Role of platelet counts to spleen length ratio and platelet-albumin to spleen length ratio as non-invasive predictors of esophageal varices in chronic liver disease patients: A cross-sectional study in Eastern India

ABSTRACT

Objective:

This study aimed to evaluate and compare the diagnostic performance of the Platelet/Spleen Length (P/SL) ratio and a novel metric, the Platelet-Albumin/Spleen Length (P*Alb/SL) ratio, in predicting esophageal varices (EVs) among patients with chronic liver disease (CLD).

Methods:

A cross-sectional study was conducted over a period of 6 months, enrolling 121 newly diagnosed CLD patients without prior treatment for EV or CLD. Data collected, included demographic and clinical details, platelet count, serum albumin, and spleen length via ultrasonography. All patients underwent upper gastrointestinal endoscopy to assess EVs. The P/SL ratio was calculated by dividing platelet count (cells/μL) by spleen length (mm), and the Platelet-Albumin to Spleen Length (P*Alb/SL) ratio by dividing the product of platelet count and serum albumin (g/dL) by spleen length. Diagnostic performance was evaluated using receiver operating characteristic curve analysis and calculating sensitivity and specificity.

Results:

The P/SL ratio demonstrated an optimal cutoff of 856 with an area under the curve (AUC) of 0.924 (95% CI: 0.849–0.998), sensitivity of 92%, and specificity of 85.7%. The P*Alb/SL ratio had an optimal cutoff of 2194.5, achieving an AUC of 0.928 (95% CI: 0.864–0.992), sensitivity of 81%, and specificity of 95.2%. Both ratios exhibited strong diagnostic performance, with no significant difference between their AUCs (P = 0.712). The diagnostic odds ratios were 69 and 85.26 for the P/SL and P*Alb/SL ratios, respectively.

Conclusion:

The P/SL ratio proved to be an effective screening tool for EVs in CLD, with high sensitivity for early detection. The P*Alb/SL ratio showed similar or slightly superior diagnostic performance, with high specificity and fewer false positives, making it ideal for confirmation. Together, the sequential tandem use of P/SL followed by P*Alb/SL provides a practical strategy for risk stratification and patient management, while reducing reliance on the endoscopy and improving resource allocation, especially in resource-limited settings.

Introduction

Chronic liver disease (CLD) is a global health challenge that leads to the significant morbidity and mortality.[1] It encompasses a spectrum of liver conditions that progress gradually, often resulting in liver cirrhosis and its associated complications, one of the most severe being portal hypertension.[2] Portal hypertension can cause the development of esophageal varices (EVs), which are abnormally dilated veins in the lower esophagus prone to rupture. Such ruptures can lead to potentially fatal gastrointestinal bleeding episodes, with mortality rates reported around 30% for re-bleeds, underscoring the need for early detection and management of EVs.[3]

The prevalence of esophageal varices in patients with cirrhosis is estimated to be around 50%,[4] and in those without existing varices, the annual risk of development is approximately 8%.[5] Given this risk, routine screening and timely intervention are critical to improving patient outcomes in CLD. Endoscopy remains the gold standard for diagnosing EVs. However, it is invasive, often uncomfortable, and resource-intensive, making it challenging to perform regular screenings, especially in low-resource settings.[6] Consequently, there is a pressing need for non-invasive and cost-effective tools that can reliably predict the presence of EVs in high-risk patients with CLD.

A variety of non-invasive markers have been explored to this end, including platelet count, spleen size, liver stiffness measurements, and serological biomarkers.[7] Among these, the platelet count to spleen length ratio (P/SL ratio) has shown promise as a potential predictor of EVs. This metric is based on the pathophysiology of portal hypertension, which causes splenic sequestration of platelets (leading to thrombocytopenia) and splenomegaly.[8]

Studies have suggested that a low P/SL ratio can be associated with elevated portal pressure, correlating with the likelihood of varices in specific populations.[9,10] However, the evidence remains inconsistent, with variable sensitivity and specificity across studies, with scarcity of data from developing countries like India. Furthermore, discrepancies in the cutoff values across studies reflect the lack of standardization, complicating its broader application in clinical settings.[10,11,12,13] Given these limitations, there is a need for further research to establish a reliable cutoff and validate the P/SL ratio’s effectiveness across diverse patient groups.

