Abstract
Background
Besides the classic logistic regression analysis, non-parametric methods based on machine learning techniques such as random forest are presently used to generate predictive models. The aim of this study was to evaluate random forest mortality prediction models in haemodialysis patients.
Methods
Data were acquired from incident haemodialysis patients between 1995 and 2015. Prediction of mortality at 6 months, 1 year and 2 years of haemodialysis was calculated using random forest and the accuracy was compared with logistic regression. Baseline data were constructed with the information obtained during the initial period of regular haemodialysis. Aiming to increase accuracy concerning baseline information of each patient, the period of time used to collect data was set at 30, 60 and 90 days after the first haemodialysis session.
Results
There were 1571 incident haemodialysis patients included. The mean age was 62.3 years and the average Charlson comorbidity index was 5.99. The mortality prediction models obtained by random forest appear to be adequate in terms of accuracy [area under the curve (AUC) 0.68–0.73] and superior to logistic regression models (ΔAUC 0.007–0.046). Results indicate that both random forest and logistic regression develop mortality prediction models using different variables.
Conclusions
Random forest is an adequate method, and superior to logistic regression, to generate mortality prediction models in haemodialysis patients.
Keywords: haemodialysis, machine learning, mortality, predictive models, random forest
INTRODUCTION
The number of haemodialysis (HD) patients increases progressively in those >75 years of age [1]. It is a health challenge with high economic cost and mortality. Risks factors of mortality in HD patients are very different from other populations. It is important to stratify HD patients according to risk and develop, as early as possible, appropriate strategies aimed at optimizing survival.
Classic statistical analysis has identified variables that predict mortality in HD patients and the results have been rather uniform among the different publications [2–11]. Risk prediction models (or ‘risk scores’) are designed to predict the probability of an adverse outcome, such as death, from different types of variables—demographic, clinical and others. Classic methods of survival analysis, such as Cox proportional hazards regression and logistic regression, rely on the assumption that the relationship between variables and outcomes is linear. This assumption is very useful to generate simple and intelligible models in which the numerical value of a coefficient represents the contribution of that variable to the overall risk [12]. More recently, machine learning methods [13], such as random forest, have been proposed as more advanced valid procedures to predict outcome if there is enough data available to perform the analysis. These new methods of analysis may identify variables, not previously recognized, that can improve prediction of mortality. Studies in patients have proven the usefulness of random forest regression models in identifying variables with high predictive power [14–16], to estimating individualized treatment effects, by investigating the performance of random forest of interaction trees via extensive numerical experiments [17]. Analyses based on random forest have been used to quantify the association between parameters of chronic kidney disease–mineral and bone disorder (CKD-MBD) in HD patients [18]. Similar methods have been used to estimate the individual effect of a treatment, based on observational data [19]. It has been reported that Cox regression was inferior to random forest in developing prognostic models of lung adenocarcinoma [20].
The objective of the present study was to compare mortality prediction models in HD patients obtained by conventional logistic regression analysis and by random forest. The accuracy of the models was obtained by comparing the prediction obtained with each method with the actual mortality.
MATERIALS AND METHODS
Patients
This study analyses data collected by the Nephrology Department Database (Reina Sofia University Hospital) from 1995 to 2015. There were 2219 patients from seven HD facilities and 1571 patients fulfilled the criteria to be included in the study. Since 1995, all patients starting maintenance HD have been informed that their identity will not be revealed to third parties. All patients included in this study were >18 years of age and signed an informed consent form allowing the use of clinical records and laboratory data for analysis aimed at improving clinical practice, providing that their identity will not be disclosed. The study was performed in accordance with relevant guidelines and regulations and was submitted and subsequently approved by the Institutional Ethics Committee of the Reina Sofia University Hospital.
Variables collected at the initiation of regular HD included age and comorbidities that generate the Charlson comorbidity index, including myocardial infarction, coronary heart disease, heart failure, stroke, peripheral vascular disease, dementia, chronic obstructive pulmonary disease (COPD), autoimmune disease, peptic ulcer, non-cirrhotic liver disease, liver cirrhosis, severe kidney disease, non-metastatic tumour disease, solid metastatic tumour, malignant haematological disease (leukaemia or lymphoma), acquired immune deficiency syndrome and diabetes mellitus. The analytical variables available during follow-up were haemoglobin, ferritin, transferrin saturation index (TSI), creatinine, albumin, C-reactive protein, phosphorus, calcium, potassium, alkaline phosphatase, magnesium, parathyroid hormone (PTH) and β2-microglobulin. Additional parameters evaluated were body mass index (BMI), residual diuresis, type of vascular access for HD and dose of dialysis expressed as Kt/Vurea.
