1 Introduction
VRC01 is a human IgG1 broadly neutralizing monoclonal antibody (mAb) directed against the CD4binding site of HIV1 ([1, 2, 3, 4, 5]). In 2016, the HIV Vaccine Trials Network and HIV Prevention Trials Network launched the VRC01 Antibody Mediated Prevention (AMP) study, the first efficacy study of a broadly neutralizing antiHIV antibody for prevention of HIV infection. The study is being conducted in two harmonized trials in two cohorts: 2700 HIVuninfected men and transgender persons in the Americas and Switzerland; and 1500 HIVuninfected sexually active women in subSaharan Africa ([6]). Within each cohort, AMP participants are randomized to receive 10 IV infusions of 10 mg/kg VRC01, 30 mg/kg VRC01, or placebo every 8 weeks through 72 weeks. Besides the evaluation of prevention efficacy of VRC01, an important secondary objective of AMP is to assess VRC01 mAb markers, e.g. serum mAb concentrations over time, as correlates of protection (CoP) against HIV1 infection. This knowledge is anticipated to help guide further development of mAbs and to provide benchmarks for HIV1 vaccine development.
In the AMP correlates study, a casecontrol sampling design is used. Markers are measured from primary endpoint HIV1 infected cases in the mAb groups and from a random sample of control participants from each mAb group who remain HIV1 negative until at least the Week 80 study visit ([6]). While complete pharmacokinetics (PK) information (e.g. concentration at any given time) is desirable especially in the study of timedependent correlates, it is infeasible to sample continuously or on an intensive time scale. Therefore, the full trajectory of VRC01 concentrations over time needs to be estimated based on the concentration data collected at selected timepoints for the correlates study. As specified in the AMP protocol, 4weekly blood samples were draw for possible marker measurements at up to 22 visits prior to Week 80 (i.e., 4 weeks and 8 weeks [trough] after each 8weekly infusion), and at the visit scheduled 5 days after the second infusion (Figure 1). Of note, in the real trials these sampling times are subject to variations as a result of imperfect study adherence due to possible missed visits, permanent infusion discontinuations and study dropout, and actual visit windows around each target visit date (Supplementary materials). Therefore, besides different marker sampling designs, we also consider different levels of study adherence and their impact on the outcomes in the simulations described herein.
In this paper, we focus on the modeling of VRC01 concentrations among hypothetical HIVuninfected control participants in AMP, defined as participants assigned to a VRC01 group who reach the Week 80 visit HIV1 negative. Because all AMP participants acquiring HIV1 infection during the study are sampled for measuring VRC01 concentrations at all available sampling timepoints, the relevant sampling question is how many control participants and what timepoints to sample in the AMP correlates study. Besides a range of sample sizes of control participants, we consider timepoint sampling according to: 1) the complete schedule of all 22 possible visits; and 2) coarsened schedules of only a subset of visits. In addition, because mAb serum concentrations often change nonlinearly over time with possible individualtoindividual variability, population PK (popPK) analysis based on nonlinear mixed effects models is used to estimate population and individual PK parameters, as well as to estimate individuallevel serum concentrations over time (with associated estimation uncertainties) that can be assessed as potential correlates.
The outline of this paper is as follows. In Section 2, we introduce the Master PK model that is used for the simulation of AMP participants’ serum concentration data; the simulation setup, including different marker sampling designs for the AMP control cohort; and the method for estimating PK model parameters based on the simulated datasets. In Section 3, we compare the performance of different complete and coarsened schedule marker sampling designs in terms of the accuracy and precision of the PK parameter estimates. We draw some conclusions and recommendations in Section 4.
2 Methods
2.1 Master PK model
A twocompartment model is deemed fitting to describe the PK of VRC01, since this mAb has limited distribution volume, slow clearance, and hence a long halflife (15 days). Nonlinear mixed effects models are used to describe individualtoindividual processes of drug absorption, distribution, and elimination and how these vary across individuals of different characteristics (e.g. weight, sex, or age). We use the popPK model that best describes the serum concentration data collected in a phase 1 study of VRC01 [7] as the prototype Master model for the simulation of concentration data from AMP participants. In the following, we briefly review the Master popPK model with two levels: the individuallevel PK (or structure) model, which describes the intraindividual patterns of serum concentration over time through the processes of drug absorption, distribution, and elimination; and the populationlevel (or variability) model, which describes the interindividual variability of the processes.
2.1.1 Individuallevel PK model
et denote the VRC01 serum concentration at the measurement for subject . In the Master individuallevel PK model, it is defined as
where denotes a twocompartment model with dose , denotes parameters of specific to individual , and the proportional error and additive constant error terms and satisfy, respectively, , and , . There are different ways of parameterizing a compartment model. For their direct physiology significance, CL: clearance rate (L/day), : volume of distribution in the central compartment (L), : volume of distribution in the peripheral compartment (L), and Q: intercompartmental clearance (L/day) are often a set of parameters used to describe PK processes underlying the observed concentration profiles for a given subject under a twocompartment model.
