Comparative Evaluation of Median Versus Youden Index Dichotomization Methods: Exposure–Response Analysis of Mycophenolic Acid and Acyl-Glucuronide Metabolite

Abstract

Background and Objectives

Dichotomization of pharmacokinetic exposure measures in exposure–response relationship studies provides results that are interpretable in clinical care. Several methods exist in the literature on how to define the cut-off values needed for the dichotomization process. Commonly, the sample median is utilized to define the dichotomizing value; however, statistical methods based on the exposure metric and its association with the outcome are argued to result in a more proper definition of the optimal cut-point. The Youden index is a recommended statistical method to define the cut-off value. The current analysis objective is to compare the dichotomization results based on the Youden index versus median methods.

Methods

Utilizing mycophenolic acid (MPA) exposure data and its related acute rejection and leukopenia outcome variables, the current study compared the MPA exposure–response relationship outcomes when MPA exposure is dichotomized via the Youden index versus median methods. Univariate logistic models were utilized to quantify the relationships between MPA exposure, including total MPA, unbound MPA, and the acyl-glucuronide metabolite of MPA, and the probabilities of acute rejection and leukopenia.

Results

The overall trend of the results of the logistic models demonstrated a general similarity in the inferred exposure–response associations when considering either the Youden index-based or the median-based dichotomization methods.

Conclusion

The results demonstrated in this analysis suggest that both the Youden index and the median methods provide similar conclusions when dichotomization of a continuous variable is considered. However, confirmation of these conclusions comes from future powered studies that include a larger number of subjects.

1. Introduction

Dichotomization of pharmacokinetic exposure measures can be advantageous as it provided results that are easily interpretable and provides a target exposure for implementation in clinical care [1]. Commonly, the sample median (or some other point in the data) is utilized to define the dichotomizing cut-off values [2]; however, there are several statistical methods that can be used to define the optimal cut-off points based on the exposure metric and its association with the response outcome. The Youden index is a recommended statistical method to define the optimal cut-off point [3, 4], and is defined as the sum of acyl-glucuronide (acyl-MPAG) sensitivity and specificity subtracted by 1. Further details about the Youden index can be found elsewhere [5, 6]. It is not well understood whether the median or a statistical method (like the Youden index) would provide a more accurate estimation of a cut-off point.

Mycophenolic acid (MPA) is an immunosuppressive drug used to prevent acute rejection; however, it is associated with numerous side effects such as leukopenia. MPA is metabolized in the liver primarily by uridine 5′-diphosphate glucuronosyltransferase (UGTs) enzymes producing metabolites including 7-O-MPA-ß-glucuronide (MPAG) and acyl-glucuronide (acyl-MPAG) metabolites [7, 8]. The primary enzyme involved in the metabolism of MPA to MPAG is UGT1A9 [9–11]. The enzyme UGT2B7 is the major isoform involved in the metabolism of MPA to a minor metabolite, acyl-MPAG [9, 11]. The metabolite MPAG is the major product of MPA metabolism; however, it has no pharmacological effect with regards to immunosuppression [12]. Unlike MPAG, the metabolite acyl-MPAG has a similar pharmacological potency as MPA [7]. MPA binding to blood cellular components is negligible (< 0.01%); however, it is highly bound to serum albumin (around 98%) [13, 14].

Several studies have evaluated the exposure–response relationship between MPA exposure and associated toxicities in transplantation [15–19]. The results of these studies are conflicting, as some studies showed an association while others did not [16, 19, 20]. The lack of a clear association in these studies could be the result of several factors, including the time of MPA exposure relative to rejection and toxicity, the assays used for exposure quantification, varying definitions of toxicities and rejection, limited exposure variability in relation to the response, and differing statistical methods used to assess the exposure–response relationship. When exposure is evaluated as a dichotomized variable, the lack of association could also be the result of a poor definition of cut-off points.

The objective of the current analysis is to compare the MPA exposure–response relationship outcomes when MPA exposure is dichotomized via the Youden index versus median methods. Logistic models will be utilized to quantify the relationships between MPA exposure, including total MPA, unbound MPA, and acyl-MPAG, and the probabilities of acute rejection and the common MPA toxicity, leukopenia.

