Sensitivity of Estimated Tacrolimus Population Pharmacokinetic Profile to Assumed Dose Timing and Absorption in Real World Data and Simulated Data

Abstract

A population pharmacokinetic (PK) study with 363 subjects was performed using real-world data extracted from electronic heath records (EHRs) to estimate the tacrolimus population PK profile. Data were extracted and built using our automated system, EHR2PKPD, suitable for quickly constructing large PK datasets from the EHR. Population PK studies for oral medications performed using EHR data often assume a regular dosing schedule as prescribed without incorporating exact dosing time. We assessed the sensitivity of the PK parameter estimates to assumptions about dose timing using last-dose times extracted by our own natural language processing system, medExtractR. We also investigated the sensitivity of estimates to absorption rate constants that are often fixed at a published value in tacrolimus population PK analyses. There was no appreciable difference in parameter estimates with assumed vs. extracted last-dose time, and our sensitivity analysis revealed little difference between parameters estimated across a range of assumed absorption rate constants. We conducted simulation studies to investigate how drug PK profiles and experimental designs such as concentration measurements design affect sensitivity to incorrect assumptions about dose timing and absorption rates. Our findings suggest that drugs with a slower elimination rate (or a longer half-life) are less sensitive to dose timing errors and that experimental designs which only allow for trough blood concentrations are usually insensitive to deviation in absorption rate.

Introduction

Tacrolimus is an immunosuppressive calcineurin inhibitor widely used after solid organ transplantation. Due to a narrow therapeutic window, inter-individual variability in pharmacokinetics (PK), and significant sequelae of both inefficacy and toxicity (transplant rejection[1] vs. nephrotoxicity, neurotoxicity, and/or diabetogenicity[2,3]), therapeutic drug monitoring (TDM) is clinically routine.[4] Predictors of individual clearance include liver function, time since transplantation,[5] age,[6,7] and genetic variation in the CYP3A5 gene.[8–12] A single variant in CYP3A5 (rs776746) is estimated to account for 39% of required dose variability.[13]

Tacrolimus TDM enables retrospective population PK studies using clinical data extracted from the electronic health record (EHR).[14–16] These studies often assume dosing time at a regular dosing schedule as prescribed (e.g., b.i.d., or once every twelve hours for immediate-release formulation). Differences in the actual dosing time from the assumed dosing time may influence PK parameter estimation. We recently developed a natural language processing (NLP) system, medExtractR,[17] to extract medication information including explicit last dosing times from free-text clinical notes, enabling incorporation of these data into PK models.[18,19] We further built our PK dataset using algorithms in the package EHR;[20] these tools will allow for easy scalability to larger studies as EHR data sources grow in size and complexity. This study therefore uses a mix of clinically validated and automatically processed data and serves as a step toward automated, scalable PK datasets from the EHR. To the best of our knowledge, no studies have investigated the sensitivity of tacrolimus PK parameter estimates to deviations from the assumed dosing time. Further, prior tacrolimus PK studies often assume a fixed value for the absorption rate constant, k_a, although the effect of this assumption has not been thoroughly investigated.

The goals of this study were fourfold: (1) to identify the important factors affecting tacrolimus PK profile through population PK analysis using real-world data processed from EHRs by our algorithms; (2) to investigate the effects of last dosing time on the tacrolimus PK parameter estimates using the data extracted from the EHRs; (3) to investigate sensitivity to assumption of k_a at a fixed value in a model on the other PK parameter estimates; and (4) to investigate the effects of last dosing time and assumption of fixed k_a on PK parameter estimates using simulation studies.

Methods

Study Design and Data Processing

This study was reviewed by the Vanderbilt Institutional Review Board and determined to be non-human subject research. Detailed description of data source and processing can be found in the Supplemental Materials. In short, our cohort is drawn from a previous study cohort of 446 patients and reduced to patients having at least 4 tacrolimus blood concentrations between 1 month and 3 years following kidney transplantation. Data were originally sourced from the Vanderbilt Synthetic Derivative, a deidentified EHR database, and BioVU[21], a deidentified biobank. Additionally, we used medExtractR[22] to extract last-dose times from the same EHR notes when the blood concentrations for our cohort were measured. This ultimately yielded 363 individuals with tacrolimus daily doses, blood concentration measurements, last-dosing times, demographics, and lab measurements.

We called this the entire cohort, and constructed one schedule of dosing using the extracted last-dose times and another schedule of dosing using twice daily assumed dose-time. These two dosing schedules then yielded two datasets we call the entire cohort with extracted last-dose times and the entire cohort with assumed last-dose times. These two datasets were further reduced by including only individuals with at least 4 extracted last-dose times to yield the reduced cohort with extracted last-dose times and the reduced cohort with assumed last-dose times which are comprised of data from 223 individuals.