Baseline data were constructed with the information obtained during the initial period of regular HD. It is important to know if the length of time collecting the data influences the results. Therefore, to be more accurate, the initial period of time used to collect data was set at 30, 60 and 90 days after the first HD session. Patients that did not survive the first 30 days on regular HD were not included. Likewise, patients with no data collected during the first 90 days after the first regular HD session were not included in the analysis. Values of variables were the mean of measurements obtained within the first 30, 60 or 90 days after the initiation of regular HD (this will be indicated as data at 30, 60 and 90 days). The missing values were handled with a single imputation approach considering the mean for continuous variables and the mode for categorical variables.
A flow chart of the patients analysed in this study is shown in Figure 1. Prediction of mortality was analysed at 6 months, 1 year and 2 years after the initiation of regular HD. Analysis was performed separately according to the time period available for the collection of baseline data (30, 60 and 90 days).
FIGURE 1:
Cohort selection flow chart. The comparison of mortality models was performed on nine different cohorts that are represented in the dashed boxes. On the left, the number of patients included to evaluate the prediction of mortality at 6 months, 1 year and 2 years. For each mortality prediction period there were three separate analyses according to the minimal period after the first HD session used for the collection of baseline data (input variables: 30, 60 or 90 days).
Prediction of mortality was calculated using two different regression models: logistic regression and random forest. Receiver operating characteristics (ROC) curves specify the sensitivity and specificity of these predictive models. The values of the area under the curve (AUC) are used to compare the predictive value obtained by logistic regression and random forest [21]. A t-test was performed to determine if the differences between the mean AUCs obtained by logistic regression and random forest were statistically significant.
Since the data set is relatively small, each AUC is computed considering a set of models configured on 30 different randomizations of the original data set. In each randomization, 70% of the patients were used to train the model (training set) and 30% of the patients were used to evaluate the accuracy (test set). The final accuracy was computed as the AUC, considering all the predictions on the test sets of the 30 randomizations.
Logistic regression analysis identifies independent variables that significantly influence the risk of death. The analysis provides a coefficient for each variable [the odds ratio (OR)] that represents the probability of an increase or decrease of death if the variable is modified by one unit (e.g. if the OR of age is 1.1, there is a 10% increase in the expected risk relative to a 1-year increase in age). In random forest analysis [15], the probability of death is computed as the average of the probabilities of a set of submodels (decision tree). Each submodel is a composition of if-then-else decision rules, which are derived considering a random subset of the data. In contrast to logistic regression, in random forest, there is not a linear coefficient for each variable; it is assumed that the effect of the variable could be much more complex. In random forest, the predictive value of a variable on mortality is given not only by the influence of that specific variable, but also by the effect of other dependent variables (covariates) that in a non-linear manner may also affect mortality. This peculiarity gives to the model a higher degree of freedom to capture complex relationships between input variables and outcome. For example, age >80 years may increase the mortality risk for a patient with haemoglobin <10 g/dL but may have less effect (or no effect) for patients with haemoglobin between 10 and 12 g/dL. So the effect of each variable cannot be isolated and measured as it is in logistic regression. Thus the evaluation of the effect of each variable on the probability of the event is difficult. In general, a clear statistical description of the effect of the variables on the prediction of the event, as in logistic regression (magnitude of the coefficient and P-value), is not computable and only an indirect qualitative measure can be obtained. For this reason, in the present study, the method of analysing the change in the AUC value was used when the effect of each specified variable is turned off. This is the method used to compare random forest and logistic regression.
The description of this study follows the Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis (TRIPOD) Guidelines [22]. Therefore the completed TRIPOD checklist is provided as Supplementary Table S1.
RESULTS
The study includes a total of 1571 incident HD patients collected throughout a period of up to 20 years who fulfilled the inclusion criteria (Figure 1).
Of the total cohort, 61% were male and the mean age at the initiation of dialysis was 62.3 years. The mean Charlson comorbidity index score was 5.99. Table 1 shows baseline comorbidities and biochemistry results obtained during the first 30 days of dialysis.