This study seeks to bridge these gaps in current knowledge, as establishing a reliable P/SL ratio cutoff could help clinicians identify patients who require endoscopic screening, improving the early detection of EVs and enhancing patient care. In resource-limited settings, a reliable screening parameter could help reduce the burden of endoscopic procedures for detecting varices.

Although a key limitation of P/SL ratio is that it primarily reflects the effects of portal hypertension, without accounting for the liver’s synthetic function, which also plays a significant role in the development of EVs.[14] Serum albumin, a marker of hepatic synthetic function, decreases in CLD as liver dysfunction progresses.[15] By incorporating albumin into the P/SL ratio to create a new ratio (Platelet-Albumin to Spleen Length, P*Alb/SL), this study introduces a novel metric that accounts for both the hematological changes due to portal hypertension and the degree of hepatic synthetic dysfunction. This modification aims to enhance the diagnostic accuracy of non-invasive predictors by capturing the multifactorial nature of EV pathogenesis.

Thus, this study aimed to evaluate and compare the diagnostic utility of the P/SL ratio and the P*Alb/SL ratio as non-invasive predictors of esophageal varices in CLD patients with the goal of identifying a more comprehensive and reliable metric for early and reliable detection, in Eastern India.

Methods

Study design and setting

This cross-sectional study was carried out in the Department of General Medicine and Gastroenterology at a hospital in Eastern India.

Study duration

The study was conducted over a period of 6 months from July 2023 to December 2023.

Study population

The study included newly diagnosed cases of CLD who had not been previously diagnosed with EVs, received no treatment for EVs or CLD in the past, or experienced hematemesis. Eligible participants were adults (aged ≥18 years) of any gender. Exclusion criteria included patients with active upper gastrointestinal (GI) bleeding, patients presenting in sepsis, a history of endoscopic sclerotherapy or band ligation for EVs, prior surgical interventions for portal hypertension (e.g. stents), use of beta-blockers, hematologic conditions such as thrombocytopenia, history of recent viral infections within the last 3 months which could affect the platelet count, and those who declined to provide consent.

Sample size

If 80% of the population has the factor of interest and a total population size of 150, a minimum sample size of 94 was calculated using the online statistical calculator- Statulator to estimate the expected proportion with 5% absolute precision and 95% confidence.[12]

Sampling technique

This study employed a complete enumeration (i.e. consecutive sampling) strategy, wherein all patients presenting to the hospital, who met the pre-defined inclusion and exclusion criteria were enrolled during the study period from July 2023 to December 2023. No random sampling or case selection was performed, minimizing selection bias. Eligibility was assessed by reviewing clinical and laboratory data at admission, ensuring that every qualifying case within the timeframe was captured.

Study protocol

The study enrolled patients from the outpatient (OPD) and inpatient (IPD) departments of General Medicine and Gastroenterology, who were screened for the diagnosis of CLD. Informed consent was obtained from each participant prior to data collection. Data collection included demographic and clinical details. Laboratory investigations conducted during the initial visit included platelet count and serum albumin levels. For radiological assessment, spleen length was measured using a Samsung RS 80 ultrasound machine equipped with a 4–6 MHz curvilinear probe, with measurements taken in the right decubitus position by a single operator to ensure accuracy and remove inter-observer measurement bias. As these investigations, including complete blood count (that includes platelet count), serum albumin (to assess liver synthetic function), and abdominal ultrasound, are routinely performed for the evaluation of suspected CLD, they were not conducted solely for research purposes. Therefore, while the patients did bear the cost of these procedures, no additional expenses were incurred specifically for participation in the study.

As per established guidelines, all CLD patients are recommended to undergo upper GI endoscopy for the evaluation of esophageal varices.[16,17] Accordingly, upper GI endoscopy was then performed for all patients using an Olympus endoscopy system to assess the presence and grading of esophageal varices. The evaluation was carried out by a gastroenterology team following standardized protocols for variceal screening in CLD patients.

Parameters:

• Platelet count-to-spleen length (P/SL): This ratio was expressed as a number and calculated by dividing the platelet count (measured in cells/μL) by the bipolar length of the spleen (measured in millimeters) obtained through ultrasonography.

• Platelet-Albumin/Spleen Length (P*Alb/SL): This ratio was calculated by multiplying the platelet count (cells/μL) by serum albumin levels (g/dL) and dividing the product by the bipolar spleen length (mm).

