Research Paper Volume 13, Issue 10 pp 14170—14184
Prediction of premature all-cause mortality in patients receiving peritoneal dialysis using modified artificial neural networks
How to Cite
Premature all-cause mortality is high in patients receiving peritoneal dialysis (PD). The accurate and early prediction of mortality is critical and difficult. Three prediction models, the logistic regression (LR) model, artificial neural network (ANN) classic model and a new structured ANN model (ANN mixed model), were constructed and evaluated using a receiver operating characteristic (ROC) curve analysis. The permutation feature importance was used to interpret the important features in the ANN models. Eight hundred fifty-nine patients were enrolled in the study. The LR model performed slightly better than the other two ANN models on the test dataset; however, in the total dataset, the ANN models fit much better. The ANN mixed model showed the best prediction performance, with area under the ROC curves (AUROCs) of 0.8 and 0.79 for the 6-month and 12-month datasets. Our study showed that age, diastolic blood pressure (DBP), and low-density lipoprotein cholesterol (LDL-c) levels were common risk factors for premature mortality in patients receiving PD. Our ANN mixed model had incomparable advantages in fitting the overall data characteristics, and age is a steady risk factor for premature mortality in patients undergoing PD. Otherwise, DBP and LDL-c levels should receive more attention for all-cause mortality during follow-up.
Materials and Methods
Study populationData from 1241 patients with ESRD who initially started PD between Jan 2006 and Dec 2019 at the First Affiliated Hospital of Wenzhou University were collected and reviewed. The inclusion criteria were as follows: 1. older than 18 years and 2. routine follow-up for more than twelve months in our PD center. The exclusion criteria were as follows: 1. a history of continuous hemodialysis for more than six months before continuous ambulatory peritoneal dialysis (CAPD) or a combination of continuous hemodialysis and CAPD, 2. a history of kidney transplantation, and 3. missing important data. Patients who met the above criteria were eventually enrolled in this study. The study protocol was reviewed and approved by the Ethics Committee of the First Affiliated Hospital of Wenzhou University before collecting any data.
Data collection and preparationThe following clinical characteristics were collected at the initiation of CAPD as predictor variables: demographic variables, including sex, age and complications such as chronic heart disease (CHD), diabetes mellitus (DM), and malignancy; and laboratory variables, including systolic blood pressure (SBP, mmHg), diastolic blood pressure (DBP, mmHg), total triglycerides (Tg), total cholesterol (Tc), low-density lipoprotein cholesterol (LDL-c), high-density lipoprotein cholesterol (HDL-c), serum albumin (g/dL), hemoglobin (g/dL), blood urea nitrogen (BUN, mg/dL), serum creatinine (Scr, μmol/L), serum phosphorus (P, mmol/l), intact parathyroid hormone (iPTH, pg/ml), and Kt/V. The causes of premature death were recorded during follow-up, and the primary endpoint of the study was all-cause mortality. We collected the data at the beginning of PD and during the follow-up period. Three datasets, namely, the 0-month, 6-month, and 12-month datasets, were collected, and the 0-month dataset (also called the total dataset) was used for training the prediction models. Missing values were imputed with values from the nearest three months. All included numerical variables were normalized by the Z-score.
Construction of prediction modelsThe TensorFlow platform (https://www.tensorflow.org/) was used for training the ANN models . We constructed two different types of ANN models. One is called the ANN classic model, which was built using a single neural network with 12 hidden layers. The numerical variables and categorical variables were input into the neural network simultaneously (Supplementary Figure 1). The other is called the ANN mixed model. Two different sub-neural networks were built for the numerical variables and categorical variables with nine hidden layers and eleven hidden layers, respectively. The two sub-networks were then merged into a new neural network with two hidden layers for predicting the outcomes (Supplementary Figure 1). The hyperparameters of the ANN models were adjusted during the study. Finally, we set the following parameters for the ANN models: epoch = 3500, batch size = 220, iteration = 0.0001, and L1 and L2 regularization penalties. The multivariable logistic model was built using the Scikit-learn platform . We selected the 0-month dataset to train the ANN models and logistic models and construct an early prediction model. The full 0-month dataset was randomly divided into three datasets: a training dataset (63.2%), validation dataset (48%), and test dataset (20%). The training dataset was used to train the ANN models and logistic models. The validation dataset displayed 31.2% overlap with the training dataset and was used to control overfitting during training of the ANN model. The test dataset did not have any overlapping data with the training dataset, and the validation dataset was used to assess the performance of the ANN models and logistic models (Supplementary Figure 2).
