Comparison of Regression and Categorical Analysis for Pharmacokinetic Data From Renal Impairment Studies

Abstract

The US Food and Drug Administration 2024 guidance prefers regression analysis over categorical analysis for pharmacokinetic data for studies that assess pharmacokinetics in patients with impaired renal functions. The objective of this study was to compare these two statistical methods for pharmacokinetic data analysis of renal impairment studies. Baseline data from seven renal impairment studies were pooled to estimate the impact of three creatinine‐based equations (Cockcroft‐Gault, CKD‐EPI₂₀₀₉, and absolute CKD‐EPI₂₀₀₉) on classification of participants into different renal impairment categories. Retrospective analyses were performed on two renal impairment studies with three distinct analytes (predominantly renally cleared; and predominantly metabolized by hepatic cytochrome P450 enzymes, or by systemic peptidase) using regression or categorical statistical analysis methods and creatine‐based equations. While the three equations were highly correlated, the use of a different equation may result in up to 50% of participants being reclassified into different renal impairment groups. Categorical analysis with analysis of variance provided different point estimates and precision of exposure difference for a given renal impairment group based on the equation used. The use of regression analysis without inclusion of data from participants on hemodialysis, as recommended by the Food and Drug Administration, showed most consistent estimate of the relationship between renal impairment and exposure of three analytes. These retrospective analyses support the Food and Drug Administration recommendations of using regression analysis without data from participants on hemodialysis as the primary analysis of data for renal impairment study; and established a modeling strategy for such analysis.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

FDA issued a new guidance on assessment of “Pharmacokinetics in Patients with Impaired Renal Function” in March 2024. Compared with the guidance on the same topic issued in 2010, the new guidance included three important changes: (1) Preference of using absolute eGFR (eGFR without BSA correction) over BSA indexed eGFR or creatinine clearance. (2) Participants on HD are not required in the full design, which is different from EMA 2017 guidance. (3) Recommended regression analysis over categorical analysis on data from renal impairment studies.

• WHAT QUESTION DID THIS STUDY ADDRESS?

This study aimed to assess the impact of these changes on data analysis of renal impairment studies by addressing three questions: (1) How does the use of different creatinine‐based equations impact the classification of participants into renal impairment groups? (2) Are there any differences in data analysis from renal impairment studies using regression analysis and categorical analysis (ANOVA)? (3) How does excluding data from participants on HD affect data analysis?

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

While there are strong correlations between all three creatinine‐based equations, notable numbers of participants may be reclassified into different renal impairment groups, which could affect both, point estimate and precision of data from renal impairment studies when performing retrospective categorical analysis, such as ANOVA. Regression analysis excluding data from participants on HD provided more consistent and precise estimate on the impact of renal impairment on exposure of three analytes with distinct ADME properties.

• HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

These retrospective analyses support FDA 2024 guidance on using regression analysis without data from participants on HD as the primary analysis on data from renal impairment studies. Various regression methods such as using: different eGFR formulae as the sole predictor, log‐transformed eGFR as the sole predictor, indexed eGFR as predictor along with other covariates such as BSA or body weight, or eGFR as predictor in participants with HD, or excluding HD, were evaluated, which may help the development of regression models for renal impairment studies.

Chronic kidney disease (CKD) affects approximately 14% of adults in the United States ¹ ; and globally, 859 million people were estimated to have CKD in 2021. ² Patients with diabetes and hypertension are at higher risk of CKD, and those with CKD are at a higher risk of major cardiovascular complications as well as in need of kidney replacement therapy. Therefore, CKD is both an unmet medical need and a common comorbidity of diseases for which new drugs are being developed. To include patients with CKD in clinical trials during drug development, or to make dosing recommendations at the time of regulatory submission, a dedicated renal impairment (RI) study is frequently conducted to assess the impact of CKD on pharmacokinetics (PK) of the investigational product.

