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European Heart Journal 2007 28(11):1334-1343; doi:10.1093/eurheartj/ehm091
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© The European Society of Cardiology 2007. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

A propensity-matched study of the association of low serum potassium levels and mortality in chronic heart failure

Ali Ahmed1,2,*, Faiez Zannad3, Thomas E. Love4, Jose Tallaj1,2, Mihai Gheorghiade5, Olaniyi James Ekundayo1 and Bertram Pitt6

1 Department of Medicine, University of Alabama at Birmingham, 1530 Third Avenue South, CH-19, Ste-219, Birmingham, AL 35294-2041, USA
2 Department of Medicine, VA Medical Center, Birmingham, AL, USA
3 Department of Medicine, University Henri Poincaré, Nancy, France
4 Department of Medicine, Case Western Reserve University, Cleveland, OH, USA
5 Department of Medicine, Northwestern University, Chicago, IL, USA
6 Department of Medicine, University of Michigan, Ann Arbor, MI, USA

Received 7 November 2006; revised 7 March 2007; accepted 15 March 2007.

* Corresponding author. Tel: +1 205 934 9632; fax: +1 205 975 7099. E-mail address: aahmed{at}uab.edu


   Abstract
Top
 Abstract
Introduction
 Patients and methods
 Results
 Discussion
 Conclusions
 Acknowledgements
 References
 
Aims: Potassium homeostasis is essential for normal myocardial function, and low serum potassium may cause fatal arrhythmias. However, the association of low potassium and long-term mortality and morbidity in heart failure (HF) is largely unknown.

Methods and results: We studied 6845 HF patients in the Digitalis Investigation Group trial with serum potassium levels ≤5.5 mEq/L. Of these, 1189 had low potassium (<4 mEq/L). Propensity scores for low potassium were calculated for each patient and were used to match 1187 low-potassium patients with 1187 normal-potassium (4–5.5 mEq/L) patients. Effects of low potassium on outcomes were assessed using matched Cox regression analyses. All-cause mortality occurred in 379 (rate, 1103/10 000 person-years) normal-potassium and 441 (rate, 1330/10 000 person-years) low-potassium patients, respectively, during 3437 and 3315 years of follow-up [hazard ratio (HR), 1.25; 95% confidence interval (CI), 1.07–1.46; P = 0.006]. Cardiovascular mortality occurred in 297 (864/10 000 person-years) normal-potassium and 356 (1074/10 000 person-years) low-potassium patients (HR, 1.27; 95% CI, 1.06–1.51; P = 0.009). Cardiovascular hospitalization occurred in 610 (rate, 2553/10 000 person-years) normal-potassium and 637 (rate, 2855/10 000 person-years) low-potassium patients (HR, 1.13; 95% CI, 0.99–1.29; P = 0.082).

Conclusion: In a cohort of ambulatory chronic systolic and diastolic HF patients who were balanced in all measured baseline covariates, serum potassium <4 mEq/L was associated with increased mortality, with a trend towards increased hospitalization.

Key Words: Heart failure • Potassium • Mortality • Hospitalization • Propensity score


   Introduction
Top
 Abstract
 Introduction
Patients and methods
 Results
 Discussion
 Conclusions
 Acknowledgements
 References
 
Potassium is an important determinant of myocardial function and low serum potassium may cause arrhythmias and sudden cardiac death.1–5 Diuretics are commonly used in heart failure (HF) and hypokalemia is an important complication of diuretic therapy.3,6 Diuretic-associated increased mortality and morbidity may in part be attributed to low potassium.7 The effects of low potassium on cardiovascular morbidity and mortality are well known from studies in human hypertension and in animal models.1,2,8–11 However, the effects of low serum potassium on long-term outcomes in HF have not been well studied. The objective of this study was to determine the long-term effects of low serum potassium on mortality and hospitalization in a cohort of propensity score matched chronic systolic and diastolic HF patients.


