### Background

### Study Design

### Setting & Participants

### Index Tests

### Reference Test

### Results

^{2}) for: (1) 2-, 3-, or 5-year trials with a high mean baseline eGFR (67.5 mL/min/1.73 m

^{2}), and (2) 2-year trials with an intermediate mean baseline eGFR (42.5 mL/min/1.73 m

^{2}). Use of the 30% versus the 40% eGFR decline end point often led to moderately larger reductions in sample size in the absence of an acute effect, but not in the presence of acute effects.

### Limitations

### Conclusions

## Index Words

*AJKD.*

^{2}

^{3}

^{4}

^{, }

^{5}

^{, }

^{6}

^{2}, a narrow range relative to a normal eGFR of ∼120 mL/min/1.73 m

^{2}. Thus, in contrast to many surrogate end points, eGFR has a close mathematical relationship with the established end point of kidney failure. The fact that kidney failure commences when a relatively narrow eGFR range is reached provides the opportunity to model relationships between treatment effects on eGFR-based surrogate end points and the time to kidney failure more precisely than is possible using general criteria for validating surrogate end points. The challenge for such a model-based approach is that patterns of eGFR decline and the relationship of these patterns with time to kidney failure can be complex. To deal with this complexity, we performed a simulation study to characterize the circumstances under which treatment effects on time-to-event end points based on lesser eGFR declines reliably predict treatment effects on time to kidney failure treated by maintenance dialysis or kidney transplantation (end-stage renal disease [ESRD]).The input parameters for the simulations were chosen to represent a wide spectrum of scenarios found in prior randomized controlled trials about CKD.

## Methods

### Framework for eGFR Trajectories

#### The Classic Slope-Intercept Model

#### Deviations From the Classic Model

^{9}

^{, }

^{10}

^{1}

^{11}

^{, }

^{12}

^{2}, (2) a logarithmic attenuation to 0 when eGFR reaches 15 mL/min/1.73 m

^{2}, and (3) persistence of the initial acute effect as eGFR declines.

^{13}

^{, }

^{14}

^{15}

^{16}

^{, }

^{17}

*t*distributions to examine the implications of outliers in the deviations of individual eGFR measurements from the underlying trajectories. Fourth, in accordance with results of analyses of prior CKD studies (see Item S1, provided as online supplementary material), we assumed that the variance of the residual eGFR deviations is proportional to eGFR level.

#### Death and ESRD

^{2}.

### Conduct of Simulations

#### Choice of Input Parameters

Category and Factor | Values Considered in Simulations |
---|---|

eGFR decline | |

1. Mean long-term slope | −2.5, −4.0, or −5.5 mL/min/1.73 m^{2} |

2. SD of long-term slope | 3.0, 3.5, or 4.5 mL/min/1.73 m^{2} per y |

3. Correlation of slope and intercept | 0, a negative correlation providing a slope 1 mL/min/1.73 m^{2} per y steeper for each 25-mL/min/1.73 m^{2} increase in baseline eGFR |

4. Slope skewness | Low, moderate, or high, characterized by a generalized log gamma distribution with shape parameter of 1.5, 3, or 5 |

5. Nonlinearity of individual trajectories | None, moderate, high (described in Item S1) |

6. Size of residuals | Residual variance = 0.67 × eGFR value (medium variability) or 1.15 × eGFR value (high variability) |

7. Frequency of residual outliers | Low, moderate, or high, represented by normal, t with 12 df, or t with 5 df distributions |

Acute effect | |

8. Mean acute effect | −2.5, −1.25, 0, or +1.25 mL/min/1.73 m^{2} at baseline eGFR = 42.5 mL/min/1.73 m^{2} |

9. Attenuation of initial acute effect | Linear to 15, logarithmic to 15, none |

10. Variability of acute effect | None, low, or high, characterized by acute-effect SDs of 0, 1, or 3 mL/min/1.73 m^{2} |

Long-term treatment effect | |

11. Type of long-term treatment effect | Proportional, uniform, intermediate (see Item S1) |

12. Size of long-term treatment effect | 0%, 20%, 25%, or 30% reduction in slope for participant with an average long-term slope in absence of treatment |

Death and ESRD | |

13. Death rate per year | Case 1: 0.03375 − 0.00025 × eGFR Case 2: 0.0675 − 0.00050 × eGFR |

14. eGFR level associated with onset of ESRD | Uniformly distributed between 6 and 15 mL/min/1.73 m^{2} or between 10 and 15 mL/min/1.73 m^{2} |