2. Methods

In the current analysis, pharmacokinetic exposure metrics were calculated from three concentration–time profiles: total MPA, unbound MPA, and acyl-MPAG. Dichotomization of these continuous exposure metrics was performed by the Youden index and the median. Using logistic regression, dichotomized variables based on the Youden index and the median were univariately examined for their effect on the development of acute rejection and leukopenia post-transplant.

2.1. Pharmacokinetic Exposure Data

Data used in this study were obtained from a pharmacogenomics study conducted in 92 individuals who were enrolled in the Deterioration of Kidney Allograft Function (DeKAF) Genomics study. DeKAF Genomics is a multicenter, prospective, observational trial aimed to evaluate the effect of individual genetic variability on clinical outcomes of kidney transplantation. Institutional Review Board approval was obtained at each participating center and all patients provided informed, written consents prior to enrollment. The study is registered at http://www.clinicaltrials.gov (NCT00270712).

Subjects received maintenance oral mycophenolate mofetil (MMF; Cellcept®) immunosuppression ranging between 500 and 1500 mg every 12 h. Subjects were included if they were adults who were ≥ 18 years, had undergone kidney or kidney-pancreas transplantation, and were receiving maintenance MMF immunosuppression. Participants also had a functioning kidney graft at the time of the pharmacokinetics visit with an estimated glomerular filtration rate > 50 ml/min/1.73 m² within 2 weeks prior to the pharmacokinetics visit. Patients were excluded if they simultaneously received another organ (other than the pancreas) with the qualifying kidney transplant, had post-transplant active gastroparesis or liver disease. Recipients also received oral immediate release tacrolimus or cyclosporine and varying durations of corticosteroids (sparing and non-sparing) with or without antibody induction as per the transplant center standard-of-care protocols. Patients on corticosteroidsparing therapy typically received 5 days of treatment and then all were off by day 14. The initial tacrolimus or cyclosporine dose was based on body weight, and doses were adjusted to achieve each transplant center’s tacrolimus or cyclosporine target concentrations. The median total daily cyclosporine dose was 4.08 mg/kg/day (range 1.49–8.09 mg/kg/day) prior to day 90 post-transplant, and 2.88 mg/kg/day (range 0.74–6.8 mg/kg/day) after day 90 post-transplant. The median total daily tacrolimus dose was 0.068 mg/kg/day (range 0.01–0.31 mg/kg/day) prior to day 90 post-transplant, and 0.05 mg/Kg/day (range 0.01–0.16 mg/kg/day) after day 90 post-transplant. Induction therapy was administered as per transplant center preference but mainly consisted of rabbit antithymocyte globulin, basiliximab or Campath1H. Immunologically high-risk patients were more likely to receive rabbit antithymocyte globulin, such as those with donor-specific antibody, prior pregnancies or repeat transplants. Recipient characteristics and outcomes were obtained from the respective medical records. Blood samples were collected at steady-state (> 48 h or more from dose change) from patients during the pharmacokinetic visit between days 15–60 post-transplant. Sampling times were pre-dose and 1, 2, 4, 6, 8, and 12 h following the oral MMF dose. Detection and quantification of unbound MPA, total MPA, MPAG and acyl-MPAG in plasma were performed using high-performance liquid chromatography (Agilent 1200 Series, Santa Clara, CA, USA) coupled with a TSQ Quantum triple-stage quadrupole mass spectrometer (Thermo-Electron, San Jose, CA, USA). Bioanalysis information is described elsewhere [21].

For each subject, exposure metrics were calculated for total MPA, unbound MPA, and acyl-MPAG concentrations using WinNonlin (Pharsight, CA, USA), and they included area under the curve at steady-state between 0 and 12 h (AUC _ss), the maximum concentration at steady-state (C_max,ss), and the minimum concentration at steady-state (C_min,ss).