   Patients and methods
Top
 Abstract
 Introduction
 Patients and methods
Results
 Discussion
 Conclusions
 Acknowledgements
 References
 
Study design
We conducted a non-randomized propensity-matched study of the Digitalis Investigation Group (DIG) trial, which was a randomized clinical trial of digoxin in HF conducted in 302 centres (186 in the United States and 116 in Canada) over 32 months during 1991–1993.12,13 Detailed descriptions of the rationale, design, implementation, and results of the DIG trial have been previously reported.12,13

Study patients
All of the 7788 DIG participants were ambulatory chronic systolic and diastolic HF patients in normal sinus rhythm. Of these, 6800 had left ventricular ejection fraction ≤45%. Most DIG participants were receiving angiotensin-converting enzyme (ACE)-inhibitors and diuretics. Beta-blockers were not approved for HF during the DIG trial and data on beta-blocker use were not collected. We restricted our analysis to a subset of 6857 patients with valid baseline data on serum potassium levels. Of these 6857 patients, 12 patients had serum potassium >5.5 mEq/L and were excluded. We restricted our main analysis to a subset of 1187 pairs of patients with normal and low serum potassium, who were matched by their propensities for low serum potassium.

Low serum potassium
Serum potassium values <3.5 or <4 mEq/L have been variously used to define low serum potassium or hypokalemia.11,14 However, values of serum potassium for hypokalemia in HF have not been clearly defined. Based primarily on the effect of aldosterone antagonists in elevating serum potassium and in reducing mortality in HF,15,16 Macdonald et al. suggested that a cut-off of serum potassium level 4 mEq/L should be used to define hypokalemia in HF and serum potassium should preferably be maintained at or above 4.5 mEq/L.1 Therefore, for the purpose of this analysis, we defined hypokalemia as serum potassium <4 mEq/L. Of the 6845 patients in our analysis, 1189 (17.4%) had serum potassium <4 mEq/L.

Study outcomes
The primary outcomes were all-cause mortality and all-cause hospitalization. We also studied other causes of mortality and hospitalizations including those due to cardiovascular causes and HF. All study outcomes were ascertained by investigators blinded to the outcomes. DIG participants were followed for a median of 38 months and vital status data were complete for 99% of the patients.17

Propensity score methods
The propensity score is the conditional probability of receiving an exposure (e.g. having low potassium) given a set of measured covariates.18–21 Propensity score matching makes it possible to design observational studies like randomized clinical trials in several key ways.21 First, it allows investigators to assemble retrospectively a study cohort, in which patients are well balanced on all measured covariates. Second, it allows investigators to measure objectively the achieved balance (i.e. bias reduction) in the study cohort. Finally, and perhaps most importantly, it makes possible to do all these without the knowledge of or access to outcomes data, as investigators of a randomized clinical trial would not know the outcomes of the trial during its design.21 Although, propensity score matching is often used to balance two treatment groups,7,22–26 the method can also be used to balance patients across non-treatment exposures.27–30

Calculation of propensity scores
We estimated propensity scores for low serum potassium for each of the 6845 patients using a non-parsimonious multivariable logistic regression model. In the model, low serum potassium was used as the dependent variable, and all measured baseline patient characteristics shown in Table 1, except for glomerular filtration rate, chronic kidney disease, and ejection fraction >45% (which are derived values), were included as covariates. We also tested the following clinically plausible interaction terms: age and serum creatinine, age and potassium supplement use, serum creatinine and ACE-inhibitor use, serum creatinine and diuretic (non-potassium-sparing) use, ACE-inhibitors and potassium supplement use, as well as potassium-sparing diuretics and potassium supplement use. None of these interactions were significant and were dropped from the final model.31 The model was well-calibrated (Hosmer–Lemeshow test: P = 0.141) with reasonable discrimination (c statistic = 0.62).31


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  		Table 1 Baseline patient characteristics, by serum potassium, before and after propensity score matching

 
Assembly of study cohort: propensity score matching
We used an SPSS macro to match each low-potassium (<4 mEq/L) patient with a normal potassium (4.0–5.5 mEq/L) patient who had similar propensity scores to five, four, three, two and one decimal places in five repeated steps. In the first step, we multiplied the raw propensity scores (e.g. 0.57520576) by 100 000 (e.g. 57520.58), then rounded it to the nearest value divisible by 0.25 (e.g. 57520.50). We then matched low-potassium patients with normal-potassium patients who had similar propensity scores by this standard. The pairs of matched patients were removed from the file. In the second step, we multiplied the raw propensity scores by 10 000, rather than 100 000, and repeated the above process. This was repeated three more times, each time, multiplying by 1000, 100, and finally 10. In all, we matched 1187 of the 1189 low-potassium patients with 1187 patients who had normal serum potassium, but had similar propensity for low potassium.32 This near 100% match is noteworthy given the modest discrimination of our propensity score model.31,33