Design and conduct | |

15. Accrual period and total F/U | Short trial: 1-y accrual and 1.5-y further F/U Medium trial: 2-y accrual and 2-y further F/U Long trial: 2-y accrual and 4-y further F/U |

16. Measurement frequency | 3, 6, and 12 mo |

17. Mean baseline eGFR | 27.5, 42.5, or 67.5 mL/min/1.73 m^{2} |

18. No. of baseline eGFRs | 1, 2, or 3 |

19. Permanent loss to F/U rate | 2% or 5% per y |

20. Intermittent missing eGFRs | 5%, 7.5%, or 10% |

^{7}

^{2}were observed frequently in the prior CKD clinical trials, with larger acute effects observed in 2 cases. Our analyses also suggest that mixed long-term treatment effects intermediate between the uniform and proportional treatment effect model may be common in CKD clinical trials.

#### Evaluation of Utility and Validity

#### End Points

#### Simulation Methods

#### Dependence of Sample Size on Percent of Patients Reaching Events and Estimated Hazard Ratio

## Results

^{2}and a proportional treatment effect (right). HRs were stable across end points with different eGFR declines when there was no acute effect and a uniform long-term effect (top left). The proportional treatment effect, which implies a larger effect on the slopes of faster progressors, strengthened the HRs for ESRD alone and for the end points based on the larger eGFR declines, where events are restricted to the fastest progressors. However, HRs attenuated toward 1 for the lesser eGFR declines. Attenuation of the HR with lesser eGFR declines was increased in the presence of a negative acute effect, reflecting a greater relative impact of an acute eGFR decline for end points based on lesser eGFR declines than for events based on larger eGFR declines. Use of lesser eGFR declines substantially increased the number of events for each scenario (middle panels). Reflecting the combined effects of the HRs and number of events, lesser eGFR declines reduced the required N in the absence of an acute effect when the treatment effect is uniform, but increased the required N in the presence of a small negative acute effect with a proportional long-term treatment effect. Requiring confirmation of eGFR events substantially reduced the required N for end points based on 30% or 40% eGFR declines, but was not a major determinant of the required N with a 57% decline. The figures in Item S3 show that using lesser eGFR declines also leads to attenuation of the HRs for an intermediate long-term treatment effect, but not as much as for a proportional treatment effect.

^{2}) mean baseline eGFRs under the intermediate long-term treatment effect model without an acute effect. The required N is stable across the different eGFR decline end points for 3- or 5-year studies when baseline eGFR is 27.5 mL/min/1.73 m

^{2}, but is reduced with lesser eGFR declines for parameter configurations where events are less frequent (ie, 2-year studies and/or high baseline eGFR).

Acute Effect = −1.25 mL/min/1.73 m^{2} | No Acute Effect | |||||
---|---|---|---|---|---|---|

N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | |

Long-term treatment effect | ||||||

Proportional | 1.45 | 0.84 | 1,405 | 0.66 | 0.64 | 1,307 |

Mixed | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

Uniform | 0.98 | 0.74 | 5,305 | 0.38 | 0.51 | 4,315 |

Mean slope | ||||||

−5.50 mL/min/1.73 m^{2} per y | 1.15 | 0.83 | 1,216 | 0.59 | 0.64 | 1,115 |

−4.00 mL/min/1.73 m^{2} per y | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

−2.50 mL/min/1.73 m^{2} per y | 1.96 | 0.91 | 5,042 | 0.51 | 0.57 | 4,650 |

Mean initial eGFR | ||||||

27.50 mL/min/1.73 m^{2} | 1.31 | 0.97 | 1,518 | 0.84 | 0.81 | 1,339 |

42.50 mL/min/1.73 m^{2} | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

67.50 mL/min/1.73 m^{2} | 57% infeasible | 57% infeasible | 57% infeasible | 57% infeasible | 57% infeasible | 57% infeasible |