Specifically, after a single IV infusion, the serum drug concentration at time (relative to the end of infusion) can be expressed as the sum of two exponential processes – distribution and elimination (i.e. a twocompartment model):
where IV dose amount (mg); duration of infusion; and are rate constants (slopes) for the distribution phase and elimination phase, respectively ( by definition); and and are intercepts on the y axis for each exponential segment of the curve. Of note, when and [as is the case for IV bolus administrations and is approximately the case for IV VRC01, where the infusion time is brief (30 minutes) relative to the halflife], because . Let and represent the firstorder rate transfer constants (1/day) for the movement of drug between the central and peripheral compartments. Mathematically, and relate to the rate constants and as and , where is the rate of drug elimination. In addition, and . After multiple doses, serum drug concentration at time after doses given at time can then be expressed as written below, based on the superimposed assumption that the PK of the drug after a single dose are not altered after taking multiple doses:
2.1.2 Population PK model
Let where denotes a dimensional function,
denotes a vector of characteristics for subject
that contribute to explaining interindividual variability, denotes fixed effects, and denotes random effects. This equation characterizes how elements of vary across individuals due to systematic association with (modeled via ) and unexplained variation in the population represented by . The usual assumptions and are implied.In the Master populationlevel PK model, all four individuallevel PK parameters are modeled as lognormally distributed with exponential interindividual variability (IIV) random effects. Let
, , , and denote individuallevel estimated , , , and , respectively, for individual . Covariates include only , body weight of subject , which has an influence on and via an exponential model as follows:2.2 Simulation setup
2.2.1 Study adherence
Each participant’s infusion and postinfusion visit schedule is simulated according to the AMP protocol specification (Supplementary Materials). Briefly, participants receive 10 IV infusions of VRC01 (or placebo). Each infusion visit has a visit window of 7 to +48 days around the scheduled 8weekly infusion visit target date. Participants’ marker measurements occur at each infusion visit, 4 weeks (visit window: 7 to +7 days) after each infusion, and 5 days (2 to +2 days) after the second infusion. In the following simulations, for infusion visits, we assume that 80% of the attended visits occur uniformly during the target window of 7 to +7 days and 20% during the allowable window of +7 to +48 days. For postinfusion visits that occur between infusion visits, we assume all attended visits occur uniformly during the specified window.
Overall, we consider four study adherence patterns defined by the combinations of four missing data probabilities: probability of an independently missed single infusion (
), probability of an independently missed postinfusion visit (), cumulative probability of permanent infusion discontinuation (), and annual dropout rate (). The four study adherence patterns in terms of (, , ,) are: perfect adherence = (0%, 0%, 0%, 0%), high adherence = (5%, 10%, 10%, 10%), medium adherence = (10%, 15%, 15%, 15%), and low adherence = (15%, 20%, 20%, 20%). At 1 year after trial initiation, the adherence is very high in the ongoing AMP study with rates of (2%, 3%, 5%, 5%). Nevertheless, a wider range of adherence levels are considered in this paper for interpolation purposes and for investigating the robustness of popPK modeling against missing data, relevant if adherence declines in AMP or for future mAb studies.
2.2.2 PK model parameter values
Once participants’ infusion and postinfusion visits are simulated according to the study adherence patterns described above, the Master popPK model described in section 2.1 is used to simulate VRC01 serum concentration at attended study visits for participants of a given body weight in each VRC01 dose group (10 mg/Kg and 30 mg/Kg). The PK parameter values used for the simulation are listed in Table 1, where low covariances between random effects are fixed at zero to increase model stability.
2.2.3 Computation software
R version 3.3.1 [8] was used for the simulation of participants’ characteristics and study visit data. The NONMEM software system (Version 7.3, ICON Development Solutions) was used for the simulation and modeling of concentration data. Parallel computing on eight central processing units was employed to speed up computation time via NONMEM.
2.2.4 Marker sampling design
We consider two types of marker sampling designs: complete schedule and coarsened schedule (Figure 2). The former design includes concentration data at all timepoints of visit attendance from each participant, whereas the latter includes concentration data only at a subset of timepoints. Because a total of 61 VRC01 HIVinfected cases are expected at 60% prevention efficacy for both dose groups pooled over both AMP trials, for the complete schedule design, we consider sample sizes of m = 30, 60, 120, and 240 HIV1 uninfected controls. The latter three sample sizes correspond to the numbers of expected controls in the casecontrol cohort with a 1:1, 1:2, and 1:4 case:control ratio, respectively, whereas m = 30 serves as a reference and represents the 1:1 case:control ratio for a single AMP trial. For the coarsened schedule design, we consider only one sample size of m=240, but 3 coarsened schedules that sample roughly half of the complete schedule timepoints per participant.