Assessment of bias reduction and balance
Balances in the distribution of baseline covariates between patients with normal and low potassium were assessed by estimating absolute standardized differences of covariates between the two groups, before and after matching.7,26,27,29,30 Standardized differences directly quantify biases in the means (or proportions) of covariates across the groups, and are expressed as percentages of the pooled standard deviations. Bias reduction was assessed by comparing the absolute standardized differences of covariates before and after matching. An absolute standardized difference of 0% on a covariate indicates no residual bias for that covariate, and an absolute standardized difference below 10% suggest inconsequential residual bias.26

Statistical analysis
We used Kaplan–Meier plots and matched Cox regression analysis to estimate associations of low potassium with various outcomes. We confirmed the assumption of proportional hazards by a visual examination of the log (minus log) curves. We then repeated our analyses using serum potassium as a continuous variable. To determine whether the loss of sample size in the matching process affected our results, we estimated the effect of low potassium on outcomes in the full pre-match cohort of 6845 patients using three different approaches: (i) unadjusted,(ii) adjusted for raw propensity scores, and (iii) adjusted for all covariates used in the propensity score model.

Sensitivity analyses
Even though our matched cohort achieved excellent balance in all measured covariates between the two groups, we do not know if there was bias due to imbalances in unmeasured covariates. Therefore, we conducted a formal sensitivity analysis to quantify the degree of a hidden bias that would need to be present to invalidate our main conclusions.34

Subgroup analyses
We conducted subgroup analyses to determine the homogeneity of the associations of low potassium with all-cause mortality. We first calculated the absolute risk differences, and then estimated the effect of low potassium on mortality in each subgroup using Cox regression model, in each case adjusting for propensity score for low potassium. Finally, we formally tested for first-order interactions using Cox proportional hazards models, entering interaction terms and adjusting for propensity scores, separately for each subgroup. All statistical tests were evaluated using two-tailed 95% confidence levels, and data analyses were performed using SPSS for Windows version 14.35


   Results
Top
 Abstract
 Introduction
 Patients and methods
 Results
Discussion
 Conclusions
 Acknowledgements
 References
 
Patient characteristics
The mean (±SD) age of the 2374 matched patients was 63 (±11) years, (median 65; range 21–92), 729 (31%) were women and 394 (17%) were non-whites. Before matching, low-potassium patients were more likely to be women, non-whites, and have hypertension, elevated jugular venous pressure and leg oedema, cardiomegaly, and be receiving diuretics and potassium supplements (Table 1). After matching, normal- and low-potassium patients were more similar in regards to all measured baseline covariates (Table 1 and Figure 1). Our propensity score matching reduced standardized differences for all observed covariates below 10% in absolute value, demonstrating substantial improvement in covariate balance across the serum potassium groups (Figure 1).


Figure 1
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  		Figure 1 Absolute standardized differences in covariates between patients with normal and low serum potassium, before and after propensity score matching.

 
Association of low potassium with all-cause mortality
During a median follow-up of 36.7 months, 820 (35%) patients in the matched cohort died from all causes, including 653 (28%) due to cardiovascular causes and 311 (13%) due to progressive HF. Kaplan–Meier survival curves for all-cause mortality are displayed in Figure 2A. All-cause mortality occurred in 379 (32%) of normal-potassium and 441 (37%) low-potassium patients, respectively, during 3437 and 3315 years of follow-up. Mortality rates for normal- and low-potassium patients were, respectively, 1103 and 1330 per 10 000 person-years of follow-up [hazard ratio (HR) 1.25; 95% confidence interval (CI) 1.07–1.46; P = 0.006; Table 2]. When we used serum potassium as a continuous variable, each unit increase in serum potassium was associated with 22% reduction in risk of total mortality (HR 0.78; 95% CI 0.66–0.92; P = 0.003).


Figure 2
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  		Figure 2 Kaplan–Meier plots for mortality due to (A) all-causes, (B) cardiovascular causes, and (C) progressive heart failure.