Size of treatment effect | ||||||

20% | 1.78 | 0.98 | 3,715 | 0.58 | 0.63 | 3,268 |

25% | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

30% | 1.00 | 0.77 | 1,664 | 0.53 | 0.59 | 1,554 |

Frequency of eGFR determination | ||||||

Every 3 mo | 1.58 | 0.84 | 2,521 | 0.55 | 0.58 | 2,187 |

Every 6 mo | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

Every y | 1.09 | 0.83 | 3,265 | 0.55 | 0.63 | 2,741 |

Long-term slope SD | ||||||

3.00 mL/min/1.73 m^{2} per y | 1.05 | 0.73 | 2,622 | 0.48 | 0.56 | 2,167 |

3.50 mL/min/1.73 m^{2} per y | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

4.50 mL/min/1.73 m^{2} per y | 1.64 | 1.00 | 2,397 | 0.72 | 0.73 | 2,122 |

eGFR variability | ||||||

0.67 mL/min/1.73 m^{2} | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

1.10 mL/min/1.73 m^{2} | 1.96 | 0.95 | 3,037 | 0.67 | 0.66 | 2,330 |

Acute-effect SD | ||||||

0 | 1.24 | 0.82 | 2,388 | 0.54 | 0.60 | 2,225 |

1.00 | 1.29 | 0.85 | 2,352 | 0.57 | 0.61 | 2,143 |

3.00 | 2.40 | 1.08 | 2,400 | 0.74 | 0.72 | 2,197 |

*Note:*Shown are ratios of required sample size (N) for 90% power with a 2-sided α = 0.05 for composite end points based on ESRD or 30% or 40% eGFR declines versus a composite based on ESRD or a 57% eGFR decline for a trial with a median planned follow-up of 2 years and mean baseline eGFR of 42.5 mL/min/1.73 m

^{2}. Scenarios with a negative acute effect and no acute effect are presented. Each block of rows shows the effect of varying 1 input parameter, with all remaining input parameters set to their base case in Table 1 (indicated by ). Simulations could not be performed for the composite of ESRD or a 57% eGFR decline when baseline eGFR = 67.5 mL/min/1.73 m

^{2}due to an insufficient number of events.

Acute Effect = −1.25 mL/min/1.73 m^{2} | No Acute Effect | |||||
---|---|---|---|---|---|---|

N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | |

Long-term treatment effect | ||||||

Proportional | 2.45 | 1.25 | 788 | 1.16 | 0.94 | 719 |

Mixed | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

Uniform | 1.07 | 0.87 | 2,080 | 0.57 | 0.68 | 1,822 |

Mean slope | ||||||

−5.50 mL/min/1.73 m^{2} per y | 1.51 | 1.07 | 669 | 0.89 | 0.85 | 592 |

−4.00 mL/min/1.73 m^{2} per y | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

−2.50 mL/min/1.73 m^{2} per y | 2.42 | 1.21 | 2,738 | 0.89 | 0.85 | 2,305 |

Mean initial eGFR | ||||||

27.50 mL/min/1.73 m^{2} | 1.55 | 1.09 | 1,082 | 1.04 | 0.95 | 983 |

42.50 mL/min/1.73 m^{2} | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

67.50 mL/min/1.73 m^{2} | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

Size of treatment effect | ||||||

20% | 2.16 | 1.22 | 1,934 | 0.88 | 0.83 | 1,724 |

25% | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

30% | 1.47 | 1.03 | 826 | 0.83 | 0.81 | 768 |

Frequency of eGFR determination | ||||||

Every 3 mo | 2.15 | 1.18 | 1,235 | 0.91 | 0.84 | 1,128 |

Every 6 mo | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

Every y | 1.45 | 1.04 | 1,184 | 0.84 | 0.83 | 1,103 |

Long-term slope SD | ||||||

3.00 mL/min/1.73 m^{2} per y | 1.50 | 1.01 | 1,105 | 0.78 | 0.78 | 962 |

3.50 mL/min/1.73 m^{2} per y | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

4.50 mL/min/1.73 m^{2} per y | 1.88 | 1.18 | 1,579 | 1.03 | 0.95 | 1,309 |

eGFR variability | ||||||

0.67 mL/min/1.73 m^{2} | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

1.10 mL/min/1.73 m^{2} | 2.27 | 1.22 | 1,420 | 0.99 | 0.88 | 1,156 |

Acute-effect SD | ||||||

0 | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

1 mL/min/1.73 m^{2} | 1.82 | 1.15 | 1,216 | 0.88 | 0.85 | 1,085 |

3 mL/min/1.73 m^{2} | 2.32 | 1.21 | 1,334 | 1.03 | 0.90 | 1,170 |

*Note:*Shown are ratios of required sample size (N) to achieve 90% power with a 2-sided α = 0.05 for composite end points based on ESRD or 30% or 40% eGFR declines versus a composite based on ESRD or a 57% eGFR decline for a randomized trial with a median planned follow-up of 3 years and mean baseline eGFR of 42.5 mL/min/1.73 m

^{2}. Scenarios with a negative acute effect and no acute effect are presented. Each block of rows shows the effect of varying 1 input parameter, with all remaining input parameters set to their base case in Table 1 (indicated by ).