First half: the first 11 timepoints (excluding time 0) out of the total 22 complete schedule timepoints are sampled. These timepoints include, for every individual the 4week and 8week postinfusion timepoints (trough) after the first 5 infusions, in addition to the 5day timepoint after the 2nd infusion.

Mixed half: timepoints after every other infusion are sampled. In addition to the 5day timepoint after the
infusion for every individual, 4week and 8week timepoints (trough) after the five odd number (
, , , , and ) infusions are included for one half of the subjects (, and 4week and 8week postinfusion timepoints after the five even number (, , , , and ) infusions are included for the other half of the subjects (). 
Trough only: trough timepoints are sampled. These include, for every individual the 8week timepoints (trough) after each of the 10 infusions, in addition to the 5day timepoint after the 2nd infusion.
Note that for all 3 coarsened schedules, the 5day timepoint after the infusion is always included because this timepoint is the only one scheduled within a few days of an infusion for the estimation of . These 3 coarsened schedules are compared to the complete schedule with , since the same number of 4week and 8week post infusion observations are made.
2.2.5 Simulation steps
For the complete schedule marker sampling design, we consider a total of 16 scenarios representing combinations of 4 study adherence patterns (perfect, high, medium, and low) and 4 sample sizes (m=30, 60, 120, and 240). For the coarsened schedule marker design, we consider a total of 12 scenarios representing the combinations of 4 study adherence patterns and 3 coarsened schedules (First half, Mixed half, and Trough only). The complete schedule datasets with m=240 are first simulated and the coarsened schedule datasets are extracted from them given the specific design. For each scenario, 1000 datasets are simulated containing participants’ demographic information (body weight and sex), study information (infusion and postinfusion visit time), and serum concentration at attended visits. Depending on the research interest, concentration values on consecutive days or flexible grid can also be simulated to evaluate the modeling/prediction of simulated concentration using sparse data. Specifically, each dataset is simulated following the steps described below:

Simulate participants’ characteristics representing the two AMP study cohorts and their corresponding VRC01 dose amounts in the low and high dose groups.