Statistical analysis

Data were organized and coded in Microsoft Excel. Statistical analyses were performed using IBM SPSS ver. 26.0 (IBM Corp., Armonk, NY, USA). Continuous variables such as platelet count, serum albumin level, spleen length, etc., were tested for normality using Q-Q plots and presented as mean ± standard deviation (SD) for normally distributed data or median ± interquartile range (IQR) for non-normally distributed data. Categorical data, such as gender, age group, grade of esophageal varices, etc., were reported as frequencies and percentages. T-test was used to compare means of various variables between those who were found to have varices and those who did not and the mean differences along with their standard error of difference (SE) were reported. Receiver operating characteristic (ROC) curve analysis was conducted to assess the diagnostic performance of the P/SL ratio and P*Alb/SL ratio, determining the area under the curve (AUC) and optimal cut-off value using Youden’s Index. Key diagnostic metrics, including sensitivity, specificity, positive likelihood ratio (LR+), negative likelihood ratio (LR−), and diagnostic odds ratio (DOR), were also calculated. DeLong’s test was used to compare the AUCs of the two predictors.

Ethical considerations

The study was conducted in accordance with the principles of the Declaration of Helsinki, following approval from the institutional ethics committee (Ref. No. AIIMS/Pat/IEC/PGTh/Jan22/45). Written informed consent was obtained from all participants prior to their inclusion in the study, and strict confidentiality was maintained with the participant data.

Results

A total of 121 study participants were included in the study. The majority of the patients i.e. 59 (48.8%) were aged between 41 and 60 years, followed by 30 (24.8%) in the 61–80 age group, and 29 (24%) in the 21–40 age group. Among them, 98 were male (81%), with females comprising 23 (19%) of the cohort.

Esophageal varices were present in 100 (82.6%) of patients, while 21 (17.4%) had no varices. Among those with varices, the most common classification was Grade III with 41 (33.9%) patients, followed by Grade II with 31 (25.6%) and Grade I with 25 (20.7%) patients. Grade IV varices were the least common, observed in only 3 (2.5%) cases [Table 1].

Table 1.

Demographic details of the study participants (n=121)

Variable	Categories	n (%)
Age (years)	20 or less	2 (1.7%)
	21–40	29 (24%)
	41–60	59 (48.8%)
	61–80	30 (24.8%)
	81 or more	1 (0.8%)
Gender	Male	98 (81%)
	Female	23 (19%)
Esophageal Varices	Present	100 (82.6%)
	Absent	21 (17.4%)
Classification of Varices (in cases present)	Grade I	25 (20.7%)
	Grade II	31 (25.6%)
	Grade III	41 (33.9%)
	Grade IV	3 (2.5%)

Patients with esophageal varices had significantly lower mean platelet counts (91.63 ± 35.1 vs. 157.33 ± 55.4 thousand cells/μL; P < 0.001) and serum albumin levels (2.64 ± 0.3 vs. 3.04 ± 0.2 g/dL; P < 0.001) compared to those without varices. Additionally, spleen length was notably higher in patients with esophageal varices (153.72 ± 25.9 mm vs. 126.33 ± 20.8 mm; P < 0.001).

The P/SL ratio was markedly lower in patients with esophageal varices (616.62 ± 342 vs. 1283.54 ± 502.9; P < 0.001), as was the P*Alb/SL ratio (1690.55 ± 1147.9 vs. 3924.98 ± 1573.5; P < 0.001) [Table 2].

Table 2.

Distribution of parameters among CLD patients with and without esophageal varices (n=121)

Parameter	Esophageal Varices Absent Mean (SD)	Esophageal Varices Present Mean (SD)	Mean Difference (SE)	P
Platelet Count (1,000 cells/μL)	157.33 (55.4)	91.63 (35.1)	−65.7 (9.4)	<0.001
Spleen Length (mm)	126.33 (20.8)	153.72 (25.9)	27.39 (6)	<0.001
Albumin (g/dL)	3.04 (0.2)	2.64 (0.3)	−0.4 (0.1)	<0.001
Platelet/Spleen Length	1283.54 (502.9)	616.62 (342)	−666.92 (89.8)	<0.001
Platelet-Albumin/Spleen Length	3924.98 (1573.5)	1690.55 (1147.9)	−2234.43 (362)	<0.001