2.2. Pharmacodynamic Response Data

Response variables evaluated in this analysis included acute rejection and leukopenia. Acute rejection was defined as the presence of features of cellular- or antibody-mediated or both on kidney biopsy at the time of diagnosis. Patients were followed up for acute rejection for 6 months beginning at the time of transplant. Rejection was determined by the treating physician. MPA-related leukopenia was defined as the use of MMF at least 14 days before a white blood cell (WBC) count less than 3000 cells/mm³ that resulted in a clinical intervention. Clinical interventions were a dose reduction lasting more than or equal to 2 weeks, discontinuation for more than or equal to 2 weeks and/or initiation of granulocyte colony-stimulating factor or granulocyte–macrophage colony-stimulating factor therapy within 30 days of the onset of the leukopenia. The leukopenia was considered not to be MPA-related if the subject had concurrent sepsis, an active Cytomegalovirus infection, or if the low WBC count was within 2 weeks after antibody administration or acute rejection. The time to leukopenia was calculated from first MPA use to the date of the first respective WBC of less than 3000 cells/mm3. Patients were followed up for leukopenia for 6 months beginning at the time of transplant.

2.3. Dichotomization of Exposure Metrics

Each exposure metric (AUC _ss, C_max,ss, and C_min,ss) was dichotomized as “low” or “high” using the two methods: the Youden index and the median. With the Youden index, different cut-off values were calculated for acute rejection and leukopenia based on the exposure metric association with each of the two response outcomes. The calculation of median and Youden index cut-off points was accomplished using the R packages, “base” and “OptimalCutpoints”, respectively [6, 22]. Optimal cut-off points were determined for total MPA, unbound MPA, and acyl-MPAG separately using each method.

Briefly, the Youden method defines the optimal cut-off point as the value that maximizes the Youden index (J) which is the difference between the true positive rate and the false positive rate over all possible cut-point values, as shown in Eq. 1 [6]. The optimal cut-point in the Youden method is considered optimal as it optimizes the differentiating ability of the data while equal weight is given to sensitivity and specificity [23].

$$J=\text{Sensitivity}+\text{Specificity}-1.$$ (1)

2.4. Logistic Regression

Logistic regression was conducted for each combination of the exposure metric and the response variable for each dichotomization method (median and Youden index). Each dichotomized exposure metric was regressed univariately against acute rejection and leukopenia.

The generalized linear model (GLM) was utilized to conduct the logistic analysis using the R package “glm” [24]. These models are defined by three components: the random component, the systematic component, and the link function. The random component defines the distribution of the outcome variable. The systematic component relates the exposure variable(s) to the parameters. Finally, the link function connects the random and systematic components.

When applied to the current logistic regression, GLM was used with a binomial distribution random component, and the logit canonical link was used as a link function throughout the entire analysis. A p value ≤ 0.05 was considered significant.

The general form of the GLM used in the analysis is described by Eq. 2:

$$\text{logit}\left({\pi }_i\right)=\alpha +\beta \times {\text{exposure}}_i$$ (2)

where 𝜋_i is the probability of having the response event in subject i, i.e., P(Y = 1) ; the variable exposure_i represents the dichotomized exposure metric in the ith subject; the parameter 𝛼represents the low group in the dichotomized variable; the parameter β describes the linear relationship between the exposure metric and the response variable. The R packages “ggplot2” [25] and “dplyr” [26] were used for plotting and data manipulation.

The bootstrap method with replacement was utilized to construct confidence intervals (CI) of the estimated parameters. Estimates from 500 bootstrapped datasets were used to calculate the 2.5th and 97.5th percentiles which defined the lower and upper limit of the 95% CIs, respectively, for each parameter.

3. Results

3.1. Pharmacokinetic and Pharmacodynamic Data

Summaries of pharmacokinetic exposure data are presented in Table 1. Density plots of the exposure metrics of total MPA, unbound MPA, and acyl-MPAG are shown in the supplementary document. With respect to the pharmacodynamic response data, 16 patients (out of 92) developed acute rejection by month 6 post-transplant, while 9 patients (out of 92) developed leukopenia by month 6.

Table 1.