The Food and Drug Administration (FDA) and the European Medicines Agency (EMA) have issued guidance regarding the design and data analysis for RI studies: While the current EMA guidance came into effect in 2016, ³ the FDA guidance was finalized in 2024. ⁴ One of the key recommendations from both agencies is the use of absolute estimated glomerular filtration rate (eGFR) in RI studies for participant enrollment, data analysis, and for making dosing recommendations. ³ , ⁴ However, in clinical practice, the most widely used eGFR equations automatically index eGFR to body surface area (BSA) (mL/min/1.73 m²) to account for differences in body size. ⁵ Absolute eGFR (or deindexed/individualized eGFR) is calculated by multiplying indexed eGFR by the individual BSA, divided by 1.73 m². The impact of using indexed eGFR vs. absolute eGFR on RI studies and dose recommendations has not been assessed.

The classification of renal function for non‐dialysis participants in dedicated RI studies in the final FDA guidance ⁴ is very similar to the EMA guidance. ³ This update improved the consistency in the design and implementation of RI studies. EMA guidance ³ recommended the inclusion of patients on dialysis in the full design. It is unclear whether this subtle difference affects the data analysis.

The objectives of this study are to perform retrospective analyses of data from previous RI studies completed by Eli Lilly and Company (Lilly) to:

1. assess the impact on the classification of participants in RI studies by different creatinine‐based equations, such as

   1. Cockcroft‐Gault (CG)
   2. 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration (CKD‐EPI₂₀₀₉), and
   3. absolute eGFR

• 2evaluate different statistical analysis approaches on the relationship between RI and PK, including the comparison of categorical analysis and regression analysis; and the inclusion or exclusion of data from participants on hemodialysis.
• 3compare the use of the indexed eGFR and absolute eGFR in RI studies.

METHODS

Data source

We pooled baseline data from seven RI studies performed by Lilly between 2008 and 2019 to assess how different creatinine‐based equations impact the classification of participants according to FDA or EMA guidance (data on file). These studies were conducted to evaluate the PK of seven compounds in participants with impaired renal function and normal renal function (control group). All participants received a single dose of the investigational product. Safety, tolerability, and PK of the analytes of interest were assessed. The following equations were tested in this study:

1. CG, which is commonly used during drug development and labeling ⁶ , ⁷ , ⁸

2. CKD‐EPI₂₀₀₉, and

3. the absolute eGFR derived from CKD‐EPI₂₀₀₉ (Table S1 ) as recommended by the final FDA and EMA guidance. ⁴

To evaluate different statistical methods for the analysis of PK data from RI studies, we conducted post hoc analyses on two RI studies, H9P‐EW‐LNCA (LNCA) ⁹ and H8Y‐EW‐HBCE (HBCE). ¹⁰ , ¹¹ Area under the time‐concentration curve (AUC) was selected as the primary PK endpoint of interest, as it is more sensitive to changes in participants with RI compared to maximum observed drug concentration (C _max). ⁴ These two studies were selected because

• both studies included multiple RI groups (a full study design based on FDA and EMA guidance), therefore allowing the exploration of the impact of RI on PK with a wide range of baseline renal function

• they evaluated PK of three analytes with distinct absorption, distribution, metabolism, and excretion (ADME) properties, and

• all three analytes had plasma protein binding of less than 90%; therefore, only total drug concentration analyses were required. ⁴ , ¹⁰

Study LNCA evaluated the effect of RI on PK of LY2216684, which is predominantly cleared by hepatic metabolism with fraction metabolized (fm) of 0.82 via cytochrome P450 (CYP) 2D6 and CYP2C19. Forty participants received a single 6 mg dose of LY2216684 orally. This study included participants with normal renal function, mild, moderate, severe renal impairment, and end‐stage renal disease (ESRD) based on creatinine clearance by CG equation. Blood samples were collected for 72 hours after dosing. For participants on hemodialysis (HD), LY2216684 was administered at least 18 hours after a HD session, and PK samples of LY2216684 were collected 48 hours after dosing during the dialysis interval. AUC_0–∞ of LY2216684 for each participant was derived using standard non‐compartment model (NCA) using WinNonLin Enterprise (version 5.2).