Extraction of Last-Dose Times and PK Data Building

Times of last dose were extracted using medExtractR.[17] The extracted data were further processed as outlined in Figure S1 and the Supplemental Materials. In brief, extracted last-dose times appeared in various formats, for example using am or pm (e.g., “10 am”, “9:30 pm”), military time (e.g., 2200, 20:30), or using a modifying word or phrase (e.g., “8 last night”, “yesterday morning at 7”). All time expressions were initially converted into the same format of HH:MM:SS based on a 24 hour clock. For example, the phrase “8:30pm” would become “20:30:00”. Concentration measurements were generally assumed to be trough levels taken at a morning appointment. For this reason, PM last-dose times were assumed to have occurred on the previous day and AM times were assumed to have occurred on the same day as the laboratory value. After the extracted last-dose time data were processed, the final four PK datasets (with extracted or assumed last-dose time) were built with an algorithm modified from a function in an R package, EHR.[20] The PK data building process is described in the Supplemental Materials.

Population PK Analysis

We performed population PK analysis of tacrolimus using a nonlinear mixed-effects model implemented by NONMEM®[23] version VII with the first order conditional estimation method with interaction. A one-compartment PK model was chosen as the base model, assuming a combined additive and proportional residual error model and lognormal distribution for the random effects PK parameters. A model with random effects with unstructured covariance for all main PK parameters except for the absorption rate constant, k_a, was assumed. As k_a cannot be reliably estimated without drug concentrations measured during the major absorption phase, it was fixed at the previously published value of 4.5.[24]

We considered the dataset of the entire cohort with extracted last-dose time as the primary dataset used to develop a population PK model. Covariate model building was performed using individual specific PK parameters estimated from the base model. Both graphical and statistical methods were considered with the following candidate covariates, which were chosen a priori based on previous research and biological plausibility: weight, age, sex, hemoglobin, albumin, race, and CYP3A5*3 single nucleotide polymorphism (SNP) rs776746; of note, alleles without the CYP3A5*3 variant were assigned as CYP3A5*1. Model selection was performed based on the objective function values (−2 log likelihood). The difference in objective functions for models fit with and without a single covariate follows a χ² distribution with one degree of freedom under the assumption of no covariate effect. The χ² statistic of 3.84 with one degree of freedom corresponds to a p-value of 0.05. Thus, we considered an objective function value decrease of 3.84 to be significant model improvement. Variable selection was performed only in the primary analysis with the dataset of the entire cohort with extracted last-dose times; selected variables were then used to build the same model from the remaining three datasets. The model was qualitatively assessed through visual examination using goodness-of-fit plots such as the observed vs. predicted concentrations, the conditional weighted residuals, and the visual predictive check that was performed using an R package, vpc.[25]

Sensitivity Analysis

The k_a in our models was assumed to be 4.5 as previously reported.[24] In order to assess whether our findings are sensitive to this selected value, we refit the model using the entire cohort with extracted last-dose times at another published k_a value of 3.09.[11] In addition, we refit the model with the published k_a value for the extended-release formulation, 0.375.[26]

Simulation Study

A complete description of the simulation study is in the Supplemental Materials and Figure S2. Briefly, we established the population PK profiles described in Table 1, simulated individuals taking oral doses, and generated blood concentrations according to various designs. The simulation study consisted of two parts, each examining sensitivity of estimated population PK parameters to incorrect assumptions; the first part was an investigation into the effect of assumed vs. true last-dose times and the second part assessed the effect of incorrect assumption of the absorption rate constant k_a. In the first part of study, dose timings deviated randomly from a strict every-12-hour schedule and we investigated the effect on PK estimation of knowing exact dose-timing vs. using incorrectly assumed every-12-hour dosing. In the second part of the study, we investigated the effect of assuming k_a to be either too high or too low in comparison to the true k_a. For the simulated datasets, models were fit using the stochastic approximation expectation-maximization estimation method implemented in Monolix.[27] We reported bias in the estimates across 200 simulations and assessed how incorrect assumptions on dose-timing and absorption impact PK parameter estimation, and how that impact is modulated by PK profile [slow elimination (SEL) vs. fast elimination (FEL)] and observation designs [full observation (FO) with sampling every 2 hours vs. 3-hour plus trough observation (3T) with sampling at 3 and 11 hours after dosing vs. trough observation (TR) with a single observation 11 hours after dosing]. We also report how the biases differ in populations with low vs. high interindividual and residual variability (LV, HV).

Table 1.

PK Profiles for Simulation Study.

