The invited Italian study centers and the patients enrolled in this study are described in detail in our previous work [18]. Briefly, as this was a cross-sectional observational multi-center study, the enrollment criteria were not questioned. Consequently, all of the consecutive patients undergoing a native kidney biopsy during the active recruitment period were considered eligible and there were no a priori exclusion criteria. In relation with the aim of this study, secondary exclusion criteria were pediatric patients (age at kidney biopsy less than 18 years), unstable patients for acute kidney injury (AKI) or AKI in patients on chronic kidney disease (CKD), unavailability of eGFR or its estimated value higher than 200 ml/min, unavailability of kidney length or of parenchymal thickness of biopsied kidney.

Data collection was centralized and made use of an ad hoc web-based database linked to the Italian Renal Biopsy Registry (http://www.irrb.net/).

All of the patients gave their written informed consent; the study protocol was approved by the Ethics Committee of Bari University and implemented in accordance with the principles of the Declaration of Helsinki. It was not appropriate to involve patients or the public in the design, or conduct, or reporting, or dissemination plans of our research. This independent study without any sponsorship was registered with ClinicalTrials.gov (No. NCT04948593).

The primary goal of this study was to define the relation between the renal length and parenchymal thickness measured with ultrasounds and the eGFR, taking into account the role of the histopathological diagnosis made by native kidney biopsy.

Relevant patient-related covariates and factors recorded included age, gender, diabetes, the clinical presentation of their renal disease, the presence of renal failure, the eGFR according to CKD-EPI equations [9], the bipolar longitudinal diameter and the parenchymal thickness of the biopsied kidney, the magnitude of proteinuria and the histopathologic kidney diagnosis. The histopathologic kidney diagnosis, defined according to our previous work [18], was treated in the statistical analysis as a categorical variable.

Ultrasound parameters were measured in the biopsied kidney, thus more frequently on the left side (95% of patients), on the midaxillary line with the patient in lateral decubitus. Parenchymal thickness was measured and reported where it was minimum in value, avoiding Bertin's columns.

To avoid bias, proteinuria, eGFR and ultrasound parameters were measured before the native kidney biopsy.

The diabetic variables were considered at three levels. The clinical diabetes status (yes/no) was defined according to the clinical diagnosis of diabetes without the knowledge of the histopathologic kidney diagnosis. In addition, the type [19] and the severity [20] of diabetic nephropathy according to Mazzucco G et al. [19] and to Tervaert TW et al. [20], respectively, were also considered.

For descriptive purposes, quantitative variables were analysed using their median values and the 10th and 90th percentiles, as indexes of central tendency and variability, respectively. Categorical variables were analysed as absolute numbers and percentages.

For inferential purposes, multivariate analysis of variance was performed, using the eGFR as dependent variable, according to CKD-EPI equation [9] expressed in ml/min/1.73 m2. To investigate the role of the various covariates, a step-by-step approach was used starting from the ultrasound parameters, such as the kidney bipolar diameter and parenchymal thickness. According to the suggestion of Lucisano et al. [21], we have considered also the role of the kidney length indexed for body height compared with the kidney length alone. The next step was adding two covariates easily available before kidney biopsy, such as the clinical diabetes status (yes/no) and proteinuria (g/day) values. To investigate the slope between US parameters and eGFR in patients with clinical diabetes compared with patients without clinical diabetes, we tested the interaction term clinical diabetes status by kidney length. Thus, we tested the histopathologic kidney diagnosis, as categorical variable, and its interaction with the US biopsied kidney length. Finally, we added in the model the type [19] and severity [20] of diabetic nephropathy. The amount of explained variance, through the adjusted R square, was used as goodness of fit. The partial Eta square of each covariate was used to test the relative net impact of each one compared to the others.

All the analyses were performed using the Statistical Package for Social Sciences (SPSS for Windows, version 23.0).