Study HBCE evaluated the effects of RI on PK of LY2140023 and its active metabolite LY404039. LY2140023 is converted to LY404039 by systemic peptidase with minimal elimination via the renal route, while LY404039 is predominantly eliminated renally with an estimated fraction excreted unchanged in urine (fe) of 0.85, and the fraction cleared by dialysis (fd) ranged from 0.20 to 0.73. A total of 80 participants with normal renal function, mild, and moderate RI based on creatinine clearance with the CG equation, or ESRD were dosed.

The dosing and PK analysis for the different RI groups were

• ESRD group (N = 8, all on stable HD) received a 5 mg dose at least 8 hours after a HD, and PK samples were collected 48 hours after dosing.

• Moderate RI participants (N = 16) were randomized to receive a single dose of 20 and 40 mg dose of LY2140023 at a 1:1 ratio, and PK samples were collected for 24 hours after dosing.

• Normal renal function (N = 27) and mild RI participants (N = 29) were randomized to receive a single dose of 20, 40, or 80 mg LY2140023 at approximately a 1:1:1 ratio, and PK samples were collected for 24 hours after dosing.

AUC of LY2140023 and LY404039 for each participant were derived from NCA model using WinNonLin (version 5.3). As various dose levels of LY2140023 were used in this study and the exposure of both analytes increased dose‐proportionally within the 5–80 mg dose range of LY2140023, dose‐normalized AUC (DNAUC) was used. DNAUC_0–∞ was used for LY2140023. DNAUC_0–t was used as the primary PK endpoint to analyze the impact of RI on PK of LY404039 (active metabolite of LY2140023) for all RI groups, since AUC_0–∞ could not be estimated due to very slow clearance of LY404039 in participants on HD, which prevented the characterization of the full PK profile of LY404039 during dialysis interval for this patient group.

Statistical analysis

Impact of renal function assessment on classification of participants in RI studies

The agreement of RI classification between the three creatinine‐based equations from pooled baseline data of 317 participants from all seven RI studies was evaluated using Kappa coefficient, and the association was assessed using both Pearson and Spearman correlation.

Impact of different statistical models on RI study data analysis

We first estimated the effect of RI on AUC for Studies LNCA and HBCE using a linear model (either analysis of variance (ANOVA) or linear regression). ⁴ Linear regression analysis was applied using renal function as a regressor and log‐transformed AUC as a response variable. As a contrast, ANOVA model was applied using renal function groups defined by various creatinine‐based equations as a fixed effect and log‐transformed AUC as a response variable. The results from these two models were compared and evaluated.

The FDA 2024 guidance ⁴ recommends performing regression analysis without data from participants on HD. In this study, we assessed the impact of removing data from participants on dialysis on the results of the regression analysis for data from Studies LNCA and HBCE. For these analyses, we used either indexed or absolute CKD‐EPI₂₀₀₉ to estimate renal function. Lastly, we tested including BSA and body weight (BW) as covariates in regression analysis when using the indexed CKD‐EPI₂₀₀₉ equation. The resultant regression model follows the structure outlined in Eq. (1), where y is the dependent variable, x ₁ is renal function; and x ₂ is BSA or BW, β ₀ is the intercept, β ₁ or β ₂ is a regression coefficient associated with its corresponding independent variable, and ε is the error term.

$$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\epsilon$$ (1)

The model uses either creatinine clearance (CrCl) with CG equation, or eGFR as the independent variable, log‐transformed AUC as the dependent variable, and either BSA or BW as the independent covariate analyzed in separate analyses for multivariate regression analysis when indexed CKD‐EPI₂₀₀₉ formula was used. AUC_0–∞ was used for LY2216684 and LY2130023, and AUC_0–t was used for LY404039.

RESULTS

The pooled demographic data from seven RI studies are summarized in Table 1 . Data from Studies HBCE and LNCA were used to test different statistical analysis approaches, so the demographic data from those studies are presented separately. In general, the demographics and baseline characteristics were similar across the pooled baseline dataset, Study HBCE, and Study LNCA.