Summary of pharmacokinetic exposure data

MPA analyte	Exposure variable	Mean	Standard deviation	Median	Minimum value	Maximum value
Total MPA	AUCss (h × mg/L)	38.9	14.3	37.06	15.68	74.7
	Cmax,ss (mg/L)	8.8	3.27	8.91	2.45	17.17
	Cmin,ss (mg/L)	2.06	1.18	1.87	0.26	6.33
Unbound MPA	AUCss (h × mg/L)	0.95	0.41	0.88	0.3	2.77
	Cmax,ss (mg/L)	0.22	0.09	0.20	0.05	0.45
	Cmin,ss (mg/L)	0.05	0.04	0.04	0.003	0.20
Acyl-MPAG	AUCss (h × mg/L)	6.23	3.41	5.68	1.40	22.68
	Cmax,ss (mg/L)	1.05	0.51	0.94	0.27	3.33
	Cmin,ss (mg/L)	0.3	0.21	0.24	0.03	1.39

MPA mycophenolic acid, MPAG acyl-glucuronide metabolite of MPA, AUC_ss area under the curve at steady-state, C_max,ss maximum concentration at steady-state, C_min,ss minimum concentration at steady-state

3.2. Dichotomization Analysis

Results of the Youden index-based dichotomization analysis are displayed in Table 2. Included in the table are the Youden index-identified cut-off values for each exposure and outcome combination. The comparison of the dichotomization results for acute rejection and leukopenia using the Youden-based and median cut-off values are displayed in Figs. 1 and 2, respectively.

Table 2.

Results of Youden method dichotomization analysis of MPA exposure metrics

MPA analyte	Exposure variable	Cut-off value
		Acute rejection	Leukopenia
Total MPA	AUCss (h × mg/L)	20.6	44
	Cmax,ss (mg/L)	6.5	5.96
	Cmin,ss (mg/L)	2.08	1.76
Unbound MPA	AUCss (h × mg/L)	0.42	0.78
	Cmax,ss (mg/L)	0.17	0.15
	Cmin,ss (mg/L)	0.06	0.03
Acyl-MPAG	AUCss (h × mg/L)	4.55	14.1
	Cmax,ss (mg/L)	0.85	0.49
	Cmin,ss (mg/L)	0.25	0.17

MPA mycophenolic acid, MPAG acyl-glucuronide metabolite of MPA, AUC_ss area under the curve at steady-state, C_max,ss maximum concentration at steady-state, C_min,ss minimum concentration at steady-state

Fig. 1.

Exposure–response plot of the MPA exposure metrics versus acute rejection. For each patient, acute rejection was coded using a binary system of [0] and [1]. The [0] value indicated that the patient did not develop the event, and the [1] value indicated that the patient had developed the event. The dashed blue and solid red vertical lines in each plot represent the cut-off values suggested by the Youden index and the median, respectively. MPA mycophenolic acid, acyl-MPAG acyl-glucuronide metabolite of MPA, AUC_ss area under the curve at steady-state, C_max,ss maximum concentration at steady-state, C_min,ss minimum concentration at steady-state

Fig. 2.

Exposure response plot of the MPA exposure metrics versus leukopenia. For each patient, leukopenia was coded using a binary system of [0] and [1]. The [0] value indicated that the patient did not develop the event, and the [1] value indicated that the patient had developed the event. The dashed blue and solid red vertical lines in each plot represent the cut-off values suggested by the Youden index and the median, respectively. MPA mycophenolic acid, acyl-MPAG acyl-glucuronide metabolite of MPA, AUC_ss area under the curve at steady-state, C_max,ss maximum concentration at steady-state, C_min,ss minimum concentration at steady-state

Taking the total MPA AUC_ss as an example, the median was 37.06 h × mg/L, and the identified Youden cut-off points were 20.6 h × mg/L and 44 h × mg/L for acute rejection and leukopenia, respectively. It is important to emphasize that the results of the dichotomization analysis, considering the median or the Youden index, do not guarantee a significant relationship between the dichotomized exposure metric and the outcome variable in the logistic regression.

3.3. Logistic Regression

To determine if the cut-off points identified by each method were associated with the binary clinical outcomes variables, logistic regression was performed. The results of the univariate logistic regression analyses with corresponding 95% CIs, obtained from bootstrapping for all the exposure metrics, using the median and the Youden index, determined against acute rejection and leukopenia are listed in Tables 3 and 4, respectively. With respect to acute rejection, the Youden index and the median dichotomization methods agreed that C_min,ss of acyl-MPAG is the only significant exposure variable (p value = 0.05). A similar slope parameter and odds ratio were also observed for C_min,ss of acyl-MPAG when considering either the Youden index or the median. In general, the bootstrapped CIs confirmed the logistic regression results with respect to parameter slope significance for both the Youden and median dichotomization methods.

