The impact of baseline glomerular filtration rate on subsequent changes of glomerular filtration rate in patients with chronic kidney disease

Higher baseline glomerular filtration rate (GFR) may yield subsequent steeper GFR decline, especially in patients with diabetes mellitus (DM). However, this correlation in patients with chronic kidney disease (CKD) and the presence or absence of DM remains controversial. We conducted a longitudinal cohort study in a single medical center between 2011 and 2018. Participants with CKD stage 1 to 3A were enrolled and divided into DM groups and non-DM groups, and then followed up at least every 6 months. We used a linear mixed regression model with centering time variable to overcome the problem of mathematical coupling in the analysis of the relation between baseline GFR and the changes, and compared the results from correct and incorrect specifications of the mixed models. A total number of 1002 patients with 285 diabetic and 717 non-diabetic persons was identified. The linear mixed regression model revealed a significantly negative correlation between baseline GFR and subsequent GFR change rate in both diabetic group and non-diabetic group (r =  − 0.44 [95% confidence interval [CI], − 0.69 to − 0.09]), but no statistical significance in non-diabetic group after within-subject mean centering of time variable (r =  − 0.09 [95% CI, − 0.41 to 0.25]). Our study showed that higher baseline GFR was associated with a subsequent steeper GFR decline in the DM group but not in the non-DM group among patients with early-stage CKD. Exact model specifications should be described in detail to prevent from a spurious conclusion.

Data collection. Basic personal information of age, sex and underlying comorbidity were recorded. Body height, weight, blood pressure and biochemical data, including serum creatinine, low-density lipoprotein cholesterol, fasting glucose and HbA1c (only for DM patients) and UPCR were recorded at baseline and every 3 to 6 months. The estimated GFR (eGFR) was calculated by the Taiwanese MDRD equation [1.309 × (186 × (serum creatinine) −1.154 × Age −0.203 × 0.742 (if female)) 0.912 ] , which was developed by using linear regression of the difference on the average of log-transformed inulin clearance and the MDRD, CKD-Epidemiology Collaboration (CKD-EPI) equations, and has been validated and shown to be more accurate and precise than MDRD-4 variables and CKD-EPI equations for Taiwanese adults 28,30 . Statistical analyses. We used the mean ± standard deviation (SD) to summarize continuous variables, and relative frequency for categorical variables. The differences between the two groups were analyzed by using the t-test or the chi-squared test. Variables with a non-normal distribution were analyzed by the Mann-Whitney U test. A two-level linear mixed regression model with the random intercept and slope was used to analyze eGFR measurements and solving the statistical problems of mathematical coupling. The dependent variable was the absolute value of eGFR. The time variable was the duration of observation starting from the date of the first visit up to that of the last visit in nephrology outpatient department. To test the appropriate null hypothesis in multivariable linear mixed regression model, we undertook within-subject mean centering for the duration of observation to correct for the effects of mathematical coupling between random intercept and slope [23][24][25][26] . The basic linear mixed model is written as: www.nature.com/scientificreports/ where eGFR ij is the observed eGFR for the jth patient on ith occasion; b 0j is the intercept for the jth patient β 0 is the average intercept for the whole patient population, and u 0j is the random intercept, i.e. the variations in the intercepts of the whole patient population, which is assumed to follow a normal distribution with the mean of zero and variance of σ 2 u0 ; Time is the centered time variable, i.e. the centered duration of observation in years for each patient; b 1j is the slope for the jth patient β 1 is the average slope for the whole patient population, and u 1j is the random slope, i.e. the variations in the slopes of the whole patient population, which is assumed to follow a normal distribution with the mean of zero and variance of σ 2 u1 ; and e ij is the residual error term for eGFR ij . u 0j and u 1j follow a bivariate normal distribution, and the parameter σ u01 is the covariance between random intercept and slope and can be used to calculate the correlation r between the baseline eGFR and the subsequent changes in eGFR by using the formulae: . The effect of an independent variable on GFR change rate in mL/ min per year was evaluated by using 2-way interaction between the independent variables and the centered time variable. The relation between baseline eGFR (ml/min/1.73 m 2 ) and succeeding eGFR changes (ml/min/1.73 m 2 per year) was evaluated by the correlation between the random intercept and slopes. We also conducted the same analyses without centering the time variables to assess the impact of mathematical coupling on the estimation of the correlation between the baseline eGFR and the change. We performed covariates adjustment, including sex and age in model 1, then plus BMI and systolic blood pressure (SBP) in model 2, and added current smoking status, HbA1c (only in diabetes mellitus group) and urine protein-creatinine ratio in model 3. A P-value < 0.05 was considered statistically significance. The statistical software Stata version 14 (Stata Corp College Station, Texas, USA) (https:// www. stata. com/) was used for data analysis. All methods carried out were in accordance with relevant guidelines and national legal regulations.