Simulate 1:1 male:female sex ratio.

Within each sex, participants are randomly assigned to the 10 mg/Kg and 30 mg/Kg dose groups at a 1:1 ratio. Each participant’s VRC01 dose amount is determined as the product of his/her body weight and dose level.


Simulate participants’ 8weekly infusion visits.

Simulate the attendance (yes or no) of each of the 10 infusion visits using a Bernoulli probability of .

If attendance is ‘yes’ for a given infusion visit, simulate the infusion visit time according to the AMP protocolspecified schedules and visit windows, assuming the probability of attending the visit within the target window (typically 7 to +7 days) is 80% and the probability of attending the visit outside the target window but within the study allowable window (typically 7 to +48 days) is 20%. The infusion time follows a piecewise uniform distribution within and outside the target window.


Simulate participants’ postinfusion visits: baseline, 4weekly, and 5day post2 infusion.

Simulate postinfusion visit attendance (yes or no) according to prior infusion attendance. If the prior infusion is administered, simulate the visit attendance using a Bernoulli probability of . If the prior infusion is missed, then the 5day post2 infusion visit (if applicable) and the following 4week postinfusion visits are all considered missed. If the last infusion (#10) is missed, then the 4week postinfusion visit is also missed. However, the 8week post infusion visit could still be scheduled.

If postinfusion attendance is ‘yes’, simulate postinfusion visit time accounting for prior infusion visit time, according to protocolspecified schedules/windows, similar to the procedure described in Step 2b.


Modify infusion attendance and postinfusion visits accounting for permanent infusion discontinuation.

Simulate time to permanent infusion discontinuation (due to reasons other than HIV infection) using a random exponent rate .

Modify infusion attendance and postinfusion visits for those who discontinue infusion permanently according to a different protocolspecified visit schedule/window (Supplementary Materials).


Modify infusion attendance and postinfusion visits accounting for dropout (study termination).

Simulate time to dropout using a random exponent rate .

Censor all previously simulated infusion and postinfusion visits at dropout time.


Simulate participants’ concentrations according to the Master PK model, with the covariate information, dose amount, infusion, and visit schedules as in the previous steps.

Simulate according to the final PK model by setting and .

Add the above value to a meanzero normally distributed and
, according to the variance estimates from the final PK model.

2.3 Estimation Method
Parameter estimation of the popPK model is based on minimizing the objective function value using maximum likelihood estimation. A marginal likelihood of the observed data is calculated based on both the influence of the fixed effect and the random effect. Different estimation methods for nonlinear mixed effects models have been extensively discussed by other authors (e.g. [13, 14]
). In this paper, due to the sparseness of the simulated data, the Markov chain Monte Carlo stochastic approximation expectationmaximization (SAEM) method
[15, 16] is applied to the modeling of the simulated timeconcentration data according to the Master PK model. The true values of each PK parameters as specified in Table 1 are used as initial values.3 Results
For each scenario of the complete schedule and coarsened schedule designs, we report

% datasets ‘converged’. Due to the Monte Carlo nature of the SAEM method, convergence testing is not formally done. Completed runs are counted as convergence successes.

For each fixed and random effect: 6 fixedeffect terms, 6 randomeffect terms, and 2 residual error terms, among the B converged models,

relative bias, RBias ,

relative root mean squared error, RRMSE , and

coverage probability, CP
proportion of datasets with 95% confidence intervals including the true value of the parameter
.


