Improving precision of glomerular filtration rate estimating model by ensemble learning

Determining glomerular filtration rate (GFR) is essential for screening early impairment of kidney function, evaluating progressive kidney deterioration and complications, adjusting the dosage of drugs, and managing the risks of chronic kidney disease (CKD) [1]. The gold standard GFR assays are inulin clearance and isotope imaging. The high cost of inulin limits its routine clinical use. Isotope imaging is moderately costly, but usage is limited by radiation exposure. Consequently, GFR is often estimated by regression analysis with sex, age and specific serum filtration markers (e.g., serum creatinine and cystatin C) as covariates. However, even the most accurate GFR estimation equations [2] are biased and imprecise [3] because they do not include physiological variables that only affect serum filtration markers other than GFR [4]. The performance of equations that estimate GFR may be improved either by adding additional covariates, or by applying more sophisticated or advanced method than traditional regression.

Ensemble learning is a simple, well-known machine learning method in which the results obtained with different mathematic models is combined to generate a better result. It is widely used in engineering applications because of its superior performance in estimation [5]. A previous study found that ensemble learning significantly outperformed single learning models for cataract detection and grading [6]. We hypothesized that performance of regression-based estimated GFR models can be improved by ensemble learning because it is more robust, allowing more complex relationship between GFR and covariates and can account for more complicated interactions among the covariates.

Regression, ANN, SVM, and ensemble learning models were developed to estimate GFR using sex, age, and serum creatinine as covariates. A single demonstration population was used to develop the models, and a single external validation data set was used to compare performance with that of the regression model. Precision was improved in the ensemble learning method, but bias and accuracy in the regression and the ensemble learning models were similar.

Ensemble learning has previously been used to estimate GFR. Inker et al. evaluated cystatin C as an additional covariate [2], finding that a model averaging creatinine and cystatin C values had similar bias (median difference) but higher precision (IQR of difference) and accuracy (the proportion of participants whose eGFR deviated from mGFR by more than 20 or 30%) than either of the two covariates used alone. In a later study, Inker et al. [10] used ensemble learning to evaluate β-trace protein (BTP) and β₂-microglobulin (B2M) as covariates to estimate GFR. Their existing CKD-EPI creatinine–cystatin C equation, and a new equation including BTP and B2M were evaluated. The precision and accuracy of average of the two equations was similar to those of the individual equations. The ensemble learning method in those two studies used different combinations of covariates. In this study, ensemble learning employed different models all with the same covariates. There was no need to perform additional testing to measure additional covariates from each patient, which did not increase patient costs.

Why did the ensemble learning model perform better than the regression model? ANN and SVM models could have relatively low bias relative to variance [11, 12]. A good single model might be constructed from theoretical data, but the expected performance might not be realized with the datasets and parameter values used during the training process. A single model might, unfortunately have a high variance, but combining several models should decrease the overall variance, as the deviations of the single models would be in different directions [5]. Ensemble learning thus results in a high level of performance together with improved variance.

Ensemble learning performed better than the other models in GFR estimation even though simple averaging was used. Other, methods more complex than averaging such as weighted averaging or stacking have been used [5]. Planning for ensemble learning when designing single models will achieve increase diversity, leading increased performance improvement after model combination. It is to be expected that using more complicated ensemble learning strategies will further improve performance in GFR estimation.

The fact that the ensemble model achieved better precision but worse bias and accuracy than current regression model, demonstrated that it was difficult to develop a new model superior to regression model in all terms of bias, precision and accuracy, especially with only three covariates. Recently deep learning has made big success in medical informatics, but the constructed models are complicated with many covariates. That is, the advantages of complicated models are obvious in dealing with complex problem such as natural language processing, image and speech recognition. However, GFR estimation as a simple regression task limits the capacity of complicated models. It’s supposed that adding more relevant but different covariates may be more promising than improving method of model construction.

The study limitations include the evaluation of data representing a specific group of CKD patients in China. Also, although there were some differences in the characteristics of the patients in the development and the external validation cohorts, both were recruited at same institution. Consequently, external validation of the effectiveness of the ensemble learning method that was used is desirable.

A novel ensemble learning model was developed to estimate GFR, and it achieved better precision than the widely used regression model. The advantage of ensemble learning method in estimation of GFR warrants further investigation.