 

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  		Table 2 Cause-specific mortalities in heart failure patients for serum potassium ≤4 mEq/L

 
In the full pre-match cohort of 6845 patients, 2260 (33%) patients died from all causes. All-cause mortality occurred in 1818 (32%) of normal-potassium patients during 16 391 years of follow-up (rate, 1109/10 000 person-years), and 442 (37%) of low-potassium patients during 3319 years of follow-up (rate, 1332/10 000 person-years; unadjusted HR 1.20; 95% CI 1.08–1.33; P = 0.001). When adjusted for all covariates (HR, 1.21; 95% CI, 1.09–1.35; P = 0.001) or propensity scores (HR, 1.19; 95% CI, 1.07–1.32; P = 0.001), the association remained essentially unchanged.

Results of sensitivity analyses
In the absence of hidden bias, a sign-score test for matched data with censoring provides the modest evidence that low potassium was associated with increased mortality. Our sensitivity analysis suggests that an unmeasured binary covariate would need to increase the odds of low potassium by more than 6.7% to explain away this association (z statistic = 2.77; two-tailed P = 0.0056), suggesting that these results are sensitive to moderately strong hidden biases.

Low potassium and cause-specific mortalities
Kaplan–Meier survival curves for cardiovascular and HF mortalities are displayed in Figure 2B and C. Mortality due to cardiovascular causes occurred in 297 (25%; rate, 864/10 000 person-years) of normal-potassium patients and 356 (30%; rate, 1074/10 000 person-years) low-potassium patients (HR, 1.27; 95% CI, 1.06–1.51; P = 0.009; Table 2). Mortality due to progressive HF occurred in 137 (12%; rate, 399/10 000 person-years) of normal-potassium patients and 174 (15%; rate, 525/10 000 person-years) low-potassium patients (HR, 1.36; 95% CI, 1.05–1.75; P = 0.020; Table 2). Associations of low potassium and other cause-specific mortalities are displayed in Table 2.

Low potassium and hospitalizations
Hospitalizations due to all causes occurred in 1564 (66%) patients, including 1247 (53%) hospitalizations due to cardiovascular causes and 764 (32%) due to worsening HF. All-cause hospitalizations occurred in 768 (65%) of normal- and 796 (67%) of low-potassium patients respectively during 1997 and 1876 years of follow-up. Rates for all-cause hospitalization per 10 000 person-years of follow-up were 3846 and 4243, respectively, for normal- and low-potassium patients (HR, 1.12; 95% CI, 0.99–1.27; P = 0.073) (Table 3).


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  		Table 3 Cause-specific hospitalizations in heart failure patients for serum potassium ≤4 mEq/L

 
Hospitalizations due to cardiovascular causes occurred in 610 (51%; rate, 2553/10 000 person-years) of normal-potassium patients and 637 (54%; rate, 2855/10 000 person-years) low-potassium patients (HR, 1.13; 95% CI, 0.99–1.29; P = 0.082). Hospitalizations due to worsening HF occurred in 371 (31%; rate, 1287/10 000 person-years) of normal-potassium patients and 393 (33%; rate, 1442/10 000 person-years) low-potassium patients (HR, 1.14; 95% CI, 0.96–1.34; P = 0.128).

Low potassium had no significant associations with hospitalizations due to supraventricular arrhythmias (HR, 1.20; 95% CI, 0.79–1.83; P = 0.394) or ventricular arrhythmias (HR, 0.94; 95% CI, 0.59–1.52; P = 0.808). It also had no significant association with hospitalizations due to myocardial infarction (HR, 1.40; 95% CI, 0.96–2.05; P = 0.085), unstable angina pectoris (HR, 1.20; 95% CI, 0.92–1.57; P = 0.176), or suspected digoxin toxicity (HR, 0.61; 95% CI, 0.29–1.29; P = 0.198).

In the full pre-match cohort of 6845 patients, low potassium had no significant association with all-cause hospitalizations (unadjusted HR 1.08; 95% CI, 1.00–1.16; P = 0.064), which remained essentially unchanged after multivariable adjustment for all covariates (HR, 1.07; 95% CI, 0.99–1.16; P = 0.087) or propensity scores (HR, 1.05; 95% CI, 0.97–1.14; P = 0.211).