Table 1.

Summary of demographics and baseline characteristics

Parameter	Overall (n = 317)	HBCE (n = 79)	LNCA (n = 41)
Age (years)	60.5 ± 11.6	62.1 ± 9.0	64.6 ± 11.0
Sex
Male	180 (56.8%)	30 (38.0%)	24 (58.5%)
Female	137 (43.2%)	49 (62.0%)	17 (41.5%)
Race
Asian	1 (0.3%)	–	–
Black or African American	44 (13.9%)	14 (17.7%)	6 (14.6%)
Native Hawaiian or Other Pacific Islander	1 (0.3%)	–	1 (2.4%)
White	268 (84.5%)	65 (82.3%)	34 (82.9%)
Multiple	3 (0.9%)	–	–
Body weight (kg)	78.1 ± 16.3	78.7 ± 17.4	73.4 ± 16.3
BMI (kg/m2)	27.3 ± 4.4	27.9 ± 4.7	26.8 ± 4.2
BSA (m2)	1.9 ± 0.2	1.9 ± 0.3	1.8 ± 0.2
Renal function estimate
CG formula (mL/min)	56.8 ± 36.1	65.9 ± 29.2	46.4 ± 29.1
CKD‐EPI2009 (mL/min/1.73 m2)	50.6 ± 33.1	60.9 ± 29.0	45.7 ± 31.4
Absolute CKD‐EPI2009 (mL/min)	54.9 ± 36.4	65.4 ± 30.8	46.3 ± 30.6

This table includes values of participants with hemodialysis. Continuous parameters are reported as mean ± SD. Categorical parameters are reported as n (%). BMI, body mass index; BSA, body surface area; CG, Cockcroft‐Gault; CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula.

Agreement in RI classification with different GFR estimation equations

There were statistically significant and strong correlations between the CG equation and indexed CKD‐EPI₂₀₀₉ (adjusted R ² = 0.8592, Spearman correlation of 0.955 (P < 0.001), and Pearson correlation of 0.927 (P < 0.001)). Absolute CKD‐EPI₂₀₀₉ and indexed CKD‐EPI₂₀₀₉ also showed a statistically significant and strong correlation (adjusted R ² = 0.9516, Spearman's correlation of 0.980 (P < 0.001), and Pearson's correlation of 0.976 (P < 0.001)) in the pooled population (n = 317) (Figure 1 ).

Figure 1.

Concordance between renal function estimation methods on RI classification. Figure (a) shows the concordance between absolute CKD‐EPI₂₀₀₉ and CKD‐EPI₂₀₀₉, and Figure (b) shows the concordance between CG formula and indexed CKD‐EPI₂₀₀₉. N = 317 for both analyses. There was overprediction against CKD‐EPI₂₀₀₉ in both panels. CG, Cockcroft‐Gault formula; CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula; ESRD, end‐stage renal disease; RI, renal impairment.

Despite strong correlation between these equations, a notable number of participants were reclassified into a different RI category when different equations were used. When switching from CG equation to indexed CKD‐EPI₂₀₀₉ equation (Table 2 ),

• 24 of the 66 (36.4%) participants with normal renal function were reclassified to mild RI category, and

• 35 of 86 participants (40.7%) with moderate RI were reclassified to normal (1.2%), mild (8.1%), or severe (31.4%) RI categories.

Similarly, when switching from indexed CKD‐EPI₂₀₀₉ equation to CG equation,

• 11 of 53 participants (20.8%) with normal renal function were reclassified to mild (18.9%) or moderate (1.9%) RI categories, and

• 27 of 53 participants (50.9%) with severe RI were reclassified to moderate RI.

The agreement between indexed CKD‐EPI₂₀₀₉ and absolute CKD‐EPI₂₀₀₉ equations was stronger (Figure 1 b ), that is, smaller number of participants (0% to < 30%) being reclassified when switching between the two equations (Table 3 ).

Table 2.