Shrinkage estimate for each randomeffect terms, i.e. one minus the ratio of the standard deviation of the individuallevel estimate and the estimated variability for the population estimate.
3.1 Master popPK model
As an illustration, Figure 2 displays two expected populationlevel timeconcentration curves for individuals who are perfectly adherent to the 8weekly infusion schedule, one for the 10 mg/Kg dose and one for the 30 mg/Kg dose, based on the master popPK model with , , and . The concentrations at each timepoint are simulated based on a body weight of 74.5 Kg and with the PK parameter values given in Table 1.
In addition, a random set of the simulated individuallevel concentration curves under low study adherence are displayed in Figure 3. For example, individual #2 in the low dose group (left panel) stayed in the study for follow up but discontinued infusions after the first infusion, whereas individuals #9 and #26 in the high dose group (right panel) dropped out of the study right after the first postinfusion visit.
3.2 Model fitting
3.2.1 Complete schedule marker sampling designs
Using the SAEM estimation method, almost all models using datasets under the complete schedule designs converged to obtain final PK parameter estimates for and , whereas a relative low convergence was observed for datasets with and (Figure 4). This result suggests that a minimal sample size of is recommended for a stable PK model fitting under the described schedule. This suggestion is further confirmed when the accuracy and precision of the fixedeffect estimates are examined (Figures 5 &6, Supplementary Materials: Table 1). Reasonable levels of bias and precision with significant improvements over the small sample sizes are observed for . On the other hand, provides relatively marginal improvements compared to except for , which characterizes the effect of each individual’s body weight on CL and requires data from a sufficient number of independent subjects for an accurate and precise estimation.
Due to the unstable estimation for , we restrict the evaluation of the estimation of random effects to larger sample sizes (Supplementary Materials: Figures S1 & S2). In general, regardless of the sample size, the random effect of the PK parameter Q (intercompartmental clearance rate) is poorly estimated with high shrinkage (Supplementary Materials: Figure S3). This poor estimation is due to the sparsity of data closer to infusion, with only one 5day post infusion timepoint, and the low interindividual variability in Q. On the other hand, the estimation of CL and seems reasonable, with shrinkage generally below 2030%. The proportional error term, is also reasonably estimated with RRMSE under all scenarios. The estimation of the additive error term, is relatively poorer possibly due to the sparsity of data around the assay limit of detection.
3.2.2 Coarsened schedule marker sampling designs
Figure 7 displays the distribution of the total number of observations (5 days after the infusion, 4 weeks and 8 weeks after each infusion) based on the 1000 simulated datasets under each of the 12 coarsened schedule scenarios with m=240, along with the complete schedule design with m=120. Because about half of the complete schedule timepoints are sampled in the coarsened schedules, the total expected number of 4week and 8week post infusion observations are the same across the 4 designs. This feature allows a fair comparison across the designs. Meanwhile, the number of 5day post second infusion observations is doubled in the coarsened schedule designs, because the 5day post infusion timepoint is the only timepoint proximal to an infusion. Hence, this timepoint is always sampled from every individual under both the complete and coarsened schedule designs. This consistency allows the assessment of the impact of 5day post infusion observations on the estimation of various PK parameters.
Results showing the accuracy and precision of the fixedeffect estimates under each coarsened schedule design with are displayed in Figures 8, 9 and Supplemental Materials (Table 2). The complete schedule design with is included as a reference for comparison purposes. In general, for the estimation of fixed effects, the complete schedule design with half of the sample size provides more accurate but less precise estimates, except that more accurate estimates are obtained for and under the ‘First half’ and ‘Mixed half’ coarsened schedule designs. This is likely due to the fact that having more 5day post infusion observations in the coarsened schedule designs helps improve the estimation of , which requires data proximal to infusion for an accurate estimation, and having more independent individuals helps improve the estimation of the covariate effect. On the other hand, the accuracy of estimates under the coarsened schedule designs are more impacted by study adherence due to the sparser timepoints compared to the complete schedule design. Among the 3 coarsened schedule designs, the ‘First half’ and ‘Mixed half’ designs have very similar performance and are generally superior to the ‘Trough only’ design, especially for the estimation of . Similar patterns are observed in the estimation of random effects (Supplemental Materials: Figures S4S6). Poor estimation of the random effect of intercompartment clearance (Q) and additive residual error are observed for all designs for reasons stated above.