Category	Description		Vocabulary (Abbreviation)
Simulation Scenario
PK profile	Two PK profiles represent drugs with fast- vs. slow-elimination.		Fast-Elimination (FEL) Slow-Elimination (SEL)
	FEL Parameters ka (h−1): 1 CL (L/h): 0.2 V (L): 2 ke (h−1): 0.1 D (mg): 300	SEL Parameters ka (h−1): 3.09 CL (L/h): 22.7 V (L): 1090 ke (h−1): 0.02 D (mg): 5
Variability	Each PK profile takes on varying levels of between- and within-subject variability: two sets of parameters, low- vs. high-variability.		Low-Variability (LV) High-Variability (HV)
	LV Parameters ωCL (%CV): 5 ωV (%CV): 5 σprop (%CV): 5 σadd,FEL (ng/ml): 1 σadd,SEL (ng/ml): 0.1	HV Parameters ωCL (%CV): 30 ωV (%CV): 30 σprop (%CV): 30 σadd,FEL (ng/ml): 5 σadd,SEL (ng/ml): 0.5
Design of concentration measurements	Concentration measurements can occur at different times across the concentration-time profile. Simulated datasets follow one of three designs, which define when observations are taken following dosing: Full Observation: collect blood concentrations at 1, 3, 5, 7, 9, and 11 hours after dosing. 3 hour + trough: collect blood concentrations at 3 and 11 hours (trough) after dosing. Trough: collect blood concentrations 11 hours after dosing.		Full observation (FO) 3 hour + trough (3T) Trough (TR)
Evaluation
Dose timing	Simulated datasets were built with accurate true dosing vs. inaccurate assumed dosing.		True dosing (TD) Assumed dosing (AD)
ka assumption	The PK model was fit with fixed absorption rate, ka, at one of three values True ka: the same fixed ka used to simulate the population. Low ka: the true ka divided by 10. High ka: the true ka multiplied by 10.		True ka Low ka High ka

Nomenclature, descriptions, and true underlying parameters are defined to describe two PK profiles with slow- (SEL) and fast-elimination (FEL). A total of four profiles, two scenarios of variability (low, high) for each of SEL and FEL, are created by taking either the low or high values for ωs and σs. The k_e, CL, V, and k_a represent population PK parameters for elimination rate constant, clearance, volume of distribution, and absorption rate constant, respectively. The D is the twice-daily dose. The ω _CL and ω _V are the between-subject variance components for clearance and volume of distribution, presented as %CV. The σ_prop and σ_add represent the proportional and additive residual errors in the combined residual error model, presented as %CV and standard deviation, respectively.

Results

Population Characteristics for the Two Cohorts

The study population characteristics for the entire cohort and the reduced cohort are displayed in Table 2. The total number of concentrations for the entire cohort (N=363) and the reduced cohort (N=223) were 3258 and 2116, respectively. Each subject had a maximum of 10 tacrolimus blood concentration measurements. These observations constituted either the first 10 concentrations or every concentration if there are fewer than 10 measurements for each subject beyond the 1 month post-transplant period. Of these concentration measurements, 52% were accompanied by an extracted last-dose time for the entire cohort. The median tacrolimus dose across all subjects was 3 mg twice daily, and the median blood concentration was 7.1 ng/mL. For the reduced cohort, the percentage of concentration measurements associated with a last-dose time was increased to 73% as designed, while median tacrolimus dose and median blood concentration remained almost the same.

Table 2.

Demographic and Clinical Characteristics.

	Entire Cohort (N=363)	Reduced Cohort (N=223)
Age (Year)	45.9 (12.7) 47.0 [37.0, 55.0]	47.2 (12.0) 48.0 [38.0, 55.0]
Sex = Female	134 (0.37)	76 (0.34)
Race
Caucasian American	266 (0.73)	164 (0.74)
African American	83 (0.23)	50 (0.22)
Hispanic	4 (0.01)	3 (0.01)
Asian	5 (0.01)	3 (0.01)
Other	3 (0.01)	3 (0.01)
Undisclosed	2 (0.01)	0 (0.00)
Weight (kg)	82.9 (20.8) 81.2 [66.7, 95.3]	83.0 (20.7) 80.0 [66.4, 94.9]
Hemoglobin (g/dL)	12.5 (2.1) 12.5 [11.1, 14.0]	12.6 (2.0) 12.5 [11.1, 14.0]
Albumin (g/dL)	4.1 (0.4) 4.1 [3.9, 4.4]	4.1 (0.4) 4.1 [3.8, 4.4]
Proportion of concentrations with extracted last-dose time	0.52	0.73
Twice-daily tacrolimus dose (mg)	3.4 (1.8) 3 [2, 4]	3.1 (1.7) 3 [2, 4]
Tacrolimus blood concentration (ng/mL)	7.6 (3.1) 7.1 [5.5, 9.0]	7.5 (3.0) 7.1 [5.5, 8.9]
Number of concentration levels per subject	9.0 (1.8) 9.0 [10.0, 10.0]	9.5 (1.2) 10.0 [10.0, 10.0]
Total number of concentrations	3258	2116
Total days of follow-up	588 (295) 557 [361, 854]	525 (268) 482 [324, 686]