For P/SL ratio, the optimal cutoff was determined to be 856, with a Youden’s Index of 0.777. The AUC was excellent at 0.924 (95% CI: 0.849–0.998). For P*Alb/SL ratio, the optimal cutoff was 2194.5, with a Youden’s Index of 0.762. The AUC for this predictor was similarly high at 0.928 (95% CI: 0.864–0.992). The various cutoffs and their corresponding sensitivity and specificity values are given in the Supplementary Material. DeLong’s test showed no significant difference between the AUCs of the two predictors (P = 0.712) [Figure 1].

Figure 1.

Receiver operating curves of the predictors for esophageal varices in chronic liver disease patients

For the P/SL ratio, the sensitivity was 92%, indicating strong ability to detect true positives, while the specificity was 85.7%, reflecting the reliable exclusion of false positives. The LR + was 6.44, showing a moderate increase in the likelihood of esophageal varices with a positive result, and the LR − was 0.093, suggesting a low probability of the condition with a negative result. The DOR, which combines sensitivity and specificity into a single measure of diagnostic effectiveness, was 69.

For the P*Alb/SL ratio, the sensitivity was 81%, with a specificity of 95.2%, indicating excellent accuracy in ruling out false positives. The LR + was 17.01, signifying a substantial increase in the likelihood of esophageal varices with a positive result, while the LR − was 0.199, showing a moderate reduction in the probability of the condition with a negative result. The DOR was 85.26, highlighting its stronger overall diagnostic utility [Table 3].

Table 3.

Diagnostic performance of the predictors for esophageal varices in chronic liver disease patients (n=121)

Predictor	AUC	95% CI of AUC	Sensitivity	Specificity	PPV	NPV	LR+	LR−	DOR
Platelet Count/Spleen Length (Cutoff: 856)	0.924	0.849–0.998	92%	85.7%	96.8%	69.3%	6.44	0.093	69
Platelet Count-Albumin/Spleen Length (Cutoff: 2194.5)	0.928	0.864–0.992	81%	95.2%	98.8%	51.4%	17.01	0.199	85.26

Discussion

This study highlights the diagnostic potential of two non-invasive markers—the P/SL ratio and the P*Alb/SL ratio—in predicting EV among CLD patients. The P/SL ratio achieved an impressive diagnostic accuracy with an AUC of 0.924, high sensitivity (92%), and specificity (85.7%), with a cut-off value of 856 determined via Youden’s Index. Similarly, the P*Alb/SL ratio exhibited a slightly higher AUC of 0.928, accompanied by greater specificity (95.2%) but slightly lower sensitivity (81%), with a cut-off value of 2194.5. While both predictors demonstrated comparable overall diagnostic performance (P = 0.712), their differing sensitivity and specificity profiles highlight their complementary roles in risk stratification and patient management.

The pathophysiological basis for the P/SL ratio lies in the effects of portal hypertension, a hallmark of advanced CLD. Portal hypertension leads to splenic sequestration of platelets, resulting in thrombocytopenia.[18] However, other factors can also contribute to the thrombocytopenia in CLD patients such as reduced production of thrombopoietin by the liver or immune-mediated platelet destruction.[19,20] Various studies have shown that thrombocytopenia and splenomegaly are the independent predictors of presence of esophageal varices.[21,22] Therefore, assessing the platelet count relative to spleen length is considered suitable, as this ratio accounts for platelet sequestration within the spleen and address the limitations of using platelet count alone, which may not accurately reflect the impact of portal hypertension. Moreover, a study by González-Ojeda et al.[12] mentions that in diagnosing esophageal varices, splenomegaly tends to exhibit high sensitivity but low specificity, while thrombocytopenia demonstrates low sensitivity with moderate specificity making the P/SL ratio a valuable composite metric for improved diagnostic accuracy.