Table 1.
Baseline comorbidities and biochemistry obtained during the first 30 days of dialysis
| Baseline | Characteristics |
|---|---|
| Gender (male/female), n (%) | 953 (61)/618 (39) |
| Age (years), mean ± standard deviation (SD) | 62.33 ± 15.89 |
| Comorbidities, n (%) | |
| Diabetes mellitus | 482 (31) |
| Cardiac failure | 319 (20) |
| COPD | 144 (9) |
| Tumoral disease (non-metastatic) | 131 (8) |
| Myocardial infarction | 102 (6) |
| Hepatopathy (non-cirrhotic) | 68 (4) |
| Stroke | 9 (1) |
| Charlson comorbidity index (mean) | 6 |
| Biochemical parameters, mean ± SD | |
| Haemoglobin (g/dL) | 10.08 ± 2.79 |
| Ferritin (ng/mL) | 290.1 ± 362.64 |
| TSI (%) | 18.73 ± 10.32 |
| Creatinine (mg/dL) | 7.3 ± 4.4 |
| Albumin (g/dL) | 3.54 ± 0.55 |
| CRP (median) (mg/L) | 8.8 (IQR: 19.5) |
| Calcium (mg/dL) | 9.04 ± 3.88 |
| Phosphorous (mg/dL) | 5.04 ± 1.66 |
| PTH (pg/mL) | 288.35 ± 297.72 |
| Alkaline phosphatase (UI/L) | 124.88 ± 108.64 |
| Potassium (mEq/L) | 4.91 ± 0.89 |
| Magnesium (mg/dL) | 2.22 ± 0.45 |
| β2-microglobulin (µg/L) | 19.44 ± 8.61 |
| Others | |
| BMI, mean ± SD | 27.1 ± 5.41 |
| Residual diuresis (mL), mean ± SD | 631.73 ± 730.6 |
| Vascular access (catheter), n (%) | 830 (53) |
Results from random forest analysis are shown in Figure 2 and from logistic regression analysis in Figure 3. For both approaches, the eight most important variables are reported. In Figures 2A-I and 3A–I, the dashed line represents the value of the AUC of the mortality prediction ROC curve obtained by both models. Each dot shows the AUC value obtained if the effect of the specified variable is turned off; this is achieved by randomly changing the values of the variable in the test set; therefore, the larger the decrease in the AUC value, the greater impact of the variable in the prediction of mortality.
FIGURE 2:
Prediction of mortality by random forest analysis. The dashed line represents the value of the AUC of the mortality prediction ROC curve obtained by the random forest regression model. Each dot shows the influence of each variable on the AUC value that is obtained if the effect of the specified variable is turned off. This is achieved by randomly changing the values of the variable in the test set. Each graph represents the result of mortality prediction (at 6 months, 1 year and 2 years) and for each mortality prediction period there were three separate analyses according to the minimal period of days after the first HD session used for the collection of the baseline data (input variables 30, 60 and 90 days). (A) Prediction of mortality at 6 months and a 30-day period after the first HD for baseline data collection. (B) Prediction of mortality at 6 months and a 60-day period after the first HD for baseline data collection. (C) Prediction of mortality at 6 months and a 90-day period after the first HD for baseline data collection. (D) Prediction of mortality at 1 year and a 30-day period after the first HD for baseline data collection. (E) Prediction of mortality at 1 year and a 60-day period after the first HD for baseline data collection. (F) Prediction of mortality at 1 year and a 90-day period after the first HD for baseline data collection. (G) Prediction of mortality at 2 years and a 30-day period after the first HD for baseline data collection. (H) Prediction of mortality at 2 years and a 60-day period after the first HD for baseline data collection. (I) Prediction of mortality at 2 years and a 90-day period after the first HD for baseline data collection.