Table 3.

Results of univariate regression analyses on acute rejection by dichotomization method

MPA analyte	Dichotomized exposure metric	Youden method					Median method
		Slope parameter	Slope SE	Slope P value	Bootstrap 95% CIa	Odds ratiob	Slope parameter	Slope SE	Slope P value	Bootstrap 95% CIa	Odds ratiob
Total MPA	AUCss	16.2	1399	0.99	15.24–17.33	-	−0.65	0.57	0.25	−1.93–0.61	-
	C max,ss	0.69	0.69	0.32	−0.59–17.84	-	0.70	0.57	0.22	−0.44–2.53	-
	C min,ss	0.87	0.57	0.13	−0.14–2.26	-	0.98	0.59	0.10	−0.03–2.5	-
Unbound MPA	AUCss	−0.14	1.15	0.9	−2.03–16.34	-	−0.59	0.57	0.30	−1.94–0.56	-
	C max,ss	0.45	0.628	0.48	−0.64–2.04	-	−0.28	0.56	0.62	−1.57–0.77	-
	C min,ss	0.93	0.6	0.12	−0.59–2.17	-	0.65	0.57	0.25	−0.49–2.08	-
Acyl-MPAG	AUCSS	0.93	0.69	0.17	−0.21–18.24	-	−0.28	0.56	0.62	−1.61–0.82	-
	C max,ss	0.15	0.57	0.79	−0.91–1.56	-	0.03	0.55	0.96	−1.14–1.32	-
	C min,ss	1.15	0.59	0.05	0.04–2.65	3.15	1.35	0.62	0.03	0.18–3.16	3.84

MPA mycophenolic acid, Acyl-MPAG acyl-glucuronide metabolite of MPA, AUC_ss area under the curve at steady-state, C_max,ss maximum concentration at steady-state, C_min,ss minimum concentration at steady-state, SE standard error, CI confidence interval

^aCalculated from 500 bootstrapped datasets with replacement

^bOdds ratios were calculated only for significant associations

Table 4.

Results of univariate regression analyses on leukopenia by dichotomization method

MPA analyte	Dichotomized exposure metric	Youden method					Median method
		Slope parameter	Slope SE	Slope P value	Bootstrap 95% CIa	Odds ratiob	Slope parameter	Slope SE	Slope P value	Bootstrap 95% CIa	Odds ratiob
Total MPA	AUCss	1.48	0.75	0.047	0.09–19.31	4.40	1.35	0.83	0.10	−0.06 to 18.83	-
	C max,ss	0.91	1.09	0.40	−0.8 to 17.72	-	−0.17	0.71	0.81	−17.65 to 1.37	-
	C min,ss	1.30	0.83	0.12	−0.22 to 18.76	-	1.40	0.83	0.09	−0.17 to 18.96	-
Unbound MPA	AUCss	1.83	1.08	0.09	0.28–18.74	-	0.79	0.74	0.28	−0.72 to 18.52	-
	C max,ss	0.91	1.09	0.40	−0.65 to 17.83	-	0.27	0.71	0.70	−1.34 to 2.26	-
	C min,ss	1.78	1.08	0.10	0.13–18.68	-	1.40	0.83	0.09	−0.18 to 19.05	-
Acyl-MPAG	AUCss	−15.42	2284	0.99	−15.82 to 13.52	-	−0.74	0.74	0.32	−18.46 to 0.54	-
	C max,ss	−0.27	1.13	0.81	−2.09 to 16.73	-	−0.74	0.74	0.32	−18.45 to 0.79	-
	C min,ss	0.02	0.85	0.98	−1.54 to 17.5	-	−0.74	0.74	0.32	−18.41 to 0.88	-

MPA mycophenolic acid, Acyl-MPAG acyl-glucuronide metabolite of MPA, AUC_ss area under the curve at steady-state, C_max,ss maximum concentration at steady-state, C_min,ss minimum concentration at steady-state, SE standard error, CI confidence interval

^aCalculated from 500 bootstrapped datasets with replacement

^bOdds ratios were calculated only for significant associations

The simple logistic regression model for the Youden index-based dichotomized acyl-MPAG C_min,ss (> 0.25 mg/L) relating to acute rejection is as in Eq. 2:

$$\text{logit}\left({\pi }_i\right)=-2.15+1.15\times \left(\text{acyl MPAG}{C}_{\text{min,ss,i}}\right)$$ (3)

where acyl MPAG C_min,ss,i is the individual acyl-MPAG C_min,ss.