A meta-analysis by Chen et al.,[23] which included 6,287 patients, reported a pooled AUC of 0.872, pooled sensitivity of 84%, and pooled specificity of 78%, highlighting the P/SL ratio’s effectiveness as a non-invasive tool for esophageal varices screening. In comparison, our study demonstrated a higher AUC of 0.924 and sensitivity of 92%, along with a low negative likelihood ratio (0.093), establishing the P/SL ratio as a robust screening tool. Regarding the cut-off values, significant variability has been observed across studies. Giannini et al.[10] and Schwarzenberger et al.[24] reported a cut-off value of 909, while González-Ojeda et al.[12] identified a cut-off value of 884.3. In our study, the identified cut-off value was 856. These discrepancies in cut-off values may be attributed to the differences in patient demographics in these studies, particularly racial characteristics, as populations with larger body frames and organ sizes, such as Caucasians and North Americans, may influence the ratio. This underscores the need for population-specific cut-off determination to optimize the utility of the P/SL ratio in diverse clinical settings.[12] Additionally, lifestyle factors such as alcohol consumption, a common cause of CLD, directly impact platelet count by reducing platelet lifespan, adding another layer of variability to the ratio’s application in clinical practice.[25] Furthermore, the P/SL ratio does not take into account the synthetic function of the liver which more directly correlates with severity of CLD.

Various studies have identified serum albumin as an independent predictor of esophageal varices in CLD patients.[26,27] Thus, in this study, we chose to incorporate serum albumin into the P/SL ratio to create and evaluate an alternative model, the P*Alb/SL ratio. We hypothesized that the modified ratio will also incorporate the synthetic function of the liver and thus, will reflect a broader systemic effect of CLD, extending beyond the more localized impact of spleen size and platelet count.

Serum albumin, a key indicator of liver synthetic function, provides additional insights into the overall severity of CLD.[28] The pathophysiology of hypoalbuminemia in CLD involves reduced oncotic pressure, leading to third spacing of fluids, which exacerbates hypovolemia and activates compensatory mechanisms, thereby increasing portal pressure. Hypoalbuminemia also promotes splanchnic vasodilation due to impaired vascular tone, further elevating portal blood flow and contributing to variceal formation. Moreover, low albumin levels reflect systemic inflammation and severe liver dysfunction, which worsen vascular remodeling and portal hypertension, leading to development of esophageal varices.[28,29]

The P*Alb/SL ratio showed a slightly higher AUC (0.928) compared to the P/SL ratio, reflecting a marginal improvement in diagnostic performance. Its specificity (95.2%) was notably higher with a significantly larger LR + of 17.01, which means it has a much lower likelihood of false-positive results, reducing unnecessary endoscopic interventions. However, this comes at the expense of sensitivity, which dropped to 81%. This trade-off suggests that while the P*Alb/SL ratio excels in confirming EV presence, it might miss a subset of patients, especially those in the early stages of variceal development. Consequently, the slight reduction in sensitivity limits its standalone use as a screening tool.

The statistical comparison using DeLong’s test revealed no significant difference between the AUCs of the two ratios (P = 0.712). However, it is worth noting that the DOR for the P*Alb/SL ratio was higher than that of the P/SL ratio (85.26 vs. 69). Their differing sensitivity and specificity profiles suggest that their utility may vary depending on clinical priorities and available healthcare resources. To optimize the detection and management of esophageal varices, these tests should be employed sequentially in tandem—one as a screening tool to identify potential high-risk patients, followed by the other for confirmation, thereby reducing reliance on routine endoscopy.

For instance, in resource-limited clinical settings with economically disadvantaged patient populations, prioritizing high sensitivity by using the P/SL ratio as a first-line screening tool in tandem with the P*Alb/SL ratio for confirmation could help allocate resources more efficiently. This approach would ensure early detection and intervention for high-risk cases while minimizing unnecessary and expensive endoscopic evaluations for patients less likely to have esophageal varices.

A cost-based analysis by Giannini et al.[10] highlighted the economic advantages of the P/SL ratio, projecting annual savings of approximately 405,000 Euros by reducing unnecessary endoscopies in 2,700 patients, a figure that is likely even higher today. Furthermore, upper GI endoscopy, which is considered as the gold standard test for EV detection, is not without complications, including risks of sedation, bleeding, and perforation.[30] These risks can potentially be minimized by employing this proposed sequential tandem application of the P/SL and P*Alb/SL ratios, and offer a pragmatic approach to risk stratification and patient management, reducing the dependency on invasive procedures.