Evaluation of the performance of the ANN and logistic modelsWe calculated the predictive outcomes of the ANN and logistic models using the test dataset and the 0-month, 6-month, and 12-month datasets during the construction of every model. Then, the areas under the receiver operating characteristic (ROC) curves (AUROCs) were calculated to filter models with extremely poor performance using a threshold of 0.6, and ROC curves were plotted to visualize the relationship between the true positive rate (TPR) and false positive rate (FPR) at different cutoff values. We also calculated the accuracy, F1 score, precision, and recall values at a fixed threshold value (0.2) to evaluate the performance of the selected models in predicting positive cases (dead patients) or negative cases (surviving patients) using the Scikit-learn application . A phi coefficient analysis was performed to measure the association between the predicted and true outcomes . The permutation feature importance, which is defined as the decrease in the score of a model when a single feature value is randomly shuffled , was calculated to evaluate the significance of the included variables.
Statistical analysisThe numerical data are presented as the means [standard deviations (SD)] or the medians [interquartile ranges (IQRs)], and differences between the groups were examined using variance analysis or the Kruskal-Wallis rank test. Categorical data are presented as counts with percentages (%), and differences between the groups were analyzed using Pearson’s chi-square test. Multivariable LR models based on the 0-month, 6-month, and 12-month datasets were built to evaluate the effects of the included variables on the primary outcomes. All reported p-values are two-tailed, and p-values less than 0.05 were considered to indicate a statistically significant difference. Python (version 3.8)  and R software (version 4.0.2, R Core Team)  and embedded packages were used to prepare the datasets, perform the analyses, and create the plots [20–24]. P<0.05 was set as statistically significant.
ResultsEight hundred fifty-nine patients who met the criteria were enrolled in the study, and 82 (9.54%) patients met the primary endpoint at a median follow-up time of 40.5 [18.2, 59.8] months. According to our 0-month dataset, the variables diabetes, CHD, age, DBP, LDL-c levels, and serum albumin levels were significantly different between the patients with and without the primary endpoint (Table 1). Supplementary Figure 3 displays the comparisons of the included variables in the 0-month, 6-month, and 12-month datasets. The plots of the three datasets showed similar differences in most of the included variables.
Table 1. Baseline characteristics of the included patients with CAPD.
|Characteristics||All-cause premature mortality||p-value|
|Age (years, median [IQR])||48.0 [38.0, 58.0]||63.0 [54.0, 70.0]||<0.001|
|Male (n, %)||432 (55.6)||51 (62.2)||0.3|
|SBP (mmHg, median [IQR])||145.0 [132.0, 159.0]||148.0 [133.2, 164.0]||0.2|
|DBP (mmHg, median [IQR])||88.0 [78.0, 97.0]||79.0 [71.0, 91.5]||<0.001|
|Tg (mmol/L, median [IQR])||1.6 [1.2, 2.1]||1.6 [1.2, 2.1]||0.9|
|Tc (mmol/L, median [IQR])||4.6 [3.9, 5.4]||4.8 [4.1, 5.5]||0.3|
|LDL-c (mmol/L, median [IQR])||2.5 [2.0, 3.1]||2.8 [2.2, 3.4]||0.01|
|HDL-c (mmol/L, median [IQR])||1.0 [0.9, 1.2]||1.0 [0.8, 1.2]||0.05|
|Serum albumin (g/L, median [IQR])||37.1 [33.5, 40.4]||35.1 [32.0, 39.0]||0.004|
|Hemoglobin (g/L, median [IQR])||95.0 [82.0, 108.0]||93.0 [81.2, 104.0]||0.2|
|BUN (mmol/L, median [IQR])||19.1 [13.9, 24.6]||18.8 [12.9, 24.8]||0.9|
|SCR (μmol/L, median [IQR])||646.0 [326.0, 888.0]||526.5 [306.2, 773.5]||0.05|
|Serum calcium (mmol/L, median [IQR])||2.2 [2.0, 2.3]||2.1 [2.0, 2.2]||0.3|
|Serum phosphorus (mmol/L, median [IQR])||1.6 [1.3, 1.8]||1.5 [1.3, 1.8]||0.3|
|iPTH (pg/mL, median [IQR])||212.6 [108.4, 371.9]||181.6 [82.0, 309.4]||0.07|
|Kt/V (median [IQR])||1.9 [1.7, 2.2]||1.8 [1.6, 2.1]||0.1|
|Diabetes (n, %)||176 (22.7)||37 (45.1)||<0.001|
|Hypertension (n, %)||619 (94.8)||78 (98.7)||0.2|
|Chronic heart disease (n, %)||178 (22.9)||38 (46.3)||<0.001|
|Malignancy (n, %)||53 (6.8)||10 (12.2)||0.1|
|Follow-up time (month, median [IQR])||38.0 [16.0, 66.0]||40.5 [18.2, 59.8]||0.9|
|SBP: systolic blood pressure; DBP: diastolic blood pressure; Tg: triglycerides; Tc: total cholesterol; LDL-c: low-density lipoprotein cholesterol; HDL-c: high-density lipoprotein cholesterol; BUN: urea nitrogen; SCR: serum creatinine; iPTH: intact parathyroid hormone.|
Table 2. Multivariable logistic regression models for the three full datasets.