Population characteristics of the entire cohort (left) and the reduced cohort (right). Values are presented as count (proportion) for categorical variables and mean (SD) median [interquartile range] for continuous variables.

Primary Population PK Analysis

Table 3 presents base model population PK parameter estimates. PK parameters such as clearance (CL, L/hr) and apparent volume of distribution (V, L) were first estimated from the base model without covariates. Note that we denote CL/F by CL and V/F by V for simplicity, where F represents relative bioavailability and is omitted elsewhere. The PK parameters varied substantially among subjects; the between-subject variation in coefficient of variation (CV) for CL and V in the base model are 52.8% and 65.5%, respectively.

Table 3.

Estimated PK Parameters.

Base Model		Covariate Models
Entire Cohort (N=363)			Entire Cohort (N=363)		Reduced Cohort (N=223)
Extracted Last-Dose Time			Extracted Last-Dose Time	Assumed Last-Dose Time	Extracted Last-Dose Time	Assumed Last-Dose Time
Objective Function	10368	Objective Function	10169	10209	6441	6486
Parameter	Estimate (SE) [95% CI]	Parameter	Estimate (SE) [95% CI]
		CLij=θ1 × SNPθ2 × (ageij/47) θ3 × (albij/4.1) θ4 × (hgbij/12.5) θ5
CL	32.5 (0.93) [30.7, 34.4]	θ1	26.2 (0.7) [24.8, 27.6]	26.5 (0.7) [25.1, 27.9]	24.7 (0.8) [23.1, 26.2]	25.0 (0.8) [23.4, 26.6]
		θ2	0.71 (0.05) [0.61, 0.81]	0.72 (0.05) [0.62, 0.82]	0.75 (0.07) [0.61, 0.89]	0.76 (0.07) [0.62, 0.90]
		θ3	−0.26 (0.08) [−0.42, −0.1]	−0.26 (0.07) [−0.40, −0.12]	−0.25 (0.10) [−0.45, −0.05]	−0.25 (0.10) [−0.45, −0.05]
		θ4	0.35 (0.12) [0.11, 0.59]	0.38 (0.12) [0.14, 0.62]	0.31 (0.14) [0.04, 0.58]	0.34 (0.15) [0.05, 0.63]
		θ5	−0.29 (0.09) [−0.47, −0.11]	−0.30 (0.09) [−0.48, −0.12]	−0.26 (0.11) [−0.48, −0.04]	−0.26 (0.10) [−0.46, −0.06]
		Vi= θ6
V	4463 (524) [3436, 5490]	θ6	3726 (844) [2072, 5379]	4140 (407) [3341, 4938]	3329 (510) [2329, 4329]	3725 (359) [3020, 4429]
ωCL (%CV)	52.8 (2.1) [48.6, 56.9]	ωCL (%CV)	40.8 (1.9) [37.1, 44.5]	41.3 (1.6) [38.1, 44.4]	40.1 (2.0) [36.1, 44.1]	40.6 (2.0) [36.8, 44.5]
ωV (%CV)	65.5 (6.1) [53.7, 77.4]	ωV (%CV)	65.3 (22.2) [21.7, 108.9]	59.2 (6.8) [45.8, 72.5]	74.4 (6.4) [60.8, 86.0]	69.9 (5.8) [58.6, 81.3]
σprop (%CV)	32.2 (1.6) [29.0, 35.4]	σprop (%CV)	31.8 (1.2) [29.4, 34.2]	32.1 (1.3) [29.6, 34.5]	31.2 (1.6) [28.0, 34.4]	31.6 (1.6) [28.4, 34.8]
σadd (ng/ml)	0.36 (0.79) [0.00, 1.91]	σadd (ng/ml)	0.52 (0.38) [0, 1.26]	0.56 (0.35) [0, 1.25]	0.38 (0.65) [0, 1.65]	0.39 (0.64) [0, 1.64]

Pharmacokinetic (PK) parameter estimates for both the entire and reduced datasets either with extracted or assumed last-dose times. Estimates are presented as mean (standard error) [Wald 95% confidence interval]. SNP is coded continuously as 1, 2, 3 for 0, 1, and 2 mutations, respectively. The age_ij, alb_ij, and hgb_ij represent covariate values for subject i at time j. CL and V are population PK parameters for clearance and volume of distribution in the base model. The ω _CL and ω _V are the between-subject variance components for clearance and volume of distribution, respectively, presented as %CV. The σ_prop and σ_add represent the proportional and additive residual errors in the combined residual error model, presented as %CV and the standard deviation, respectively. The θs denote model parameters as typically used in statistical models.