Acute Effect = −1.25 mL/min/1.73 m^{2} | No Acute Effect | |||||
---|---|---|---|---|---|---|

N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | |

Long-term treatment effect | ||||||

Proportional | 2.76 | 1.39 | 751 | 1.33 | 1.04 | 676 |

Mixed | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 95 |

Additive | 1.14 | 0.93 | 1,644 | 0.64 | 0.72 | 1,482 |

Mean slope | ||||||

−5.50 mL/min/1.73 m^{2} per y | 1.58 | 1.11 | 605 | 0.96 | 0.90 | 534 |

−4.00 mL/min/1.73 m^{2} per y | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

−2.50 mL/min/1.73 m^{2} per y | 2.59 | 1.31 | 2,418 | 0.97 | 0.90 | 2,132 |

Mean initial eGFR | ||||||

27.50 mL/min/1.73 m^{2} | 1.60 | 1.13 | 1,034 | 1.06 | 0.97 | 959 |

42.50 mL/min/1.73 m^{2} | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

67.50 mL/min/1.73 m^{2} | 1.28 | 0.95 | 1,643 | 0.64 | 0.69 | 1,360 |

Size of treatment effect | ||||||

20% | 2.23 | 1.26 | 1,754 | 0.97 | 0.90 | 1,529 |

25% | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

30% | 1.52 | 1.07 | 756 | 0.91 | 0.87 | 676 |

Frequency of eGFR determination | ||||||

Every 3 mo | 2.24 | 1.23 | 1,105 | 1.01 | 0.92 | 995 |

Every 6 mo | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

Every y | 1.53 | 1.08 | 1,095 | 0.89 | 0.87 | 1,020 |

Long-term slope SD | ||||||

3.00 mL/min/1.73 m^{2} per y | 1.63 | 1.08 | 936 | 0.88 | 0.84 | 824 |

3.50 mL/min/1.73 m^{2} per y | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

4.50 mL/min/1.73 m^{2} per y | 1.99 | 1.25 | 1,466 | 1.08 | 0.98 | 1,252 |

eGFR variability | ||||||

0.67 mL/min/1.73 m^{2} | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

1.10 mL/min/1.73 m^{2} | 2.42 | 1.29 | 1,230 | 1.08 | 0.93 | 1,032 |

Acute-effect SD | ||||||

0 | 1.79 | 1.15 | 1,070 | 0.97 | 0.91 | 953 |

1.00 | 1.87 | 1.18 | 1,102 | 0.95 | 0.91 | 979 |

3.00 | 2.36 | 1.29 | 1,183 | 1.12 | 0.97 | 1,032 |

*Note:*Shown are ratios of required sample size (N) to achieve 90% power with a 2-sided α = 0.05 for composite end points based on ESRD or 30% or 40% eGFR declines versus a composite based on ESRD or a 57% eGFR decline for a randomized trial with a median planned follow-up of 5 years and mean baseline eGFR of 42.5 mL/min/1.73 m

^{2}. Scenarios with a negative acute effect and no acute effect are presented. Each block of rows shows the effect of varying 1 input parameter, with all remaining input parameters set to their base case in Table 1 (indicated by ).