Subgroup analyses
The associations of low potassium and all-cause mortality were observed in a wide spectrum of HF patients (Figure 3). There were no significant interactions between low potassium and any of the subgroups, except for ischaemic heart disease and chronic kidney disease (P for interactions, respectively, 0.002 and 0.047). Of interest, the association of low potassium and mortality was comparable, with 37 and 38% of total mortality, respectively, among patients receiving and not receiving digoxin. The effects of low potassium on cardiovascular and HF mortality were also similar in patients receiving and not receiving digoxin.


Figure 3
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  		Figure 3 Hazard ratio and 95% confidence interval for all-cause mortality associated with low serum potassium in subgroups of patients with chronic heart failure.

 

   Discussion
Top
 Abstract
 Introduction
 Patients and methods
 Results
 Discussion
Conclusions
 Acknowledgements
 References
 
The results of the current analysis demonstrate that in ambulatory chronic HF patients who were well-balanced in all measured baseline covariates, compared to serum potassium levels between 4 and 5.5, serum potassium levels <4 mEq/L were associated with increased risk of mortality due to all causes, cardiovascular causes, and progressive HF, with trends toward increased hospital admissions due to all causes and cardiovascular causes. To the best of our knowledge, this is the first report of long-term effect of baseline serum potassium on outcomes in a propensity matched cohort of chronic HF. These findings are important as low serum potassium is relatively common in HF, often precipitated by diuretics, also commonly used in HF.

Possible mechanistic explanations
Low potassium may affect myocardial resting membrane potential, repolarization and relative refractory times, and conduction velocity.9 Data from animal models suggest that low potassium, even when within the conventional range of serum potassium, may cause lethal ventricular arrhythmias, impair myocardial responses to hypoxia, and may also impair myocardial contractile and relaxation responses to epinephrine.9,10,36

Low potassium may also be a marker for the use of diuretics, and more symptomatic HF by indication. Use of non-potassium-sparing diuretics has been shown to increase mortality and hospitalization in HF.3,7,37 There were no imbalances in any of the measured covariates, including the use of diuretics, between patients with normal and low potassium in the matched cohort. Diuretic-associated hypokalemia has been shown to be more severe in patients receiving higher doses of diuretics.11 However, we had no data on diuretic dosage. We observed that low potassium was significantly associated with increased cardiovascular and HF mortality, but not with hospitalization suggesting fatal arrhythmias as a possible mechanistic explanation of sudden cardiac deaths associated with low potassium. However, we had no data on sudden cardiac death.

Aldosterone, a mineralocorticoid and a potent neurohormone that is activated in HF,38 stimulates exchange of sodium and potassium in distal renal tubules, resulting in increased excretion of potassium into the urine. Data from human hypertension suggest that non-potassium-sparing diuretics are more likely to cause hypokalemia when serum aldosterone is elevated.8,39,40 Thus, low potassium may be a marker of elevated aldosterone, which has been shown to cause myocardial fibrosis and progression of HF.38,41 Suppression of aldosterone, on the other hand, reduces mortality in HF.15,16

Data from our subgroup analyses suggest that low serum potassium was significantly associated with increased all-cause mortality among patients with ischaemic heart disease, but not among those without ischaemic heart disease (Figure 3). Data from animal and human studies suggest that hypokalemia is associated with increased risk of ventricular arrhythmias in ischaemic heart.42–44 We observed low serum potassium associated with increased all-cause mortality only among patients with chronic kidney disease, but not among those without chronic kidney disease (Figure 3). Diuretic use is a common cause of hypokalemia, and HF patients with chronic kidney disease are more likely to use diuretics.45 Yet, hyperkalemia, rather than hypokalemia, is more common in chronic kidney disease, and is a reason for concern for adverse outcomes in these patients.46 However, our data suggest that in the context of HF and chronic kidney disease, low serum potassium may be associated with increased adverse outcomes.