Agreement of RI classification between GFR estimation equation (CG and indexed CKD‐EPI₂₀₀₉)

	CG formula
		Normal	Mild	Moderate	Severe	ESRD	Total
CKD‐EPI2009	Normal	42	10	1	0	0	53
	Mild	24	48	7	0	0	79
	Moderate	0	12	51	1	0	64
	Severe	0	0	27	26	0	53
	ERSD	0	0	0	13	55	68
	Total	66	70	86	40	55	317

Table presents the number of participants being classified into each RI group with CG formula and indexed CKD‐EPI₂₀₀₉ across the 7 RI studies (n = 317). Bold font indicates numbers of participants classified into the same categories by both equations.

CG, Cockcroft‐Gault; CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula; ESRD, end‐stage renal disease; RI, renal impairment.

Table 3.

Agreement of RI classification between GFR estimation equation (Absolute and indexed CKD‐EPI₂₀₀₉)

	Absolute CKD‐EPI2009
		Normal	Mild	Moderate	Severe	ESRD	Total
CKD‐EPI2009	Normal	49	4	0	0	0	53
	Mild	19	59	1	0	0	79
	Moderate	0	10	53	1	0	64
	Severe	0	0	11	42	0	53
	ERSD	0	0	0	2	66	68
	Total	68	73	65	45	66	317

Table presents the number of participants being classified into each RI group with absolute CKD‐EPI₂₀₀₉ and indexed CKD‐EPI₂₀₀₉. Bold font indicates numbers of participants classified into the same categories by both equations.

CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula; ESRD, end‐stage renal disease; RI, renal impairment.

Both CG and absolute CKD‐EPI₂₀₀₉ equations predicted higher GFR than indexed CKD‐EPI₂₀₀₉ for the pooled participants in these seven studies, thus classifying more participants into the less severe RI groups compared to indexed CKD‐EPI₂₀₀₉. Given the small number of participants evaluated in RI studies, the reclassification of participants into different RI categories may affect mean and precision estimation on the impact of RI on PK using categorical analysis.

Comparisons of statistical analyses using categorical vs. regression model

The impact of RI on AUC is shown in Figure 2 for each GFR estimation equation and based on ANOVA and linear regression model. Overall, all the analyses provided similar directionality of the impact of RI on AUC. For LY404039, which was predominantly cleared by the kidneys, all analyses demonstrated that participants with moderate, severe RI, or ESRD had a marked increase in LY404039 exposure that may necessitate dose adjustment in patients with RI. For analytes that were not predominantly cleared renally, all analyses demonstrated marginal (LY2216684) or minimal (LY2140023) impact of renal function on exposure, which makes dose adjustment unnecessary except for compounds with a narrow therapeutic index.

Figure 2.

Statistical analyses with and without dialysis participants on RI estimates of drug exposure. The forest plots show the differences between ANOVA and regression analysis with and without dialysis participants for LY2216684, LY2140023, and LY404039 in Figure (a), (b), and (c), respectively. AUC, area under the curve; CG, Cockcroft‐Gault formula; CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula; ESRD, end‐stage renal disease; GFR, glomerular filtration rate; GMR, geometric mean ratio; HD, hemodialysis; RI, renal impairment.

Nonetheless, the estimated impact of RI on PK differed based on the choice of creatinine‐based equation and statistical analysis methods. ANOVA resulted in an inconsistent estimate of the impact of RI on AUC when the severity of RI was estimated using different equations. For example, in Study LNCA, when renal function was estimated by CG or CKD‐EPI₂₀₀₉ equations, participants with moderate RI showed the greatest increase in AUC compared to the control group. However, when RI was categorized with absolute CKD‐EPI₂₀₀₉, participants with severe RI showed the greatest increase in AUC (Figure 2 a ). When analyzing data from Study HBCE using the CG equation, no participants met severe RI criteria, which makes it difficult to estimate the impact of RI on PK for participants with severe RI. The point estimates for AUC ratio for LY2140023 (Figure 2 b ) were similar for both CKD‐EPI₂₀₀₉ equations. For LY404039 (Figure 2 c ), which is highly renally cleared, the AUC_0–t ratios of severe RI groups vs. control groups were greater when RI was defined based on the two CKD‐EPI₂₀₀₉ equations, with the ratios being

• 4.61 (90% CI: 3.49 to 6.09) when CKD‐EPI₂₀₀₉ was used to define RI groups, and

• 5.38 (90% CI: 3.88 to 7.45) when absolute CKD‐EPI₂₀₀₉ was used.