FIGURE 3:
Influence of variables on mortality by logistic regression. The dashed line represents the value of the AUC of the mortality prediction ROC curve obtained by the logistic regression model. Each dot shows the AUC value obtained if the effect of the specified variable is removed. Each graph represents the result of mortality prediction at 6 months, 1 year and 2 years and for each mortality prediction period there were three separate analyses according to the minimal period of days after the first HD session used for the collection of baseline data (input variables 30, 60 and 90 days). (A) Prediction of mortality at 6 months and a 30-day period after the first HD for baseline data collection. (B) Prediction of mortality at 6 months and a 60-day period after the first HD for baseline data collection. (C) Prediction of mortality at 6 months and a 90-day period after the first HD for baseline data collection. (D) Prediction of mortality at 1 year and a 30-day period after the first HD for baseline data collection. (E) Prediction of mortality at 1 year and a 60-day period after the first HD for baseline data collection. (F) Prediction of mortality at 1 year and a 90-day period after the first HD for baseline data collection. (G) Prediction of mortality at 2 years and a 30-day period after the first HD for baseline data collection. (H) Prediction of mortality at 2 years and a 60-day period after the first HD for baseline data collection. (I) Prediction of mortality at 2 years and a 90-day period after the first HD for baseline data collection.
Table 2 shows a comparison of the AUCs obtained by random forest and logistic regression for different baseline collection periods (30, 60 and 90 days) and prediction of mortality at 6 months, 1 year and 2 years.
Table 2.
Comparisons of AUCs obtained by random forest and logistic regression
| Prediction of mortality |
Number of patients | Deaths | AUC |
Difference in AUC (RF − LR) (%) | P-value | ||||
|---|---|---|---|---|---|---|---|---|---|
| Prediction pPeriod | Period (days) after first HD for baseline data collection | Random forest |
Logistic regression |
||||||
| AUC (%) | 95% CI | AUC (%) | 95% CI | ||||||
| 6 months | 30 | 1456 | 80 | 70.14 | 67.95–72.33 | 69.01 | 66.8–71.21 | 1.13 | 0.32 |
| 60 | 1432 | 56 | 67.55 | 64.88–70.22 | 66.84 | 64.15–69.52 | 0.71 | 0.61 | |
| 90 | 1419 | 43 | 71.75 | 68.84–74.65 | 67.15 | 64.18–70.13 | 4.60 | 0.18 | |
| 1 year | 30 | 1336 | 166 | 73.31 | 71.8–74.82 | 71.16 | 69.62–72.7 | 2.15 | 0.01* |
| 60 | 1312 | 142 | 73.19 | 71.56–74.81 | 71.22 | 69.57–72.87 | 1.97 | 0.02* | |
| 90 | 1299 | 129 | 72.82 | 71.12–74.52 | 71.94 | 70.22–73.65 | 0.88 | 0.32 | |
| 2 years | 30 | 1244 | 271 | 72.59 | 71.37–73.81 | 68.73 | 67.47–69.99 | 3.86 | <0.001 |
| 60 | 1220 | 247 | 72.42 | 71.14–73.7 | 68.64 | 67.33–69.96 | 3.78 | <0.001 | |
| 90 | 1207 | 234 | 72.06 | 70.75–73.37 | 69.78 | 68.45–71.12 | 2.28 | <0.001 | |
For each mortality prediction period (6 months, 1 year and 2 years), analysis was based on baseline variable values obtained during a minimum number of days after the first HD session: 30 days, 60 days and 90 days.
Prediction of mortality of HD patients by random forest and logistic regression
Prediction of mortality after 6 months on HD
Separate analyses were performed using the baseline data collected at 30, 60 and 90 days. Results from the random forest analysis are shown in Figure 2A–C and from logistic regression in Figure 3A–C.
Using baseline data at 30 days (Figure 2A), the AUC obtained by the random forest mortality prediction model is 0.70. The most influential variable is serum creatinine; the absence of serum creatinine reduced the AUC value from 0.70 to 0.68. The next two most influential variables are Kt/Vurea and BMI. Using baseline data at 60 days (Figure 2B), the AUC is 0.68 and the three variables with the most predictive power are haemoglobin, calcium and potassium. With baseline data at 90 days, the AUC is 0.72 (Figure 2C) and Kt/Vurea becomes the variable with the greatest predictive power.
The results from logistic regression analysis are shown in Figure 3. Using the 30-day baseline data, the AUC is 0.69 and serum creatinine had the highest predictive power, followed by vascular access and Kt/Vurea. Using the 60-day data, diuresis becomes the variable with the highest predictive power, followed by vascular access and haematologic disease. Using data collected at 90 days, diuresis becomes the variable with the highest predictive power.