Inclusion of CYP3A5 decreased the objective function by 144 from 10368 for the base model; hence the SNP was always included in the following covariate model selection considering strong evidence for its causal effect on clearance in the literature as well as our own results. Inclusion of age, albumin level, and hemoglobin level all improved the model fit from the SNP only model – decreasing the objective function value by 18, 10, and 20, respectively. The final covariate model with these 3 additional covariates improved the model fit by 55 from the SNP only model. Other covariates did not yield significant improvement in the model fit. The final covariate model is presented as follows:

$$C{L}_{ij}={\theta }_1\times {(SN{P}_i)}^{{\theta }_2}\times {\left(ag{e}_{ij}/47\right)}^{{\theta }_3}\times {\left(al{b}_{ij}/4.1\right)}^{{\theta }_4}\times {\left(hg{b}_{ij}/12.5\right)}^{{\theta }_5}\times \text{exp}[{\eta }_{\text{i}}{}^{\text{CL}}],$$

and

$$V_{ij}={\theta }_6\times \text{exp}[{\eta }_{\text{i}}{}^{\text{V}}],$$

where CL_ij and V_ij are the subject-specific CL and V for subject i at time j. The age_ij is subject age in years, alb_ij is blood albumin level in g/dL, and hgb_ij is blood hemoglobin level in g/dL for subject i at time j, each of which is standardized by dividing by its population median. SNP is continuously coded as 1, 2, 3 corresponding to 1 plus the number of CYP3A5*1 alleles. The η_i^CL and η_i^V are random effects explaining between-subject variability for CL and V, which follow a bivariate normal distribution with mean zeros and covariance matrix with ω ²_CL and ω ²_V in its diagonal. The θs in the equations denote model parameters as typically used in statistical models.

The estimates of typical values of CL and V were 26.2 L/hr and 3726 L for a 47-year-old with CYP3A5*3/*3, albumin 4.1 g/dL, and hemoglobin 12.5 g/dL. Subjects with *1/*3 and *1/*1 increased clearance 1.6 (i.e., 2^0.71 =1.6) and 2.2 (i.e., 3^0.71 =2.2) times compared to clearance for those with *3/*3, respectively. The between-subject variation in %CV for CL and V were 40.8% and 65.3%, respectively. Especially, the variability for CL was substantially reduced from the base model estimate of 52.8% as the inclusion of covariates explains a part of variability in clearance.

Model diagnostics plots are shown in Figure S3 in the Supplemental Materials. Overall, the goodness-of-fit plots present reasonable model fit although slight deviation from normality is apparent in the observed vs. predicted concentration plots. The weighted residuals show some deviation from normality, but most residuals fall within the range of −2 to 2. The visual predictive check also supports reasonable model fit in that the simulation-based model-predicted 95% confidence intervals (CIs) well cover the corresponding observed values across the follow-up time.

Last-Dose Time Inclusion

Table 3 also presents parameter estimates in both the entire and reduced cohorts with extracted and assumed last-dose times. While there is considerable difference in the estimates derived from different cohorts, there were little differences in parameter estimates based on extracted vs. assumed dose times. Figure 1 shows the difference in extracted last-dose times and assumed last-dose times generated by a regular dosing assumption as prescribed. The median difference was −3 hours, suggesting actual doses were typically taken earlier than assumed.

Figure 1. Differences in Extracted- and Assumed-Dose Time.

Histogram depicting the distribution of the difference between extracted dose times and assumed dose times observed in the entire cohort. Negative values represent instances where the extracted dose time precedes the assumed dose time. Extracted dose times, which are likely close to actual dose times, tend to be earlier than assumed dose times; the median difference is 3 hours early. Extracted dose times which occur more than 12 hours before assumed dose times could potentially be due to a missed dose, accurately captured in the electronic health record.

Sensitivity Analysis of k_a in Tacrolimus Population PK Model

Table 4 shows parameter estimates from the entire cohort with extracted last-dose times when k_a is either assumed to be 4.5, 3.09, or 0.375. The estimates (± SE) of typical values for CL at median covariate values and no CYP3A5*1 allele were 26.2 ± 0.7, 26.2 ± 0.7, and 26.6 ± 0.7, and those for V were 3726 ± 844, 3730 ± 788, and 3633 ± 628 for k_a assumed to be 4.5, 3.09, and 0.375, respectively. None of the estimates for k_a = 3.09 and k_a = 0.375 models fall outside of the 95% Wald CIs for the corresponding parameters of the k_a = 4.5 model.