4 Conclusions
PopPK analysis is known to be suitable for datasets consisting of a few data points per individual over the course of product administration(s) from many individuals, in order to estimate popPK parameters adjusting for variability among individuals. In this paper, we investigated how the accuracy and precision of the estimated population parameters (fixed effects) and variabilities among individuals (random effects) are influenced by the number of individuals and by the number and type (i.e. timepoint) of observations per individual.
In the context of the AMP study, where participants receive ten 8weekly IV infusions of VRC01, we considered complete schedule marker sampling designs where approximately 4weekly observations from up to 22 timepoints over the course of 80 weeks are included in the popPK modeling, with 4 different levels of study adherence (perfect, high, medium, and low) and 4 different sample sizes (m= 30, 60, 120, and 240). We found that a sample size of 120 or higher could render reasonably unbiased and consistent estimates of most fixed and random effect terms. The central volume parameter is the most challenging fixed effect parameter to estimate due to the lack of concentration data proximal to infusion as specified in the AMP protocol.
We also considered coarsened schedule marker sampling designs with , where the first half (‘First half’), alternate (‘Mixed half’), or ‘Trough only’ timepoints are included in the popPK modeling. These designs often provide less accurate but more precise estimates of various popPK parameters than the complete schedule design with . In terms of overall estimation performance as measured by RRMSE, the ‘First half’ and ‘Mixed half’ designs render similar performance, but are generally superior to the ‘Trough only’ design and the complete schedule design. We note that the ‘First half’ design is less subject to missing data, but provides limited data in the assessment of the steady state and the effect of a higher number of repeated doses. On the other hand, the ‘Mixed half’ design is more subject to missing data due to infusion discontinuation and study drop out as the study progresses. Based on these simulation results, we favor using the ‘Mixed half’ design for the AMP casecontrol study, given that it provides the best overall accuracy and precision for various PK parameter estimates in studies of high adherence like the current AMP study. In addition, the ‘Mixed half’ design allows the assessment of concentrations after any of the ten infusions (as opposed to only the first five infusions in the ‘First half’ design); these data may be helpful in the analysis and interpretation of other study endpoints including longterm safety and antidrug activity that may occur later in the study. If adherence declines in AMP, the advantages of the coarsened schedule designs will diminish and the full schedule design may be considered.
In summary, this paper provides a simulationbased framework to evaluate sampling designs of multipledose PK studies using a stochastic process for participants’ characteristics (e.g. sex and body weight) and infusion/measurement timepoints. It also provides a simulator for studying statistical methods for assessing prevention efficacy and correlates of prevention efficacy. This simulator not only accounts for participant characteristics that influence PK processes, but also accounts for possible missed or terminated product administrations, protocolspecific study visits and visit windows, and potential drop out. Thus, this framework provides a realistic simulator of PK data for future studies of repeatedlyadministered drugs.
Disclosure statement
No potential conflicts of interest were disclosed.
Funding
This work was supported by the National Institute of Allergy and Infectious Diseases (NIAID) US. Public Health Service Grant UM1 AI068635 [HVTN SDMC FHCRC]. The content of this manuscript is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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Supplemental materials
Parameter 
Sample size  Study adherence  RBias (%)  RRMSE  CP (%) 