Across all three analytes, ANOVA provided consistent estimates of AUC difference between the control group and the ESRD group regardless of renal function classification approach. This may be due to a large portion of ESRD participants in these studies being on HD, and therefore not affected by the difference in GFR equations.

In contrast to ANOVA, all regression analyses showed relatively consistent trends of increased AUC in participants with more advanced RI when the same datasets were used. The CIs of geometric mean AUC estimates along with the geometric mean ratio of AUC between RI groups, relative to participants with normal renal function obtained with regression analysis, were narrower than those obtained using ANOVA, indicating higher precision.

Comparison of statistical analyses with and without data from participants on hemodialysis

The impact of regression analysis on excluding data from participants on dialysis was further explored (Figure 3 ). For LY2216684 (predominantly hepatically cleared), regression analysis that included data from participants on HD demonstrated no correlation between eGFR and exposure (Figure 3 a ). Consequently, this predicted minimal impact of RI on exposure of LY2216684 for all RI categories with maximum AUC ratio of 1.22 (90% CI of 0.86 to 1.72) for participants with severe RI (Figure 2 a ).

Figure 3.

Regression analysis with and without participants on HD. Figure (a, b) regression analysis on CKD‐EPI₂₀₀₉ (left panel) and absolute CKD‐EPI₂₀₀₉ (right panel) vs. Log AUC_0–∞ for LY22166884 and LY2140023 respectively. Figure (c) regression analysis on CKD‐EPI₂₀₀₉ (left panel) and absolute CKD‐EPI₂₀₀₉ (right panel) vs. Log AUC_0–tlast for LY404039; Figure (d) regression analyses of regression analysis on Log CKD‐EPI₂₀₀₉ (left panel) and absolute CKD‐EPI₂₀₀₉ (right panel) vs Log AUC_0–tlast for LY404039. Points represent observed individual data. Blue lines show regression with 90% confidence interval when data from participants on HD were included. Red lines show regression line with 90% CI when data from participants on HD were excluded. The data from participants on dialysis skewed the regression slope for LY2216684 and LY404039. AUC_inf, area under the curve from time zero to infinity; AUC_tlast, area under the curve from time zero to the last measurable concentration; CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula; HD, hemodialysis; lnabsckd, logarithmic absolute CKD‐EPI₂₀₀₉; lnckd, logarithmic CKD‐EPI₂₀₀₉.

When data from dialysis participants were excluded (Figure 3 a ), a trend of increased AUC of LY2216684 in participants with reduced renal function was observed. As a result, this model predicted greater increase in AUC for all RI categories with maximum increase in AUC ratio of 1.77 (90% CI of 1.08 to 2.88) for participants with severe RI (Figure 2 a ). For LY2140023, which is predominantly cleared by systemic peptidase, the regression lines for analyses with and without data from participants on dialysis overlap (Figure 3 b ). Therefore, the estimated AUC ratios based on regression analysis were similar across all RI categories, regardless of whether data from participants on HD were included.

However, for LY404039, which is predominantly cleared renally, the scatter plot suggested a non‐linear relationship between eGFR and AUC (Figure 3 c ) especially when including data from participants on dialysis. Therefore, inclusion of data from participants on HD resulted in a steeper relationship between eGFR and AUC, leading to a higher estimated AUC ratio for all RI categories. For example, AUC ratio for severe RI group to normal renal function was 7.41 (90% CI of 5.91 to 9.29) when data from dialysis participants were included, compared to 3.81 (90% CI 3.17 to 4.57) when these data were excluded (Figure 2 c ).