Table 4.

Sensitivity Analysis.

	ka = 4.5	ka = 3.09	ka = 0.375
Objective Function	10169	10169	10170
Parameter	Estimate (SE) [95% CI]
CLij=θ1 × SNPθ2 × (ageij/47) θ3 × (albij/4.1) θ4 × (hgbij/12.5) θ5
θ1	26.2 (0.7) [24.8, 27.6]	26.2 (0.7) [24.8, 27.6]	26.6 (0.7) [25.2, 28.1]
θ2	0.71 (0.05) [0.61, 0.81]	0.71 (0.05) [0.61, 0.81]	0.73 (0.05) [0.63, 0.83]
θ3	−0.26 (0.08) [−0.42, −0.1]	−0.26 (0.08) [−0.42, −0.10]	−0.26 (0.07) [−0.40, −0.12]
θ4	0.35 (0.12) [0.11, 0.59]	0.35 (0.12) [0.11, 0.59]	0.36 (0.12) [0.12, 0.60]
θ5	−0.29 (0.09) [−0.47, −0.11]	−0.29 (0.09) [−0.47, −0.11]	−0.30 (0.09) [−0.48, −0.12]
Vi= θ6
θ6	3726 (844) [2072, 5379]	3730 (788) [2185, 5275]	3633 (628) [2401, 4864]
ωCL (%CV)	40.8 (1.9) [37.1, 44.5]	40.8 (1.8) [37.2, 44.4]	41.2 (1.6) [38.0, 44.4]
ωV (%CV)	65.3 (22.2) [21.7, 108.9]	65.4 (21.4) [23.6, 107.3]	65.0 (6.4) [52.5, 77.5]
σprop (%CV)	31.8 (1.2) [29.4, 34.2]	31.8 (1.2) [29.4, 34.2]	31.8 (1.2) [29.4, 34.2]
σadd (ng/ml)	0.52 (0.38) [0, 1.26]	0.52 (0.38) [0, 1.26]	0.52 (0.37) [0, 1.25]

Pharmacokinetic (PK) parameter estimates for models assuming k_a to be 4.5, 3.09, 0.375 (left to right). Estimates are presented as mean (standard error) [Wald 95% confidence interval]. SNP is coded continuously as 1, 2, 3 for 0, 1, and 2 mutations, respectively. The age_ij, alb_ij, and hgb_ij represent covariates values for subject i at time j. CL and V are population PK parameters for clearance and volume of distribution in the base model. The ω _CL and ω _V are the between-subject variance components for clearance and volume of distribution, respectively, presented as %CV. The σ_prop and σ_add represent the proportional and additive residual errors in the combined residual error model, presented as %CV and the standard deviation, respectively. The θs denote model parameters as typically used in statistical models.

Simulation Study

Figure 2 and Figure 3 show results of the simulation study investigating the impact of misspecified last-dose times and incorrect specification of absorption rate constant k_a, respectively. We summarize our findings related to estimation of CL and V. We restrict our analysis to biases in the TR and FO designs as the 3T estimates typically lie somewhere between these two, as expected.

Figure 2: Simulation Results from 200 repetitions of a total of 12 scenarios: two PK profiles (FEL, SEL), three observation designs (FO, 3T, TR), and two last-dose times (AD, TD).

Boxplots summarize estimate bias across simulations. The V and CL represent population PK parameters for volume of distribution and clearance, respectively. True underlying parameters are shown in Table 1. Complete results are tabulated in Table S1 in the Supplemental Materials.

Figure 3: Simulation Results from 200 repetitions of a total of 18 scenarios: two PK profiles (FEL, SEL), three observation designs (FO, 3T, TR), and three assumed values for k_a (True k_a, k_a × 10, k_a / 10).

Boxplots summarize estimate bias across simulations. The V and CL represent population PK parameters for volume of distribution and clearance, respectively. True underlying parameters are shown in Table 1. Complete results are tabulated in Table S2 in the Supplemental Materials.

Impact of misspecified last-dose times:

The magnitude and direction of bias due to misspecified last-dose times were impacted by PK profile and observation design, which was especially exacerbated in FEL profile. For example, in the FO design, minimal bias was observed for the SEL profile, but CL was overestimated in the FEL profile. In the TR design, the SEL profile yielded underestimates for V but little bias in CL, while the FEL profile demonstrated overestimation in both parameters.