30  Low  11.9  26.07  95.12  
Medium  7.91  24.27  97.54  
High  5.7  16.84  97.98  
Perfect  4.6  18.78  98.14  
60  Low  0.43  10.87  98.85  
Medium  0.56  9.7  99.29  
High  0.45  9.61  98.79  
Perfect  1.9  8.93  99.4  
120  Low  0.88  6.99  98  
Medium  0.11  6.37  99  
High  0.18  5.77  98.9  
Perfect  0.4  5.17  99.4  
240  Low  1.36  4.46  98  
Medium  0.69  4.07  98.6  
High  0.4  3.99  99.1  
Perfect  1.23  3.77  99.5  
30  Low  35.46  90.46  94.7  
Medium  17.68  76.53  95.47  
High  12.83  68.4  96.79  
Perfect  4.05  62.86  96.83  
60  Low  1.09  47.74  97.49  
Medium  6.91  42.71  97.35  
High  5.62  42.12  97.37  
Perfect  9.96  38.26  97.7  
120  Low  3.03  35.48  98.2  
Medium  1.39  31.61  99.1  
High  2.83  28.33  98.6  
Perfect  5.51  25.32  99.2  
240  Low  3.39  23.28  99.1  
Medium  1.14  20.82  99.4  
High  2.3  20.38  98.9  
Perfect  9.65  19.31  98.4  
30  Low  9.63  53.81  97.77  
Medium  7.13  50.32  98.96  
High  6.75  49.24  99.52  
Perfect  2.93  37.07  99.45  
60  Low  0.06  31.05  99.69  
Medium  1.15  28.55  99.69  
High  0.43  27.7  100  
Perfect  3.51  24.35  99.5  
120  Low  3.65  20.78  99.5  
Medium  2.76  20.01  99.5  
High  2.92  17.74  99.5  
Perfect  1.37  15.5  99.8  
240  Low  5.53  14.18  99.4  
Medium  4.13  13.58  99  
High  3.62  12.69  98.9  
Perfect  0.83  10.86  99.4  
30  Low  3.86  33.95  99.58  
Medium  2.19  34.38  99.35  
High  0.6  22.19  99.64  
Perfect  1.08  25.84  99.78  
60  Low  1.44  13.76  99.79  
Medium  1.57  11.94  99.49  
High  1.44  11.95  99.9  
Perfect  2.14  10.7  99.9  
120  Low  0.64  7.95  99.3  
Medium  0.43  7.27  99  
High  0.81  6.46  98.8  
Perfect  0.27  5.92  99  
240  Low  1.92  4.77  97.9  
Medium  1.64  4.49  98.2  
High  1.26  4.45  98.3  
Perfect  0.13  3.95  99  
30  Low  12.15  68.68  97.21  
Medium  17.1  67.58  96.89  
High  17.78  63.76  98.1  
Perfect  13.88  60.21  97.49  
60  Low  14.27  50.84  89.44  
Medium  17.63  50.81  86.85  
High  14.88  46.7  86.94  
Perfect  14.61  43.61  87.88  
120  Low  9.1  35.43  86.17  
Medium  7.43  32.67  87.2  
High  4.72  28.63  90.4  
Perfect  5.11  25.98  92.2  
240  Low  2.98  20.97  92.2  
Medium  3.4  21.33  90.4  
High  1.38  16.18  95.7  
Perfect  2.24  13.88  96.2  
30  Low  83.58  175.16  96.79  
Medium  99.46  405.73  97.67  
High  70.13  195.68  97.62  
Perfect  69.14  152.71  98.14  
60  Low  28.14  97.78  97.8  
Medium  22.03  89.87  98.27  
High  20.75  90.84  98.18  
Perfect  12.48  80.15  97.7  
120  Low  0.83  70.7  98  
Medium  0.23  66.91  97.3  
High  5.68  64.54  96.5  
Perfect  1.52  58.06  97.4  
240  Low  1.85  51.33  96.7  
Medium  0.5  50.1  96.7  
High  2.36  46.26  95.5  
Perfect  1.55  40.76  95.6  