|Variables||Model 0||Model 1||Model 2|
|β (se)||p-value||β (se)||p-value||β (se)||p-value|
|Age||0.071 (0.013)||<0.001*||0.065 (0.013)||<0.001*||0.068 (0.013)||<0.001*|
|CHD||0.578 (0.272)||0.03*||0.479 (0.276)||0.08||0.462 (0.274)||0.09|
|DBP||-0.014 (0.012)||0.2||-0.028 (0.015)||0.07||-0.026 (0.016)||0.1|
|Diabetes||0.355 (0.294)||0.2||0.051 (0.305)||0.9||-0.023 (0.315)||0.9|
|Malignancy||0.342 (0.416)||0.4||0.272 (0.416)||0.5||0.308 (0.411)||0.5|
|Albumin||-0.041 (0.029)||0.2||-0.1 (0.033)||0.003*||-0.117 (0.034)||0.001*|
|BUN||0 (0.024)||1||0.006 (0.028)||0.8||-0.015 (0.031)||0.6|
|Ca||0.854 (0.682)||0.2||1.469 (0.876)||0.09||1.379 (0.87)||0.1|
|SCR||-0.001 (0.001)||0.2||-0.001 (0.001)||0.2||0 (0.001)||0.4|
|Hb||-0.014 (0.008)||0.09||-0.015 (0.009)||0.09||-0.013 (0.009)||0.2|
|HDL-c||-0.457 (0.562)||0.4||-0.162 (0.632)||0.8||0.345 (0.264)||0.2|
|LDL-c||0.514 (0.309)||0.1||0.87 (0.412)||0.04*||0.791 (0.36)||0.03*|
|P||0.478 (0.423)||0.3||0.343 (0.49)||0.5||0.488 (0.51)||0.3|
|iPTH||0.054 (0.158)||0.7||0.061 (0.172)||0.7||0.12 (0.178)||0.5|
|Tc||-0.134 (0.272)||0.6||-0.532 (0.364)||0.1||-0.554 (0.289)||0.06|
|Tg||-0.177 (0.192)||0.4||0.2 (0.216)||0.4||0.282 (0.173)||0.1|
|SBP||0.012 (0.007)||0.1||0.014 (0.009)||0.1||0.015 (0.009)||0.1|
|Sex||0.293 (0.291)||0.3||0.421 (0.318)||0.2||0.56 (0.321)||0.08|
|Kt/V||-0.259 (0.313)||0.4||0 (0.376)||1||0.124 (0.395)||0.8|
|Model 0: 0-month datasets; Model 1: 6-month datasets; Model 2: 12-month datasets; iPTH: intact parathyroid hormone; SBP: systolic blood pressure; DBP: diastolic blood pressure; MAP: mean arterial pressure; BMI: body mass index; RAAS: renin–angiotensin–aldosterone system agents; CCBs: calcium channel blockers.|
Figure 1. ROC curves of selected models for predicting the primary outcome in different datasets. The dark solid lines indicate the median curve of the three types of models (ANN mixed model, ANN classic model, and logistic model). (A) Performance of selected models in the test dataset, (B) Performance of selected models in the total dataset, (C) Performance of selected models in the 6-month dataset, (D) Performance of selected models in the 12-month dataset.
Figure 2. Post hoc test of performance. (A) Performance of the models for the negative prediction in the test dataset; (B) performance of the models for the positive prediction in the test dataset; (C) performance of the models for the negative prediction in the total dataset; and (D) performance of the models for the positive prediction in the total dataset. The short bar indicates the difference in the mean value with a 95% confidence interval.