Results
Baseline characteristics of study population. The baseline characteristics of diabetes mellitus and non-diabetes mellitus groups is shown in Table 1. A total number of 1002 patients with early-stage CKD (717 in non-DM group and 285 in DM group, respectively) and 7621 nephrology clinic visits were identified between January 1, 2011, and December 31, 2018. More than 70 percent of patients in both DM and non-DM groups were male (79.6% and 72.9%, respectively). Patients in DM group were 4.4 years older than those in non-DM Table 1. Baseline characteristics of study population. Estimates are given as number (percent) and mean ± standard deviation. DM diabetes mellitus, BMI body-mass index, SBP systolic blood pressure, DBP diastolic blood pressure, LDL low-density lipoprotein, Hemoglobin A1c, UPCR urine protein-creatinine ratio, eGFR estimated glomerular filtration rate.  Fig. 1), but the lengths of follow-up varied greatly among participants.
Fixed effects of risk factors on the baseline eGFR and changes of eGFR. Our multivariable mixed model (model 3) showed that males and older age had a significantly negative association with baseline eGFR; the average baseline eGFR of men was 4.61 ml/min/1.73 m 2 lower than that of women, and the average baseline eGFR decreased by 0.50 ml/min/1.73 m 2 when a patient's age increased by 1 year. UPCR had a significantly negative relationship to the changes of eGFR in the DM group; the average change in eGFR decreased by 0.10 ml/ min/1.73 m 2 as UPCR increased by 10 mg/g ( Table 2). In the non-DM group, male and older age also had a negative association with baseline eGFR; the average baseline eGFR of men was 10.85 ml/min/1.73 m 2 lower than that of women, and the average baseline eGFR decreased by 0.44 ml/min/1.73 m 2 when a patient's age increased by 1 year, and higher systolic blood pressure showed greater changes in eGFR; the average change in eGFR increased by 0.02 ml/min/1.73 m 2 when systolic blood pressure increased by 1 mmHg (Table 3).

Association between baseline eGFR and subsequent eGFR change.
In the DM group, a significantly consistent negative correlation between GFR at baseline (random intercept) and GFR change rate (random slope) was found after multivariable adjustment (r = − 0. 46 (Fig. 2).

Discussion
To our best knowledge, this study is the first to explore the relation between baseline eGFR and subsequent GFR decline in DM and non-DM patients with early-stage CKD in a long-term population-based cohort. After multivariable adjustment, we found that male and increased age had a significantly negative effect on the baseline eGFR, and only UPCR showed a significant relation to the decrease in eGFR in patients with CKD and DM. In patients with CKD and non-DM, males and older age also showed a significantly negative association with the baseline eGFR but males (in model 1 and 2) and higher systolic pressure were associated with a significantly www.nature.com/scientificreports/ smaller decrease in eGFR. Naïve analyses without centering of the time variable found a significantly negative correlation between GFR at baseline and GFR change in DM and non-DM patients with CKD. After withinsubject mean centering, a significant but moderate correlation were observed only in DM patients with CKD. This indicates the impact of mathematical coupling on the estimation of the correlation between GFR at baseline and GFR change cannot be overlooked, and this is consistent with findings in the previous methodological studies 23,25,[31][32][33] . It is still controversial whether hyperfiltration with higher baseline GFR is related to subsequent GFR decline. Some studies revealed that hyperfiltration with higher eGFR was associated with more rapid eGFR decline in patients with type 1 or type 2 DM 16-19,34-36 . Moreover, Melsom et al. showed that this significant correlation existed not only in patients with DM but also in those without DM 17 . In contrast, no substantial correlation