The β parameter estimate was 1.15, which represents the log odds that a patient will have acute rejection versus a patient not having acute rejection. Interpreted as an odds ratio, there is a 215% increase in the odds of acute rejection with the high acyl-MPAG C_min,ss group compared to the low group. On the other hand, the simple logistic regression model for median-based dichotomized acyl-MPAG C_min,ss (> 0.24 mg/L) relating to acute rejection is as in Eq. 3:

$$\text{logit}\left({\pi }_i\right)=-2.32+1.35\times \left(\text{acyl MPAG}{C}_{\text{min,ss},i}\right)$$ (4)

where acyl MPAG C_min,ss,i is the individual acyl-MPAG C_min,ss.

The β parameter estimate was 1.35. Interpreted as an odds ratio, there is a 284% increase in the odds of acute rejection with the high acyl-MPAG C_min,ss group compared to the low group.

When considering leukopenia, total MPA AUC _ss was the only exposure variable to be found significant using the Youden index-based dichotomization; while no exposure variable was found to be significant using the median-based dichotomization. Even though the two methods did not provide the same conclusions given the pre-specified 0.05 p value, there was a general agreement in the p value trends for most evaluations between the Youden index-based and the median-based results.

The simple logistic regression model for the Youden index-based dichotomized total MPA AUC_ss (> 44 h × mg/L) metric relating to leukopenia is as in Eq. 4:

$$\text{logit}\left({\pi }_i\right)=-0.7885+1.4816\times \left(\text{Total MPA}{\text{AUC}}_{\text{ss},i}\right)$$ (5)

where Total MPA AUC_ss,i is the individual total MPA AUC_ss.

The β parameter estimate for the dichotomized total MPA AUC_ss was 1.48, meaning that the high total MPA AUC_ss group is associated with larger logits of leukopenia than the low group. In terms of odds ratio, there is around a 340% increase in the odds of leukopenia in the high total MPA AUC_ss group compared to the low group.

4. Discussion

The current analysis explored the relationship between dichotomized exposure metrics of total MPA, unbound MPA, and acyl-MPAG and transplant outcomes of acute rejection and MPA-related leukopenia. The dichotomization of the exposure metrics, AUC_ss, C_max,ss, and C_min,ss, was performed using the Youden index and median methods. As response variables were binary, univariate logistic regression analyses were conducted on each combination of the exposure metric and the response.

The comparative results of dichotomization by the Youden index and median methods demonstrated general agreement in the inferred exposure–response associations. Interestingly, a significant relationship was demonstrated between acute rejection and the C_min,ss of acyl-MPAG when considering either the Youden index or the median dichotomization methods (Table 3). Being in the high group of acyl-MPAG C_min,ss is associated with a trend of higher odds of acute rejection in comparison to the low group. Acyl-MPAG C_min,ss has been shown to be significantly higher during acute rejection episodes [27]. A possible explanation of this acyl-MPAG association with acute rejection is related to acyl-MPAG hypersensitivity and drug toxicity, as it has been shown that acyl-MPAG can induce cytokine release and cytokine messenger RNA expression in leukocytes [28, 29]. Another speculated explanation of this association is that it could be a result of impaired renal elimination of acyl-MPAG at the time of acute rejection, which manifests as an elevated serum creatinine rather than a cause–effect relationship. The results also demonstrate the absence of a significant relationship between acute rejection and any of the unbound or total MPA exposure metrics, when using either of the dichotomization methods. These observations demonstrated consistency in the identified cut-points and exposure–response associations between the Youden index and median dichotomization methods when considering the acute rejection outcome.