Clinical implications
Low potassium, well tolerated in healthy adults, is believed to increase risks of morbidity and mortality in patients with cardiovascular disease.44 However, the effect of low potassium on outcomes in HF is not well studied. Our findings suggest that maintaining serum potassium >4 mEq/L may improve survival in chronic HF. Serum potassium of <3.5 mEq/L is clinically considered as low potassium. However, our findings suggest that serum potassium <4 mEq/L may be associated with increased mortality. Data from hypertension studies indicate that use of diuretics is an important cause of low potassium.8,44 Diuretics are commonly used in HF and may be associated with increased mortality and morbidity in HF.7 Diuretics should be avoided in New York Heart Association (NYHA) class I and II patients who are euvolemic and are receiving appropriate neurohormonal blockade. For patients with NYHA class III and IV symptoms with fluid overload, who must be treated with diuretics, spironolactone (or eplerenone for post-myocardial infarction patients) may be used to antagonize the effects of aldosterone and prevent hypokalemia, carefully avoiding hyperkalemia.15,16 Alternately, potassium supplement may also be used to avoid hypokalemia. However, unlike aldosterone antagonists, the long-term effect of potassium supplements in chronic HF is largely unknown. Data from rat hypertension models suggest that a high-potassium diet may be protective, in part, through the inhibition of cardiac nicotinamide-adenine dinucleotide phosphate oxidase activities.47 However, no such data are available for human HF. Our findings also suggest that despite the known potential short-term adverse effects of digoxin in patients with low potassium, no such interaction of digoxin and low potassium on mortality were observed in our analysis.

Comparison with other published studies
The effects of low sodium on HF outcomes are well reported in the literature.48,49 The effects of low potassium on outcomes in hypertension is also well reported.5,8,11 However, to the best of our knowledge, this is the first report of the long-term effect of low potassium on mortality and hospitalization in HF.

Strengths and limitations
Propensity score matching was an obvious strength of our study. However, like any non-randomized design, propensity matching may not be able to balance unmeasured confounders. Even though a sensitivity analysis cannot confirm the presence of such an unmeasured confounder, the results of our sensitivity analysis suggests that our main conclusions may be sensitive to a hidden confounder.34 However, for any unmeasured or hidden covariate to become a confounder, it must be strongly associated with both low potassium and mortality, and not be strongly associated with any of the covariates used in the propensity score model.

We were able to match all but two patients with low potassium, in contrast to typical approximately 60% matching in other studies.26,50 Our matching protocol also allowed near-exact matching by the propensity score. The results of our study are based on predominantly white, male, and relatively younger HF patients with normal sinus rhythm and not receiving beta-blockers, thus limiting their generalizability. Other limitations of our study include lack of data on dose of diuretics and sudden cardiac deaths. Finally, we had no data on serum magnesium, and thus do not know to what extent the observed effect may be caused by low magnesium.


   Conclusions
Top
 Abstract
 Introduction
 Patients and methods
 Results
 Discussion
 Conclusions
Acknowledgements
 References
 
We observed associations between low potassium and increased mortality in a wide spectrum of ambulatory patients with chronic, mild to moderate systolic and diastolic HF. Low serum potassium in HF may be caused by diuretic therapy or may be a marker of increased neurohormonal activity and disease progression. Diuretics should be avoided in HF patients who are asymptomatic or minimally symptomatic without fluid overload. In symptomatic HF patients with fluid overload and receiving diuretics, normal serum potassium should be maintained using potassium-sparing diuretics or potassium supplementation.


   Acknowledgements
Top
 Abstract
 Introduction
 Patients and methods
 Results
 Discussion
 Conclusions
 Acknowledgements
References
 
The Digitalis Investigation Group (DIG) study was conducted and supported by the NHLBI in collaboration with the DIG Investigators. This manuscript was prepared using a limited access dataset obtained by the NHLBI and does not necessarily reflect the opinions or views of the DIG Study or the NHLBI.

Grant Supports

A.A. is supported by the National Institutes of Health through grants from the National Institute on Aging (5-K23-AG019211-04) and the National Heart, Lung, and Blood Institute (5-R01-HL085561-02 and P-50-HL077100).

Authors' Contributions

A.A. conceived the study hypothesis, designed the study, and wrote the first and the subsequent drafts of the manuscript. A.A. conducted statistical analyses in consultation with T.E.L. All authors interpreted the data, participated in critical revision of the paper for important intellectual content, and approved the final version of the article. A.A. had full access to the data.

Abstract Presentation

An abstract based on a preliminary analysis of these data was presented at the American Society for Clinical Investigation and the Association of American Physicians 2007 Joint Meeting, on April 14, 2007 in Chicago, Illinois, USA.

Conflict of interest: none declared.


   References
Top
 Abstract
 Introduction
 Patients and methods
 Results
 Discussion
 Conclusions
 Acknowledgements
 References
 

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