Strengths and limitations: This study’s use of complete enumeration of all eligible CLD patients over a 6-month period reflects real-world clinical practice and minimizes selection bias. By standardizing key measurements such as spleen length assessed by a single experienced operator on the same ultrasound machine, and platelet counts and albumin assays performed in a central laboratory, both inter-observer and inter-instrument variability were substantially reduced. Importantly, conducting a head-to-head comparison between the well-established P/SL ratio and our novel P*Alb/SL ratio within the same cohort, directly demonstrates the incremental diagnostic value of incorporating hepatic synthetic function.

While this study provides compelling evidence for the utility of these ratios, certain limitations must be acknowledged. The relatively small sample size limits the generalizability of the findings. Additionally, due to the variations across different populations, the single-center design of this study serves as a limitation in capturing broader applicability. The cross-sectional nature of the study precludes the evaluation of these ratios in monitoring disease progression or predicting outcomes over time. Furthermore, although diagnostic equipment was standardized throughout the study to minimize instrument bias, the reliance on a specific ultrasound machine and endoscopic protocols may limit reproducibility across different clinical settings. Future studies should validate these findings in larger, multicenter cohorts and evaluate their utility in longitudinal monitoring for comprehensive risk stratification.

Conclusion

In conclusion, the P/SL ratio demonstrated excellent diagnostic performance as a reliable screening tool for esophageal varices with a high sensitivity, making it particularly effective for early detection in CLD patients. The newly proposed P*Alb/SL ratio exhibited a comparably great, or even slightly superior, diagnostic performance, with its very high specificity and lower likelihood of false-positive results, making it more suitable for confirmation. Together, the sequential tandem application of these two non-invasive ratios offers a practical and resource-efficient strategy for risk stratification and patient management. By using the P/SL ratio for initial screening to identify high-risk patients and the P*Alb/SL ratio for confirmation, this approach not only optimizes diagnostic accuracy but also reduces reliance on routine endoscopy, minimizes unnecessary procedures, and improves resource allocation, particularly in resource-limited settings.

Recommendations

• Based on our findings, we recommend adopting a sequential non-invasive screening algorithm in clinical practice: first apply the P/SL ratio to identify patients at highest risk of esophageal varices, then use the P*Alb/SL ratio to confirm prior to endoscopy to improve the efficiency of endoscopy utilization.

• To build on this work, prospective validation in larger, multicenter cohorts across diverse geographic regions is essential for confirming the optimal cut-off values and for assessing these ratios’ performance over time.

Data availability statement

The datasets are available from the corresponding author upon reasonable request.

Author contributions

Conceptualization – SVY, VK, RB, VSO, DB, RK, RNP; Data curation – SVY, RK, RNP; Data analysis – RB; Methodology – SVY, VK; Supervision – VK, DB; Writing (original draft) – RB, VSO; Writing (review and editing) – SVY, VK, DB, RK, RNP.

Ethical approval

The study was conducted following approval from the institutional ethics committee of AIIMS Patna (Ref. No. AIIMS/Pat/IEC/PGTh/Jan22/45).

Conflicts of interest

There are no conflicts of interest.