The apparent clearance of LY404039 was highly correlated with GFR (data not shown), leading to an inverse relationship between exposure and clearance. Log‐transformed eGFR was used as the independent variable (Figure 3 d ). This transformation appeared to minimize the issue of non‐linear relationship between eGFR and exposure, as the regression lines overlapped regardless of whether data from participants on HD were included.

The relationship between eGFR and AUC for LY404039 and LY2216684 suggested that the linear relationship between eGFR and AUC may not extend to participants on HD for these compounds; therefore, regression analysis without data from participants on HD appeared to be a more appropriate approach. Log‐transformation of eGFR as a predictor may also address the issue of nonlinear relationships between eGFR and exposure in some cases.

Control of body size in regression models

To control body size as a potential confounding factor in the regression analysis of renal function and AUC, we further evaluated BSA or BW as a covariate on exposure in participants with RI (Figure 4 ). Four regression analyses were performed for each analyte, with either indexed CKD‐EPI₂₀₀₉, absolute CKD‐EPI₂₀₀₉ in univariate regression, or indexed CKD‐EPI₂₀₀₉ regression analysis with either BSA or BW as a covariate. All four analyses showed very similar estimates of changes in AUC compared to control groups in participants with RI. For LY2216684, when either BSA or BW was incorporated as a covariate for the indexed CKD‐EPI₂₀₀₉ model, there was a slightly greater increase in AUC ratio of each RI group to control group compared to univariate analysis when only indexed CKD‐EPI₂₀₀₉ was used in the model (Figure 4 a ). Results from the other two analytes from all regression analyses were very consistent (Figure 4 b,c ).

Figure 4.

Regression analysis with covariates BSA and BW on RI estimates of drug exposure. The impact of BSA and BW as independent covariates on drug exposure for RI groups for LY2216684, LY2140023, and LY404039 are shown in Figure (a), (b), and (c), respectively. No substantial differences were observed across all GFR estimation methods for all compounds. AUC, area under the curve; CKD‐EPI₂₀₀₉, 2009 creatinine‐based Chronic Kidney Disease Epidemiology Collaboration formula; GMR, geometric mean ratio; RI, renal impairment.

DISCUSSION

Dedicated RI studies are important in drug development, as they support benefit–risk assessment and associated dose recommendations for patients with CKD. FDA and EMA guidance provide important recommendations on the design and data analysis of such studies to ensure appropriate conclusions are drawn and, if necessary, suitable dosing recommendations can be made for patients with impaired renal function.

One of the key recommendations from FDA and EMA guidance is to prefer regression analysis over categorical analysis. Our retrospective analyses from two completed full RI studies strongly support this recommendation. Retrospective ANOVA analysis of PK data using different creatinine‐based equations showed some differences when estimating the impact of RI on AUC of two of the three analytes. This is likely due to discordance in classifying the participants into different RI groups in a study when different creatinine‐based equations were used (Tables 1 and 2 ; Figure 1 ). A meaningful number of participants were reclassified from one group to another when equations different from the original design were used in this post hoc analysis (Figure 2 b,c ). This reclassification can lead to inconsistent estimation of the impact of CKD on the PK of the same drug, even when based on the same clinical data.

Wider CIs were observed for some groups when fewer participants remained in certain categories compared to the original design. This discrepancy may also cause a mismatch of important covariates such as age, sex, and weight. Therefore, post hoc ANOVA analysis of data from RI studies using a different equation to estimate renal function should be avoided as it introduces inconsistent results. In contrast, regression analysis demonstrated a much more consistent estimate of the impact of CKD on PK for all three analytes within the same population. This is likely due to the higher correlation among all three creatinine‐based equations in estimating renal function. The regression analysis also improved the precision of the estimation because data from all participants were used to estimate the relationship between eGFR and PK.