Prediction of mortality after 1 year on HD
Results of random forest analysis are shown in Figure 2D–F. Using the baseline data collected at 30 days (Figure 2D), the AUC by random forest is 0.73. The most influential variable is BMI, followed by serum albumin and serum creatinine. Using the 60-day baseline data (Figure 2E), the AUC is 0.73 and the variables with the most predictive power are BMI, serum albumin and Kt/Vurea. With 90-day data, the AUC is 0.73 (Figure 2F) and serum albumin becomes the variable with the most predictive power, followed by BMI and haemoglobin.
The results of logistic regression analysis are shown in Figure 3D–F. Considering the 30-day baseline data, the AUC is 0.71. The variables with the highest predictive power are age, diuresis and serum creatinine. With the 60-day data, the AUC is 0.71 and the variables with the most predictive power are age, diuresis and haemoglobin. With the 90-day data, the AUC is 0.72 and the variables with the most predictive power are age, albumin and haemoglobin.
Prediction of mortality after 2 years on HD
The results of the random forest analysis are shown in Figure 2G–I. With baseline data at 30 days (Figure 2G), the AUC is 0.73 and the most influential variable is BMI, followed by age and serum albumin. Using the 60-day data (Figure 2H), the AUC is 0.72 and the variables with the most predictive power are the same as with 30-day data. With 90-day data, the AUC is 0.72 (Figure 2I) and the variables with significant predictive power are the same as with 30- and 60-day data.
Figure 3G-I shows the results of logistic regression analysis. Considering data collected at 30, 60 and 90 days, the AUCs are 0.69, 0.69 and 0.70, respectively. Age, BMI and Kt/Vurea are the variables with significant predictive value for data at 30 days (Figure 3G). Age, diuresis and BMI are the variables with significant predictive value for data at 60 days (Figure 3H). Age, serum albumin and BMI are the variables with significant predictive value for data at 90 days (Figure 3I).
Comparison of results obtained with logistic regression and random forest
Using the baseline data collected at 30 days, the AUCs predicting mortality at 6 months, 1 year and 2 years obtained with random forest are greater than with logistic regression (Table 2). The difference in AUC in favour of random forest is greater in the prediction of 2-year mortality (3.86%, P < 0.001).
Similar results were obtained for data collected at 60 days. The AUC by random forest is significantly greater than that of logistic regression (3.78%, P < 0.001). The AUC by random forest is also superior to logistic regression for the 90-day data collection period at 2 years (2.28%, P < 0.001). In all the prediction periods, the benefit of random forest tends to increase with the number of events (deaths).
DISCUSSION
The aim of the present study was to compare models to predict mortality in HD patients based on conventional logistic regression and random forest analysis [23]. The mortality of incident HD patients at 6 months, 1 year and 2 years was analysed using baseline data collected during the 30, 60 and 90 days after the initiation of regular HD. The main finding was that the mortality prediction models obtained with the random forest method were more accurate than with logistic regression. The superiority of random forest versus logistic regression was greater in the prediction of mortality at 2 years. Furthermore, the variables that each method identified as predictors of mortality were not always the same.
Logistic regression showed that the most determinant variables predicting mortality were age, type of vascular access (the fistula being protective of mortality) and also the residual diuresis volume. These results agree with studies such as the Dialysis Outcomes and Practice Patterns Study [24], which identified age, vascular access, albumin and other comorbidities as variables that may influence mortality. Other studies [25] have shown that mortality at 6 months is determined by age, dementia, peripheral vascular disease and low serum albumin. The England registry [7], which included 5447 patients on HD and peritoneal dialysis (PD) followed for 3 years, showed that mortality was associated with the following variables: advanced age, being white, diabetes as the cause of end-stage renal disease, HD (versus PD), vascular disease, smoking, haemoglobin and serum values of albumin, creatinine, calcium and phosphorus.
According to random forest analysis, the main variables predicting mortality in HD at 6 months are serum albumin, Kt/Vurea and haemoglobin. Variables predicting mortality at 1–2 years were BMI, age, serum albumin and Kt/Vurea.
Interestingly, random forest identifies serum albumin more often as one of the most important predictive variables and logistic regression identifies residual diuresis and vascular access as predictors of mortality.