Impact of incorrect specification of k_a:

Incorrect specification of k_a was more impactful in the FEL profile than in the SEL profile and varied in magnitude and direction based on the observation design being used. In the FO design, CL was unbiased in both profiles while V was biased. The magnitude of this bias was much greater when k_a was assumed to be low than when k_a was assumed to be high and was greater in the FEL profile than in the SEL profile. In the TR design, CL was minimally affected when k_awas assumed to be high and greatly affected when k_awas assumed to be low in the FEL, but not SEL, profile.

Regarding low- vs. high-variability populations, we observed that the direction of bias in estimation of PK profiles in the LV and HV populations were the same, but generally more extreme in the HV population, and thus restrict our observations to the HV population. Notably, the FEL profile tended to be more affected by high interindividual and residual variability. The complete results including scenarios with low variability and residual/interindividual error parameters are tabulated as Table S1 and Table S2 in the Supplemental Materials.

Discussion

Our tacrolimus population PK study using automatically processed real-world EHR data reproduced the well-established impact of CYP3A5*3 on tacrolimus clearance. This finding suggests that our algorithms are suitable for building datasets to study tacrolimus disposition using EHR data. Although the typical value of CL is not completely comparable due to different covariate models used across studies, our study estimated CL of 26.2 [24.8–27.6] for a 47-year-old with no *1 allele in CYP3A5, albumin 4.1 g/dL, and hemoglobin 12.5 g/dL, while the other studies reported 15.9 [13.2–18.6][10] and 26.6 [18–35.2].[11] Any difference may be due to the difference in the study populations. Our cohort included data from 1 month to 3 years after transplant (median 482 days), while the median (range) post-transplantation days for prior studies were 14 (1–175) and 9 (0–95). In addition, Li et al.[10] studied liver transplant subjects, which would have additional impact on clearance as poor liver function would reduce tacrolimus clearance.[28,29]

The differential frequency distribution of CYP3A5 genotypes between populations of African ancestry (AA) and Northern European ancestry (NE) is well established and is apparent in our study population (Figure S4 in the Supplemental Materials). It is well known that presence of CYP3A5*1 increases tacrolimus clearance. We observed greater CYP3A5*1 genotype prevalence in the AA population compared to the NE population. Thus, clearance for AA subjects is much higher than for NE subjects if CYP3A5*1 genotype is not accounted for. However, once genotype is accounted for, PK parameters in NE and AA subjects are comparable, and inclusion of race as a covariate did not sufficiently improve model fit. AA patients are known to require higher doses of tacrolimus, but it is unknown to what extent this is due to greater prevalence of CYP3A5*1 rather than differences in bioavailability or absorption rates.[30]

The inclusion of extracted vs. assumed last-dosing time did not meaningfully alter the estimation of PK parameters or covariate effects in the analysis performed using datasets with either the entire cohort or the reduced cohort which oversampled subjects for which more last-dosing time information was available. The lack of a difference may be because the assumed timing of the last doses are close enough to the actual times, particularly for the organ transplant patient population given the serious consequence of noncompliance. Also, since tacrolimus has a long half-life, trough concentrations approximate the average steady-state concentration,[31] making PK modeling less sensitive to deviation of actual dosing time. V is, however, consistently estimated to be larger in the assumed last-dose time datasets; perhaps this can be attributed to the increased uncertainty due to incorrect last-dose times.

Our findings support the general modeling approach used in several tacrolimus population PK studies,[10,11] where k_a was fixed at a published value as our estimates for clearance and covariate effects were not sensitive to our selection for k_a. The choice of k_a in a range of a 12-fold difference (from 0.375 to 4.5) had little impact on parameter estimates. This is likely due to the use of trough concentrations, which are taken well after the absorption phase is dominant and are therefore less impacted by the absorption process. Given the twice-daily dosing schedule and clinical goals of tacrolimus blood concentration maintenance via TDM, any reasonable selection for k_a is not likely to impact tacrolimus PK modeling.

The simulation study gives some insight into the findings of our study. The effect of incorrectly assumed dose times is more impactful on PK parameter estimation in the FEL scenarios, especially when the experimental design only includes trough concentrations. With the TR design in the SEL profile (which is closest to our study design), we found bias of only about 10% when estimating V, but CL was always well estimated. This suggests that, even when trough concentrations alone are collected, the population PK analysis for drugs with slower elimination or clearance may provide a reasonable estimate for clearance even when exact dose timing is not known. This finding should give confidence to clinical dosing decisions based on these estimates as clearance is the most relevant parameter to determine proper dosage. On the other hand, estimates from the FEL scenarios are more sensitive to the dose time errors, which is further affected by greater interindividual and residual variability. Thus, analysis of drugs with faster elimination than tacrolimus warrants some caution as they could be more sensitive to dose-time errors. Additionally, the simulated random deviation between assumed and true dose times was centered at −4 hours – this was reflective of our dataset (Figure 1) but could be considerably larger based on the drug and population of interest. At the extreme, this manifests as non-adherence which may or may not be represented in the EHR. Researchers interested in utilizing EHR TDM data should consider these factors.