Supplementary Material

Coordinates of ROC Curve Variable: Platelet Count/Spleen Length (P/SL Ratio)				Coordinates of ROC Curve Variable: Platelet Count-Albumin/Spleen Length (P*Alb/SL Ratio)
Cut-off value of P/SL			Youden's	Cut-off value of P*Alb/SL			Youden's
Ratio	Sensitivity	Specificity	Index	Ratio	Sensitivity	Specificity	Index
69.1	0.00	1.00	0.00	68.2	0.00	1.00	0.00
110.0	0.01	1.00	0.01	219.1	0.01	1.00	0.01
193.4	0.03	1.00	0.03	362.5	0.03	1.00	0.03
237.7	0.04	1.00	0.04	477.9	0.04	1.00	0.04
245.6	0.05	1.00	0.05	524.2	0.05	1.00	0.05
266.4	0.06	1.00	0.06	581.7	0.06	1.00	0.06
284.1	0.07	1.00	0.07	615.9	0.07	1.00	0.07
289.3	0.08	1.00	0.08	627.4	0.08	1.00	0.08
290.5	0.09	1.00	0.09	639.1	0.09	1.00	0.09
291.7	0.10	1.00	0.10	671.0	0.10	1.00	0.10
296.0	0.11	1.00	0.11	710.5	0.11	1.00	0.11
311.2	0.12	1.00	0.12	747.0	0.12	1.00	0.12
328.2	0.13	1.00	0.13	798.4	0.13	1.00	0.13
338.1	0.14	1.00	0.14	827.4	0.14	1.00	0.14
350.0	0.15	1.00	0.15	835.8	0.15	1.00	0.15
364.5	0.16	1.00	0.16	847.3	0.16	1.00	0.16
372.1	0.17	1.00	0.17	873.9	0.17	1.00	0.17
373.7	0.18	1.00	0.18	905.1	0.18	1.00	0.18
378.6	0.19	1.00	0.19	945.5	0.19	1.00	0.19
385.5	0.20	1.00	0.20	989.1	0.20	1.00	0.20
402.8	0.21	1.00	0.21	1009.2	0.21	1.00	0.21
417.9	0.22	1.00	0.22	1027.1	0.22	1.00	0.22
423.9	0.23	1.00	0.23	1089.1	0.23	1.00	0.23
433.0	0.24	1.00	0.24	1142.8	0.24	1.00	0.24
439.3	0.25	1.00	0.25	1156.9	0.25	1.00	0.25
447.1	0.26	1.00	0.26	1165.7	0.26	1.00	0.26
468.9	0.27	1.00	0.27	1168.0	0.27	1.00	0.27
489.5	0.27	0.95	0.22	1175.3	0.28	1.00	0.28
495.5	0.28	0.95	0.23	1212.1	0.29	1.00	0.29
498.4	0.29	0.95	0.24	1246.4	0.30	1.00	0.30
507.1	0.33	0.95	0.28	1275.0	0.31	1.00	0.31
516.4	0.35	0.95	0.30	1306.8	0.32	1.00	0.32
524.0	0.36	0.95	0.31	1313.9	0.33	1.00	0.33
530.7	0.37	0.95	0.32	1322.5	0.34	1.00	0.34
538.2	0.38	0.95	0.33	1334.0	0.35	1.00	0.35
545.9	0.39	0.95	0.34	1339.4	0.36	1.00	0.36
551.5	0.40	0.95	0.35	1345.8	0.37	1.00	0.37
559.0	0.41	0.95	0.36	1369.3	0.38	1.00	0.38
564.6	0.45	0.95	0.40	1397.3	0.39	1.00	0.39
567.8	0.46	0.95	0.41	1414.6	0.39	0.95	0.34
570.2	0.47	0.95	0.42	1436.5	0.40	0.95	0.35
575.0	0.48	0.95	0.43	1456.3	0.41	0.95	0.36
579.1	0.49	0.95	0.44	1466.3	0.43	0.95	0.38
587.7	0.50	0.95	0.45	1474.3	0.44	0.95	0.39
597.9	0.51	0.95	0.46	1484.0	0.45	0.95	0.40
610.7	0.52	0.95	0.47	1494.7	0.46	0.95	0.41
623.2	0.53	0.95	0.48	1527.8	0.47	0.95	0.42
626.3	0.54	0.95	0.49	1565.3	0.48	0.95	0.43
630.5	0.55	0.95	0.50	1580.8	0.49	0.95	0.44
633.5	0.56	0.95	0.51	1587.1	0.50	0.95	0.45
634.4	0.57	0.95	0.52	1598.1	0.51	0.95	0.46
636.7	0.58	0.95	0.53	1614.3	0.52	0.95	0.47
640.7	0.59	0.95	0.54	1621.6	0.53	0.95	0.48
644.0	0.61	0.95	0.56	1681.6	0.54	0.95	0.49