In our study, the ability to predict mortality by both tests was compared by analysing the AUC of the ROC curves obtained by both methods (Table 2). The superiority of random forest versus logistic regression in predicting mortality was statistically significant at years 1 and 2, but it was more evident in the prediction of mortality at year 2. At 6 months, random forest was not significantly superior to logistic regression, probably due to the small number of events (deaths). Furthermore, logistic regression has the worst prediction accuracy (67.2%) and random forest has the best (73.3%).
There are studies that demonstrate the superiority of random forest if the data include variables that have an influence on each other [14, 15]. The use of random forest was instrumental in establishing an association among parameters of mineral metabolism in HD patients [18]. The identification of variables that predict outcome has allowed the construction of models and formulating algorithms with a specific objective, such as anaemia treatment with erythropoiesis-stimulating agents [26]. Other studies have shown the utility of random forest interaction trees on predictive covariates and the estimation of individualized treatment effects [17].
One limitation of our study is that the data come from a single centre and the values of mortality may not be extrapolated to other populations; however, comparison of different methods of analysis should be valid. Another limitation is that information on tobacco use and treatment with erythropoietin, intravenous iron and vitamin D was not included. Data collection was rigorous and the number of patients and follow-up periods were adequate and therefore the results obtained should be applicable to this type of population. Prospective studies are necessary to confirm our results. Analysis based on the artificial intelligence approach generally requires a large amount of data, which is now expedited by advances in computer processing power, relatively cheap digital storage and a flood of available digital data. The inherent requirement for large-scale, high-quality, well-structured data might ultimately limit the areas in which artificial intelligence can bring benefits to healthcare [13].
Not all published studies have found the same variables as predictors of mortality. In the present study, the analysis of the same data by two different methods did not identify the same variables as predictors of mortality. The diversity of methods may not allow uniformity of results.
The ability to interpret the logistic regression variable coefficients (ORs) is an important advantage of this method, but this oversimplification may limit the accuracy of the prediction with respect to random forest. Therefore one must be inclined to recognize that the variables identified by random forest are more reasonable than logistic regression. This last statement is not easy to assume after years of logistic regression analysis. Nevertheless, the analysis of the predictive value of single variables should be interpreted cautiously. In random forest, the predictive value of a variable on mortality is given not only by that specific variable, but also by the effect of other dependent variables (covariates) that in a non-linear manner may also affect mortality. It is easy to compare the predictive values of variables obtained by logistic regression and random forest.
Cox regression is another popular method for survival analysis and mortality prediction. Since with Cox the patients lost to follow-up are generally considered to build the model, we preferred comparing random forest with logistic regression so as to have the two models trained on exactly the same set of patients. Furthermore, different from random forest and logistic regression, Cox regression cannot be considered a binary classifier.
Additional studies will be needed to determine if one method like random forest is more accurate and useful than other more classical methods. The authors of the present work have no opinion as to whether one method of analysis is better than another; however, the information obtained clearly indicates that the applicability of artificial intelligence in determining mortality in HD patients is more than acceptable.
In conclusion, random forest regression analysis is an alternative valid method to identify variables and generate models that are useful to predict mortality in HD patients. The incorporation of statistical methods based on artificial intelligence holds promise for substantially improving healthcare delivery. It is predicted that familiarity with these methods for analysing big data will be a fundamental requirement for the next generation of physicians [27]. They will become important actors in the therapeutic relationship and will need to be bound by the core ethical principles, such as beneficence and respect for patients, that have guided clinicians [28].
SUPPLEMENTARY DATA
Supplementary data are available at ckj online.
Supplementary Material
FUNDING
This study was supported by grants from the National Institute of Health Carlos III (FIS 17/01785, FIS 17/01010), RETICs Red Renal RD06/0016/0007, the Consejeria de Salud of Junta de Andalucia (PI-0311-2014), the REDinREN from the National Institute of Health Carlos III (RD16/0009/0034) and the European group EUTox and CKD-MBD group.
CONFLICT OF INTEREST STATEMENT
M.R. has received research grants from Amgen and lecture fees from the following companies: Amgen, Vifor Pharma, Kyowa and Sanofi. A.M.-M. has received lecture fees from Medtronic/Bellco, Vifor Pharma, Astellas and AstraZeneca in the last 3 years. C.B. and F.B. are employed by Fresenius Medical Care. There are no patents, products in development or marketed products to declare. All the other authors declare no potential conflicts of interest. The results presented in this article have not been published previously in whole or part, except in abstract format.
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