Sensitivity to k_a was also greater in FEL than in SEL. The effect was more extreme under high interindividual and residual variability. We again attribute this to the faster elimination. In particular, the ratio of absorption to elimination rates, k_a/k_e, appears to determine the magnitude of bias. In the FEL scenarios, k_a is one order of magnitude greater than k_e so that when we assume k_a to be one tenth its true value, we assume them to be equal. In our simulation, however, k_e never exceeded about one third of k_a so this assumption of equality was always far from true and, importantly, there was no flip-flop effect or identifiability issue. In the SEL profile where true k_a is two orders of magnitude greater than k_e, k_a/10 is still much larger than k_e and hence the effect of k_a misspecification is less profound, particularly for the TR design. If k_a is sufficiently large relative to k_e, estimation results are not sensitive to incorrect assumptions about k_a. Sampling design also impacts the magnitude of bias due to the incorrect k_a assumptions, as earlier observations can reduce or increase sensitivity to incorrect assumptions. Fortunately, there is little need to fix k_a at a certain value (or assume k_a incorrectly) in PK modeling when such data is available. In general, the scenarios of SEL were less sensitive to incorrect k_a assumptions than those of FEL where estimates of CL could be biased up to 31%. The only significant bias in SEL was the estimation of V when k_a was assumed to be lower than the true k_a. Bias in CL never exceeded 5.3% in SEL even when estimates of V were substantially biased. Again, all these results suggest that tacrolimus PK modeling may be less sensitive to incorrect assumptions about k_a than would be the case in a drug with faster elimination.

Saint Marcoux et al.[32] used simulation to investigate the impact of missing or delayed tacrolimus doses on peak, trough, and the area under the concentration curve. Among other investigations, the authors demonstrate how delays in dosing result in reductions of observed trough concentrations. Though we are concerned with errors in the data as opposed to issues of adherence, these simulations illustrate how dose timing errors would impact PK profile estimation.

Our study has some limitations. First, the last-dose time information was not available for all drug concentration measurements. However, based on the results from the reduced cohort that included the last-dose time information for 73% of drug levels, it does not appear that including last-dose times in PK modeling will result in meaningful changes if medications share a similar PK profile with tacrolimus, such as a long half-life. Second, we did not study medications with different PK profiles compared to tacrolimus to investigate the effects of last-dose time and fixed k_a on estimation. However, based on the simulation study we performed, medications with a faster elimination rate (or a shorter half-life) would be more sensitive to dose time errors and incorrect assumptions about k_a. Our simulation also revealed issues with establishing PK profiles solely from trough concentrations; some PK parameters could be estimated with bias under this design. However, CL was relatively well estimated compared to other PK parameters. This reassures the common practice in TDM where trough concentrations have been commonly used as they are considered to give a good representation for drug clearance based on pharmacokinetic theory. To the best of our knowledge, the relationship between observation density across the concentration-time profile and PK parameter estimability has not yet been comprehensively studied. We hope that our simulations would help to facilitate development of such work that would guide post-marketing population PK studies. For now, complete PK profiles estimated from trough concentrations at steady state, common in EHR derived TDM data, can be treated with some skepticism.

Although medExtractR was used in the extraction of certain data and the package EHR was used to build the datasets, some of the information, such as tacrolimus dosing data, was manually validated. We want to continue to move away from costly clinical validation and demonstrate that findings are reproducible with entirely automated EHR data extraction. For this reason, our future work will aim to replicate these results using our complete medication information extraction system and PK data building pipeline, and compare it to the results obtained through clinically validated data. Replication of PK parameters and covariate effects would indicate that our system is viable to replace costly manual information extraction to build PK data.

What is already known about this subject?

Use of electronic health records (EHRs) such as therapeutic drug monitoring data to perform population pharmacokinetic (PK) studies often requires some assumptions. The impact of violating these assumptions on PK parameter estimation have not been assessed.

What does this study add?

While the tacrolimus PK profile estimated using EHR extracted data was insensitive to assumptions about dose timing and absorption rate constants, our simulation study found that sensitivity varies according to observation times and pharmacokinetic profile; drugs with faster elimination rates are generally more sensitive.

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to institutional policy.