Effects on baseline eGFR (intercept)
Sex ( www.nature.com/scientificreports/ between baseline GFR and subsequent GFR decline was also found in other investigations 37,38 . This inconsistency may be attributed to considerable GFR variations over time, such as age-related GFR decline, GFR measurements, and inappropriate statistical methods for assessing the relation between GFR at baseline and its changes 39,40 . In our study, a negative relation between the baseline eGFR and subsequent decline was found only in patients with DM but not in patients without DM. The accurate measurement of GFR should examine the clearance of materials which are only through renal filtration, such as iohexol, iothalamate, inulin, etc. 41 . However, the estimated GFR was more readily available and cost-effective in the clinical practice than GFR via direct measurement, which was difficult to replicate due to different physiological conditions and great variations over time. Two of the most common equations for estimating GFR were MDRD-4 variables and CKD-EPI worldwide. However, the MDRD-4 equation was created by using data from Caucasians and African Americans with CKD and is likely to underestimate GFR, when eGFR greater than 60 mL/min/ 1.73 m 242, 43 . The KDIGO 2012 guidelines recommend using the CKD-EPI equation in adults, unless an alternative equation has been shown to be more accurate in the specific population 44 . In our study, we Table 4. Correlation between baseline eGFR and eGFR decreased rates (random effects) in patients with DM. Model 1: sex and baseline age. Model 2: sex, baseline age, BMI, and SBP. Model 3: sex, baseline age, BMI, SBP, smoking, HbA1c, and UPCR. eGFR estimated glomerular filtration rate, DM diabetes mellitus, CI confidence interval, BMI body mass index, SBP systolic blood pressure, HbA1c hemoglobin A1c, UPCR urine proteincreatinine ratio. *P < 0.05.  Analysis of the relation between the baseline and changes suffered from mathematical coupling, which gives rise to misleading results and invalid testing of the null hypothesis 23,25 . Some studies applied a linear mixed regression model with random intercept and slope to resolve this statistical issue and to attain correct results 17 . However, the correct null hypothesis for testing the correlation between the baseline value and subsequent change is not zero, because these two variables have an underlying mathematical relation by sharing a common component of the baseline value 23,25 . It has been shown that centering the time variable could overcome this underlying mathematical relation and then attain an accurate result of null hypothesis test [23][24][25]45 . In this study, we undertook within-subject mean centering for the time variable to investigate the relationship between the baseline eGFR and its changes. We observed that the negative correlations are always attenuated after centering when compared with those given by the conventional approach without centering, in DM and non-DM patients with CKD. Moreover, in non-DM patients, this negative correlations were no longer statistically significant, after correct methodologies were used. This implied that higher baseline eGFR or renal hyperfiltration may be only a subclinical indicator but not the major cause of renal damage in patients with DM and early-stage CKD. Furthermore, when patients' GFR was lower than 45 ml/min/1.73 m 2 , they would be transferred to the Pre-ESRD program, and their eGFR values were no longer being included in our analysis. This may lead to the truncation of low eGFR values, resulting in the reduction in the variances of follow-up eGFR and the over-estimation of the negative relation between the baseline eGFR and its changes. Our study suggests that previous evidence on the relation between the baseline eGFR and the decline in eGFR should be interpreted with great cautions and may require reevaluation.
Limitations. Our study has some limitations. First, we included a relatively small number of participants, especially in patients with DM. Despite this problem, our study collected sufficient data of repeated measurements during the long-term follow-up to achieve robust inference. Second, our study included a higher proportion of men and elderly in DM and non-DM groups. According to previous national study, near two thirds of adults with CKD was more than 60 years old (63.3%), and men had a higher prevalence of early-stage CKD than did women (11.7% versus 9.9%) 46 . These data showed a similar distribution to our study. Therefore, it needs to be cautious to apply findings in our study to other populations with different sex proportions or age distributions. Third, the mean eGFR in our study was lower than the traditional definition of hyperfiltration with high GFR. The focus of our study is not the consequence of renal hyperfiltration but proper analyses of the relation between higher baseline GFR and subsequent GFR change. Moreover, the number of nephrons varied among individuals and usually decreased with age or renal injury 39 . Glomerular hyperfiltration or single-nephron hyperfiltration in people with fewer numbers of nephrons may show a normal or mildly low level of whole-kidney GFR, which is equal to single-nephron GFR multiplied by nephron numbers 47 . Therefore, results from our study still provides evidence on the relation between higher eGFR and subsequent eGFR changes. Finally, patients with GFR lower than 45 ml/min/1.73 m 2 or UPCR≧1000 mg/gm were transferred to the Pre-ESRD program for further management. Therefore, informative censoring may be a concern, since the information from those with rapidly deteriorating kidney function were selectively missing. This may be regarded as a problem with the truncated data, since GFR lower than a threshold was unavailable. This is likely to lead to a decrease in the variance of GFR with the increase in follow-up of the cohort, yielding a spurious, negative correlation between the baseline GFR and changes in GFR 25 . Therefore, the negative correlation between GFR at baseline and GFR changes in patients with CKD and DM may be weaker than what has been observed. Table 5. Correlation between baseline eGFR and eGFR decreased rates (random effects) in patients without DM. Model 1: sex and baseline age. Model 2: sex, baseline age, BMI, and SBP. Model 3: sex, baseline age, BMI, SBP, smoking, HbA1c, and UPCR. eGFR estimated glomerular filtration rate, DM diabetes mellitus, CI confidence interval, BMI body mass index, SBP systolic blood pressure, UPCR urine protein-creatinine ratio. *P < 0.05.

Conclusion
In conclusions, a significantly negative correlation between GFR at baseline and GFR changes was found in patients with CKD and DM, but no such correlation was found in non-DM patients with CKD when correct statistical analyses were undertaken. Higher baseline eGFR or renal hyperfiltration may be only a subclinical indicator but not the major cause of renal damage in patients with DM and early stage CKD. Our findings suggest that higher baseline GFR was associated with a greater GFR decline in DM patients but not in non-DM patients. Investigations about baseline value to subsequent changes should describe model specifications in detail to assure resolving mathematical coupling and then prevent from a spurious conclusion.