Figure 3. Distribution of the performance outcomes of the models for the 6-month and 12-month datasets. (A) Performance of the models for the negative prediction in the 6-month dataset, (B) Performance of the models for the positive prediction in the 6-month dataset, (C) Performance of the models for the negative prediction in the 12-month dataset, (D) Performance of the models for the positive prediction in the 12-month dataset.
Table 3. Performance of the models in the follow-up datasets.
|Performance||Negative prediction||p-value||Positive prediction||p-value|
|ANN mixed model||ANN classic model||Logistic model||ANN mixed model||ANN classic model||Logistic model|
|Accuracy||0.89 (0.07)||0.85 (0.03)||0.80 (0.02)||<0.001||0.89 (0.07)||0.85 (0.03)||0.80 (0.02)||<0.001|
|F1 score||0.93 (0.08)||0.92 (0.02)||0.89 (0.01)||<0.001||0.43 (0.07)||0.05 (0.04)||0.09 (0.02)||<0.001|
|Precision||0.93 (0.08)||0.90 (0.00)||0.90 (0.00)||<0.001||0.44 (0.09)||0.06 (0.04)||0.08 (0.02)||<0.001|
|Recall||0.93 (0.08)||0.93 (0.03)||0.87 (0.02)||<0.001||0.44 (0.10)||0.05 (0.04)||0.11 (0.03)||<0.001|
|Accuracy||0.88 (0.07)||0.85 (0.03)||0.80 (0.02)||<0.001||0.88 (0.07)||0.85 (0.03)||0.80 (0.02)||<0.001|
|F1 score||0.93 (0.08)||0.92 (0.02)||0.89 (0.01)||<0.001||0.39 (0.07)||0.05 (0.03)||0.09 (0.03)||<0.001|
|Precision||0.93 (0.08)||0.90 (0.00)||0.90 (0.00)||<0.001||0.40 (0.07)||0.07 (0.04)||0.08 (0.02)||<0.001|
|Recall||0.93 (0.08)||0.93 (0.03)||0.88 (0.02)||<0.001||0.39 (0.10)||0.05 (0.04)||0.10 (0.04)||<0.001|
|Values are presented as the means (SDs).|
DiscussionAccording to our baseline dataset, the traditional risk factors age, diabetes, albumin level and cardiovascular disease were significantly different between the surviving patients and patients who experienced premature mortality, consistent with the findings of previous studies [25, 26]. Furthermore, DBP and LDL-c levels were also significantly different between the two groups. Our multivariable LR models based on the baseline, 6-month and 12-month datasets further confirmed that an older age combined with cardiovascular disease, lower serum albumin levels, and higher LDL-c levels were independent risk factors for premature mortality in patients receiving PD. Different performance outcomes of the LR models and ANN models for the test dataset and whole dataset were observed in our study. This difference may be attributed to the different algorithms used by LR and ANN. LR is a linear classification method, and its cost function is convex. Thus, it is guaranteed to find the global cost minimum [27, 28]. Although the ANN model is a nonlinear classification model and can fit perfectly to the training dataset, the cost function of a neural network is generally neither convex nor concave, and it easily falls into a local optimum . Thus, the ANN model displayed an inferior performance compared to the LR model when analyzing a small sample but fit better in a large-scale population. Papadrakakis et al. found that the performance of the ANN model can be significantly improved by adjusting the network structure and hyperparameters of the model . Our study developed a new structure for the ANN model, which was called the ANN mixed model. Our external validation of the follow-up dataset showed the predictive performance increased significantly using the ANN mixed model to analyze the 6-month and 12-month datasets than using the LR model and ANN classic model. Thus, we considered that the ANN mixed model has a higher efficiency of generalization performance. However, the mean precision and recall for the positive prediction of the ANN mixed models in the 6-month and 12-month datasets was approximately 40%, suggesting that our model might be insufficient to detect positive cases in an external dataset. One reason is the imbalanced category of premature all-cause mortality in our cohort, which significantly increased the difficulty of identifying the positive cases. Furthermore, the validation of the 6-month and 12-month datasets included patients who had been receiving treatment, and the treatment significantly affects the clinical characteristics of patients receiving PD, which potentially affected the prediction accuracy of our model. The classic studies constructing prediction models or identifying risk factors mostly included categorical and continuous variables simultaneously [25, 31–33]. Our study showed that the ANN classic and LR models, which were similar to the classic studies, were inaccurate in the 6-month and 12-month datasets. Burrett et al. considered that differences in the populations studied may have contributed to the loss of predictive power for the prognostic score . We assumed that the significance of the scalar was different between categorical variables and continuous variables. The simultaneous inclusion of categorical and continuous variables in an identical vector space for fitting a model may increase overfitting and adversely affect the generalization performance. Based on our results, the construction of separate vector spaces for categorical and continuous variables in a model significantly improved the generalization performance. An ANN is a black-box model, and it does