance
- random forest multiple imputation by chained equation
- receiver operator characteristics
- right ventricular failure
- right ventricular failure risk score
- structural modeling, inference, and learning engine
- visual analog scale
- white blood cell
- Received August 10, 2015.
- Revision received April 11, 2016.
- Accepted April 14, 2016.
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