Acute Effect = −1.25 mL/min/1.73 m^{2} | No Acute Effect | |||||
---|---|---|---|---|---|---|

N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | N Ratio 30% vs 57% | N Ratio 40% vs 57% | Required N With 57% | |

Long-term treatment effect | ||||||

Proportional | 1.34 | 0.85 | 1,165 | 0.63 | 0.64 | 1,027 |

Mixed | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

Uniform | 0.66 | 0.65 | 6,572 | 0.32 | 0.47 | 4,441 |

Mean slope | ||||||

−5.50 mL/min/1.73 m^{2} per y | 1.04 | 0.84 | 1,077 | 0.58 | 0.65 | 943 |

−4.00 mL/min/1.73 m^{2} per y | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

−2.50 mL/min/1.73 m^{2} per y | 1.53 | 0.90 | 4,801 | 0.53 | 0.61 | 3,720 |

Mean initial eGFR | ||||||

27.50 mL/min/1.73 m^{2} | 1.55 | 1.09 | 1,082 | 1.04 | 0.95 | 983 |

42.50 mL/min/1.73 m^{2} | 1.64 | 1.06 | 1,224 | 0.87 | 0.84 | 1,077 |

67.50 mL/min/1.73 m^{2} | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

Size of treatment effect | ||||||

20% | 1.48 | 0.94 | 3,591 | 0.53 | 0.62 | 2,869 |

25% | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

30% | 0.91 | 0.76 | 1,527 | 0.49 | 0.57 | 1,354 |

Frequency of eGFR determination | ||||||

Every 3 mo | 1.38 | 0.89 | 2,125 | 0.55 | 0.61 | 1,776 |

Every 6 mo | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

Every y | 0.96 | 0.80 | 2,293 | 0.51 | 0.60 | 1,924 |

Long-term slope SD | ||||||

3.00 mL/min/1.73 m^{2} per y | 0.91 | 0.74 | 2,294 | 0.40 | 0.50 | 2,015 |

3.50 mL/min/1.73 m^{2} per y | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

4.50 mL/min/1.73 m^{2} per y | 1.52 | 1.05 | 2,143 | 0.71 | 0.73 | 1,731 |

eGFR variability | ||||||

0.67 mL/min/1.73 m^{2} | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

1.10 mL/min/1.73 m^{2} | 1.63 | 0.99 | 2,318 | 0.58 | 0.59 | 1,931 |

Acute-effect SD | ||||||

0 | 1.10 | 0.86 | 2,199 | 0.51 | 0.59 | 1,834 |

1.00 | 1.19 | 0.86 | 2,246 | 0.51 | 0.59 | 1,869 |

3.00 | 1.83 | 1.00 | 2,533 | 0.68 | 0.68 | 2,004 |

*Note:*Shown are ratios of required sample size (N) to achieve 90% power with a 2-sided α = 0.05 for composite end points based on ESRD or 30% or 40% eGFR declines versus a composite based on ESRD or a 57% eGFR decline for a randomized trial with a median planned follow-up of 3 years and mean baseline eGFR of 67.5 mL/min/1.73 m

^{2}. Scenarios with a negative acute effect and no acute effect are presented. Each block of rows shows the effect of varying 1 input parameter, with all remaining input parameters set to their base case in Table 1 (indicated by ).

^{2}

Baseline eGFR | 2-y Trial | 3-y Trial | 5-y Trial |
---|---|---|---|

27.5 mL/min/1.73 m^{2} | In Select Cases | No Exceptions: Uniform treatment effect, low-slope SD | No Exceptions: Uniform treatment effect |

42.5 mL/min/1.73 m^{2} | Yes Exception: Substantial increase in required N if a negative acute effect does not attenuate | No Exceptions: Uniform treatment effect, low-slope SD | No Exceptions: Uniform treatment effect |

67.5 mL/min/1.73 m^{2} | Yes | Yes | Yes |

Yes scenarios require:1) compared to a 57% eGFR decline, a 40% eGFR decline reduces the required N by at least 20% if there is no acute effect; 2) compared to a 57% eGFR decline, a 40% eGFR decline either reduces the required N or requires an increase in N by no more than 10% when there is a negative acute effect of −1.25 mL/min/1.73 m ^{2}; and3) type 1 error relative to the clinical end point of end-stage renal disease is <10% in the presence of a positive acute effect not greater than 1.25 mL/min/1.73 m ^{2}. |

Baseline eGFR | 2-y Trial | 3-y Trial | 5-y Trial |
---|---|---|---|

27.5 mL/min/1.73 m^{2} | No Exceptions: Uniform treatment effect, low-slope SD | No Exception: Uniform treatment effect | No |

42.5 mL/min/1.73 m^{2} | Yes | No Exceptions: Uniform treatment effect, low-slope SD | No |

67.5 mL/min/1.73 m^{2} | Yes | Yes | Yes |

Yes scenarios require:Compared to a 57% eGFR decline, a 30% eGFR decline reduces the required N by at least 20% if there is no acute effect. Caution:Use of a 30% decline will lead to large increases in required N compared to both 40% and 57% declines if the treatment unexpectedly produces a negative acute effect with magnitude of at least 1.25 mL/min/1.73 m ^{2}, and to severely inflated type 1 error if the treatment unexpectedly produces a positive acute effect of 1.25 mL/min/1.73 m^{2} or greater. |

## Discussion

^{2}and for trials of 2 to 3 years in patients with a high mean baseline eGFR of 67.5 mL/min/1.73 m

^{2}.