not easily display the relationship between features and outcomes . We used a permutation feature importance analysis, which is used for interpreting the importance of variables in a model [35–37], to identify the important characteristics contributing to premature death. Importantly, age, DBP, and LDL-c levels were the top three important variables in the ANN mixed model. The LR models based on the 6-month and 12-month datasets also showed that DBP and LDL-c levels were independent risk factors for premature all-cause death. Sakacı et al. also found that age is an independent risk factor for mortality in patients undergoing dialysis . Although age is an unmodifiable variable, some age-related variables, such as nutritional status, can still be improved by better management . Previous studies have mainly focused on the significance of SBP in patients with ESRD . Our research identified DBP as a crucial risk factor for predicting death in patients undergoing PD and one of the most valuable variables in the ANN model. Lip et al. observed a reverse J-shaped relationship between DBP and death from cardiovascular events. Cardiovascular death was also the primary factor contributing to premature mortality in our patients receiving PD [31, 41]. Therefore, DBP should receive more attention in patients receiving PD during clinical practice. Lowering LDL-c levels can significantly improve the prognosis of patients with chronic kidney disease (CKD) stage 1-4, but researchers have not clearly determined whether it can improve the prognosis of patients with CKD5 or CKD5d [42–44]. Strict lipid control may also cause malnutrition in patients receiving dialysis, which is an important factor contributing to the death of patients receiving dialysis [45, 46]. LDL-c levels were closely related to the premature mortality of patients treated with PD in our study. As the life span of patients treated with dialysis increases, the effect of dyslipidemia on patients receiving PD cannot be ignored. Therefore, further studies of the role of lipids in patients undergoing PD are still necessary. Our research had some limitations. First, the study is based on a single center and a relatively insufficient sample size, which may contribute to overfitting and affect generalization performance. Although L1 and L2 regularization were used during ANN training and follow-up datasets were used for external validation, the initial PD data must still be collected from other centers for external verification. Second, a few patients receiving PD withdrew during follow-up, and these patients may have died at home or in other departments but were not categorized into the premature mortality group, resulting in an endpoint determination bias affecting the accuracy of our model. Third, the proportion of patients with premature all-cause mortality is small in our cohort, leading to a significant imbalance in classification, which affects the detection power of our model. In summary, our study compared the value of traditional logistic models and ANNs in predicting all-cause mortality in patients treated with PD and showed that ANNs had incomparable advantages in fitting the overall data characteristics. Thus, a highly precise ANN model for the early prediction of premature all-cause mortality in patients receiving PD was established. Our study also showed the importance of DBP and LDL-c levels in predicting the premature all-cause mortality of patients receiving PD; thus, these factors should receive more attention during follow-up.
PD: peritoneal dialysis; LR: logistic regression; ANN: artificial neural network; ROC: receiver operating characteristic; AUROC: area under the receiver operating characteristic curve; DBP: diastolic blood pressure; LDL-c: low-density lipoprotein cholesterol; ESRD: end-stage renal disease; CAPD: continuous ambulatory peritoneal dialysis; CHD: chronic heart disease; DM: diabetes mellitus; SBP: systolic blood pressure; Tg: total triglycerides; Tc: total cholesterol; HDL-c: high-density lipoprotein cholesterol; BUN: blood urea nitrogen; Scr: serum creatinine; iPTH: intact parathyroid hormone; TPR: true positive rate; FPR: false positive rate; SD: standard deviation; IQR: interquartile range.
Research idea and study design: QXZ, XHY and JZ; data acquisition: QXZ, XHY, HYD and ZL; data analysis/interpretation: QXZ, XHY, YLS and JZ; statistical analysis: JZ; and supervision or mentorship: ZS, CSC, and RRS. Each author contributed important intellectual content during manuscript drafting and accepts accountability for the overall work by ensuring that questions pertaining to the accuracy or integrity of any portion of the work are appropriately investigated and resolved. All authors have read and approved the manuscript.
The authors would like to thank their colleagues in the Department of Nephrology at the First Affiliated Hospital of Wenzhou Medical University for their invaluable support and selfless assistance during this study.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This study was supported by grants from the Wenzhou Committee of Science and Technology of China (2020Y0611).
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