To further explore the comparative results of the Youden index and median dichotomization methods, an evaluation was conducted considering the leukopenia outcome. The current analysis demonstrated the presence of a significant association between leukopenia and total MPA AUC _ss when using the Youden index-based dichotomization method, while no significant association was observed when the median-based dichotomization was considered (Table 4). With regards to the logistic results of the Youden index-based dichotomization, the odds of leukopenia are greater in the high total MPA AUC_ss group (> 44 h × mg/L) when compared to the low group. Similar association results between total MPA AUC_ss and leukopenia have been reported with a cut-off value of 60 h × mg/L [27, 30–32].

It is common in clinical research to dichotomize patientspecific variables to simplify the decision-making process. As an example, high blood pressure is usually defined as having ≥ 90 mm Hg systolic blood pressure and/or ≥ 140 mm Hg diastolic blood pressure. Several examples can also be found in the drug development literature when it comes to utilizing dichotomization [33, 34]. For instance, in a phase 2 study that aimed to evaluate the efficacy and safety of rilotumumab, the levels of MET (tyrosine–protein kinase) in patients were dichotomized into high versus low groups [34].

Dichotomization is also helpful when dealing with crude exposure variables (high noise in the data) where it would be difficult to specify a particular model. This could be the reason why no association was observed in the continuous variables of the exposure metrics (data on file), while associations and trends were observed with the dichotomized variables. On the other hand, there are several problems associated with dichotomizing an exposure variable. Dichotomization results in losing the statistical power necessary to signify a relationship between an exposure metric and an outcome. Another issue faced in conducting dichotomization is how to determine the cut-off point.

Most commonly, the dichotomization process is performed at the sample median; however, there is no scientific reason why the cut-off should be at the median [2]. Also, different studies may have different medians which may result in hampering meta-analysis studies [35]. Therefore, it could be more desirable to define the cut-off values based on the exposure metric and its association with the specific response outcome. In theory, this results in appropriately classifying most of the individuals in the analysis, i.e., the optimal cut-off point [3]. The Youden index is a recommended statistical method to define the optimal cut-off value [3,4], and it has been utilized in several clinical applications [36–39]. With the Youden index, the chosen cut-off point is invariant to small changes in the cut-point, therefore making it a valuable characteristic in a meta-analysis setting [40]. On the other hand, the Youden index has been demonstrated to show overly optimistic estimates especially in small studies [41]. Further details about the Youden index can be found elsewhere [5, 6].

The current analysis has some limitations. First, the study population has a narrow dose range that comes from a controlled medical setting. This will limit the ability to fully capture the exposure–response association with acute rejection or leukopenia. Second, the dataset comes from a study that was not powered specifically for this analysis, thereby increasing the chance of type 2 errorss. Finally, the use of univariate logistic regression does not account for other factors associated with acute rejection (i.e., donor status, type of antibody induction) or leukopenia (i.e., concomitant medications with hematologic toxicities). In cut-pointfuture, multivariate analysis will be necessary to identify these potential effects.

5. Conclusion

In conclusion, the current study compared the results of logistic regression for dichotomized exposure metrics based on two dichotomization methods, the Youden index and the median. The trend of the results demonstrated general similarity in the inferred exposure–response associations when considering either the Youden index-based or median-based dichotomization methods. The similarity in the results between the Youden index and the median dichotomization methods in the current analysis ciould be the result of similarity in the statistical inferences from these two methods. However, given the descriptive nature of this report, further confirmation of the conclusions must come from future powered studies that include a larger number of patients. Such studies will help to confirm the universal applicability of the current analysis conclusions. Future directions will also include simulation studies that aim to compare the results of the dichotomization methods and therefore provide more insight into the superiority of either method, if it exists. Future work should also focus on exploring strategies that would allow dichotomizations based on combined pharmacologically active analytes, i.e., MPA + acyl-MPAG. This may enhance our understanding and clinical application of the exposure–response relationship.

Key Points.

Logistic exposure response analysis of mycophenolic acid (MPA) exposure data, dichotomized via Youden index and median, and its related acute rejection and leukopenia outcome was conducted.

The current analysis demonstrated general similarity in results when considering the Youden index and median dichotomization methods.

These results imply that either of two dichotomization methods can be used; however, further confirmation of the universal applicability of these results comes from future powered studies that include a larger number of subjects.