To understand whether data from participants on dialysis should be included in regression analyses, we performed retrospective regression analysis with and without data from participants on HD. Our findings supported FDA's recommendation to exclude data from participants on HD in regression analyses. For example, regression analysis that included participants on HD showed no effect of CKD on the PK of LY2216684, which is predominantly cleared by hepatic CYP2D6 and CYP2C19. In contrast, analysis that excluded data from participants on HD consistently showed a modest increase in exposure, which is more consistent with literature data suggesting participants with CKD may have reduced CYP2D6 activity. ¹²

This phenomenon has been reported with substrates of other CYPs and transporters. ¹³ As a result, participants with severe RI or ESRD and not on HD often had greater increase in exposure of some nonrenally cleared drugs compared with participants on HD. ¹⁴ These observations suggested that for compounds that are predominantly cleared via hepatic metabolism, the increase in exposure is not “linear” in participants on HD. Furthermore, a wide fluctuation in serum creatine levels can be observed in participants on HD, ¹⁵ due to factors such as time elapsed since the last HD, fluid balance, and nutritional status. Therefore, serum creatine is not a reliable measure for renal function, and using calculated “eGFR” value in participants on HD as the same predictor variable as participants not on HD is likely inappropriate.

Our retrospective analysis showed that when data from participants on HD were excluded from regression analysis, the impacts of RI on PK of all three analytes were highly consistent whether the equations used for renal function estimation was CG equation, indexed CKD‐EPI₂₀₀₉, or absolute CKD‐EPI₂₀₀₉ (Figures 2 and 3 ). This is probably due to the strong correlation among these three creatinine‐based equations. The differences in the estimated geometric mean AUC ratio of participants with different stages of CKD were minimal when using indexed vs. the absolute eGFR equation. Given indexed eGFR is widely used in clinical practice to determine the severity of CKD, using this equation may be more user‐friendly and convenient for clinicians and patients, particularly when both equations provide similar estimates of changes in exposure in patients with CKD.

It is well‐documented that clinicians commonly use BSA‐indexed eGFR reported by clinical laboratories to adjust the dose for direct oral anticoagulants, rather than the CG equation recommended by the label. This practice can lead to both overdosing and underdosing, leading to a higher rate of thromboembolic events or bleeding. ¹⁶ , ¹⁷ Therefore, it is important to design and analyze data for RI studies and make dosing recommendations using the eGFR equation that aligns as closely as possible to the equation used by clinicians. This approach can avoid dosing errors, especially for drugs with a narrow therapeutic index.

Despite the inclusion of baseline data from seven completed RI studies, and retrospective analysis of two studies that include three analytes representing distinct ADME profiles, these observations should be validated by more RI studies. Furthermore, we did not test other creatinine‐based equations such as CKD‐EPI₂₀₂₁ used in clinical practice. Therefore, more data from RI studies, and testing of additional contemporary equations, are necessary to confirm the observations from this study.

In conclusion, our retrospective analyses showed that in small renal impairment studies, the use of different creatinine‐based equations could result in a notable number of participants being reclassified into different RI groups, and cause inconsistency in the estimation of AUC change in participants with renal impairment when categorical analysis, such as ANOVA, is used. Regression analysis without data from participants on hemodialysis provided the more precise and consistent estimate on the effect of RI on AUC of the three analytes. Our analyses support the FDA 2024 guidance for the use of regression analysis without data from participants on HD as the primary analysis for assessing the impact of CKD on the PK of drugs. The performance of this analysis method should be confirmed with data from additional RI studies and other equations for renal function estimation.

FUNDING

This work was funded by Eli Lilly and Company. Gerald C. So was supported by the National Institutes of Health, National Institute of General Medical Sciences (Grant T32GM008425).

CONFLICT OF INTEREST

Y.G.L., J.C., C.D.P., M.M.P., M.L.B.P., and Y.J. are employees and shareholders of Eli Lilly and Company, and G.C.S. is a business guest with Eli Lilly and Company. All other authors declared no competing interests for this work.

AUTHOR CONTRIBUTIONS

All authors wrote the manuscript; Y.J. designed the research; all authors performed the research; all authors analyzed the data.

Supporting information

Table S1