646.1	0.62	0.95	0.57	1748.6	0.55	0.95	0.50
653.7	0.63	0.95	0.58	1767.7	0.56	0.95	0.51
663.5	0.64	0.95	0.59	1780.4	0.57	0.95	0.52
673.5	0.65	0.95	0.60	1791.3	0.58	0.95	0.53
690.1	0.66	0.95	0.61	1802.5	0.59	0.95	0.54
707.7	0.67	0.95	0.62	1806.1	0.60	0.95	0.55
720.2	0.68	0.95	0.63	1809.5	0.61	0.95	0.56
731.7	0.68	0.90	0.58	1830.9	0.62	0.95	0.57
738.7	0.69	0.90	0.59	1857.1	0.63	0.95	0.58
744.4	0.70	0.90	0.60	1875.0	0.64	0.95	0.59
753.8	0.72	0.90	0.62	1895.2	0.65	0.95	0.60
766.1	0.73	0.90	0.63	1912.9	0.66	0.95	0.61
778.2	0.74	0.90	0.64	1926.3	0.67	0.95	0.62
781.8	0.75	0.90	0.65	1933.5	0.68	0.95	0.63
783.8	0.76	0.90	0.66	1947.7	0.69	0.95	0.64
787.2	0.78	0.86	0.64	2001.4	0.70	0.95	0.65
794.4	0.79	0.86	0.65	2043.0	0.71	0.95	0.66
805.9	0.81	0.86	0.67	2044.3	0.72	0.95	0.67
817.5	0.82	0.86	0.68	2056.6	0.73	0.95	0.68
828.3	0.83	0.86	0.69	2073.8	0.74	0.95	0.69
835.5	0.85	0.86	0.71	2085.8	0.75	0.95	0.70
838.2	0.86	0.86	0.72	2095.8	0.76	0.95	0.71
842.4	0.87	0.86	0.73	2114.8	0.77	0.95	0.72
848.6	0.88	0.86	0.74	2152.3	0.78	0.95	0.73
852.4	0.89	0.86	0.75	2176.4	0.79	0.95	0.74
853.8	0.90	0.86	0.76	2183.4	0.80	0.95	0.75
854.4	0.91	0.86	0.77	2194.5	0.81	0.95	0.76
856.1	0.92	0.86	0.78	2214.3	0.81	0.90	0.71
869.7	0.93	0.81	0.74	2238.0	0.81	0.86	0.67
883.2	0.94	0.81	0.75	2248.8	0.81	0.81	0.62
888.5	0.95	0.81	0.76	2261.5	0.82	0.81	0.63
893.7	0.95	0.76	0.71	2285.9	0.83	0.81	0.64
895.2	0.96	0.76	0.72	2301.8	0.84	0.81	0.65
909.8	0.97	0.76	0.73	2352.4	0.85	0.81	0.66
945.7	0.97	0.71	0.68	2405.4	0.86	0.81	0.67
983.9	0.98	0.71	0.69	2417.0	0.86	0.76	0.62
1014.8	0.98	0.67	0.65	2449.4	0.87	0.76	0.63
1035.6	0.98	0.62	0.60	2492.2	0.88	0.76	0.64
1060.8	0.99	0.62	0.61	2523.6	0.89	0.76	0.65
1081.2	0.99	0.57	0.56	2548.6	0.90	0.76	0.66
1110.2	0.99	0.52	0.51	2560.2	0.91	0.76	0.67
1177.3	0.99	0.48	0.47	2572.4	0.92	0.76	0.68
1275.0	0.99	0.43	0.42	2588.6	0.93	0.76	0.69
1380.3	0.99	0.38	0.37	2616.1	0.94	0.76	0.70
1428.0	0.99	0.33	0.32	2644.3	0.95	0.76	0.71
1514.3	0.99	0.29	0.28	2803.1	0.96	0.76	0.72
1635.0	0.99	0.24	0.23	2977.9	0.96	0.71	0.67
1678.8	0.99	0.19	0.18	3009.7	0.97	0.71	0.68
1836.1	0.99	0.14	0.13	3124.3	0.98	0.71	0.69
2023.1	0.99	0.10	0.09	3262.0	0.99	0.71	0.70
2303.5	0.99	0.05	0.04	3297.4	0.99	0.67	0.66
2929.0	0.99	0.00	-0.01	3324.0	0.99	0.62	0.61
3313.5	1.00	0.00	0.00	3380.9	0.99	0.57	0.56
				3438.9	0.99	0.52	0.51
				3617.8	0.99	0.48	0.47
				3957.3	0.99	0.43	0.42
				4204.8	0.99	0.38	0.37
				4345.7	0.99	0.33	0.32
				4692.4	0.99	0.29	0.28
				4985.0	0.99	0.24	0.23
				5205.0	0.99	0.19	0.18
				5776.2	0.99	0.14	0.13
				6271.5	0.99	0.10	0.09
				7013.6	0.99	0.05	0.04
				9283.8	0.99	0.00	-0.01
				11031.3	1.00	0.00	0.00

Funding Statement

Nil.