^{2}or more). Acute effects resulting from hemodynamic changes in GFR have been common among interventions that previously have been evaluated for CKD progression, including renin-angiotensin system blockade, low blood pressure, low-protein diet, dihydropyridine calcium channel blockers, and cyclosporine.

^{9}

^{, }

^{10}

^{, }

^{18}

^{, }

^{19}

^{, }

^{20}

^{, }

^{21}

^{, }

^{22}

^{2}and increases type 1 error, leading to false conclusions of treatment benefit for treatments causing an acute increase in eGFR of a similar magnitude. The adverse consequences of acute effects on type 1 error and statistical power were substantially greater for 30% declines than 40% declines.

^{2}typically requires a data set with 600 to 1,200 participants, which may not be available to the investigators prior to the start of the definitive trial. It would be prudent to restrict the use of lesser eGFR declines to situations in which the projected reduction in the required sample size is substantial (ie, ≥15%-20%). If there is doubt about whether an acute effect is present, it also would be prudent to restrict use of these end points to situations in which it can be verified that performance is not seriously compromised by acute effects of up to ±1.25 mL/min/1.73 m

^{2}.

^{2}in magnitude if baseline eGFR is high or baseline eGFR is intermediate and the planned trial duration is short (ie, 2 years). A 40% eGFR decline can be a useful option in certain other situations, but these should be evaluated on a case-by-case basis. A composite end point of a confirmed 30% eGFR decline or ESRD may be appropriate in select circumstances in which there is high confidence that an acute effect is absent (Table 7).

## Acknowledgements

*Support:*The workshop was supported and facilitated by the NKF. The NKF gratefully acknowledges Abbott, Amgen, ChemoCentryx, Lilly, Mitsubishi Tanabe Pharma, Novartis, Pfizer, Reata, Sanofi, and Takeda, which provided grants to the NKF to support the workshop and the supporting data analysis. This research was also supported by the University of Utah Study Design and Biostatistics Center , with funding in part from the National Center for Research Resources and the National Center for Advancing Translational Sciences , National Institutes of Health , through grant 8UL1TR000105 (formerly UL1RR025764 ).

*Financial Disclosure:*Dr Greene is a consultant for the following companies: Keryx Biopharmaceuticals, Jansen Pharmaceuticals, Pfizer, GenKyoTex S.A. The other authors declare that they have no other relevant financial interests.

*Contributions:*Research idea and study design: TG, LAI, ASL, JC; data acquisition: LAI, ASL; statistical analysis/interpretation: TG, C-CT, JY, MW; software development and validation: C-CT, JY, AR. Each author contributed important intellectual content during manuscript drafting or revision 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. TG takes responsibility that this study has been reported honestly, accurately, and transparently; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned have been explained.

## Supplementary Material

- Supplementary Item S1 (PDF)
Analyses of prior CKD randomized controlled trials.

- Supplementary Item S2 (PDF)
Details of simulations and eGFR trajectories and clinical events.

- Supplementary Item S3 (PDF)
Detailed summaries of simulation results.

- Supplementary Item S4 (PDF)
List of participating CKD-EPI clinical trials/collaborators.

## References

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*JAMA.*2014; 311: 2518-2531 - GFR decline and subsequent risk of established kidney outcomes: a meta-analysis of 37 randomized controlled trials.
*Am J Kidney Dis.*2014; 64: 860-866 - Surrogate end points in clinical trials: are we being misled?.
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## Article Info

### Publication History

### Footnotes

Because an author of this article is an editor for AJKD, the peer-review and decision-making processes were handled entirely by an Associate Editor (Paul Muntner, PhD, MHS) who served as Acting Editor-in-Chief. Details of the journal’s procedures for potential editor conflicts are given in the Information for Authors & Editorial Policies.