Parameter  Sampling design  Study adherence  RBias (%)  RRMSE  CP (%) 

m=240 First half  Low  2.4  5.24  95.5  
Medium  1.83  4.78  96.9  
High  1.6  4.76  96.8  
Perfect  0.35  4.05  98.3  
m=240 Mixed half  Low  2.23  5.49  96.5  
Medium  1.8  5.13  96.3  
High  1.85  4.54  97.3  
Perfect  0.43  3.93  98.9  
m=240 Trough only  Low  4.25  6.74  92.4  
Medium  3.28  6.02  93.7  
High  2.75  5.34  95.2  
Perfect  1.8  4.56  97.2  
m=120 Full  Low  0.88  6.99  98  
Medium  0.11  6.37  99  
High  0.18  5.77  98.9  
Perfect  0.4  5.17  99.4  
m=240 First half  Low  11.34  29.68  98.6  
Medium  7.35  25.86  98.7  
High  6.4  25.73  98.2  
Perfect  0.72  20.42  98.8  
m=240 Mixed half  Low  11.51  31.2  98.6  
Medium  7.51  27.46  98.5  
High  7.21  24.45  99.1  
Perfect  0.71  19.47  98.9  
m=240 Trough only  Low  21.97  37.87  97.4  
Medium  16.57  33.08  97.8  
High  13.65  29.21  98.4  
Perfect  10.85  25.2  99  
m=120 Full  Low  3.03  35.48  98.2  
Medium  1.39  31.61  99.1  
High  2.83  28.33  98.6  
Perfect  5.51  25.32  99.2  
m=240 First half  Low  7.71  15.94  98.8  
Medium  6.69  15.05  98.5  
High  6.32  14.64  97  
Perfect  3.21  12.31  97.9  
m=240 Mixed half  Low  6.79  15.98  99.4  
Medium  6.47  15.99  98  
High  7.05  14.4  98.1  
Perfect  3.4  11.71  98.4  
m=240 Trough only  Low  1.04  13.55  98.3  
Medium  0.99  13.71  98.3  
High  3.52  13.98  99  
Perfect  4.12  13.12  98.6  
m=120 Full  Low  3.65  20.78  99.5  
Medium  2.76  20.01  99.5  
High  2.92  17.74  99.5  
Perfect  1.37  15.5  99.8  
m=240 First half  Low  1.66  4.75  97.5  
Medium  1.55  4.54  97.4  
High  1.17  4.56  97.7  
Perfect  0.68  4.03  98  
m=240 Mixed half  Low  1.1  4.86  98.4  
Medium  1.24  4.71  97.4  
High  1.47  4.3  97.8  
Perfect  0.78  4.13  98.2  
m=240 Trough only  Low  1.37  5.01  98  
Medium  1.21  4.69  97.9  
High  1.1  4.48  98.5  
Perfect  0.77  3.94  98.8  
m=120 Full  Low  0.64  7.95  99.3  
Medium  0.43  7.27  99  
High  0.81  6.46  98.8  
Perfect  0.27  5.92  99  
m=240 First half  Low  2.11  23.94  90.3  
Medium  1.6  22.91  89.7  
High  0.68  20.43  91.4  
Perfect  1.14  18.12  93  
m=240 Mixed half  Low  4.17  27  87.7  
Medium  2.49  24.61  89.6  
High  1.09  21.12  92.2  
Perfect  0.63  16.9  94.3  
m=240 Trough only  Low  3.73  33.35  85.6  
Medium  5.87  33.07  86  
High  3.31  30.86  88.3  
Perfect  2.91  25.49  89.8  
m=120 Full  Low  9.1  35.43  86.17  
Medium  7.43  32.67  87.2  
High  4.72  28.63  90.4  
Perfect  5.11  25.98  92.2  
m=240 First  Low  2  54.42  96.7  
Medium  1.1  54.68  96.2  
High  0.84  50.76  95.6  
Perfect  2.45  45.73  95.2  
m=240 Mixed half  Low  5.88  58.98  96.7  
Medium  2.13  55.02  95.8  
High  1.15  52.32  95.7  
Perfect  2.98  45.23  94.3  
m=240 Trough only  Low  2.14  68.17  94.8  
Medium  2.06  63.8  95.1  
High  2.49  64.63  94.4  
Perfect  1.45  56.91  96.3  
m=120 Full  Low  0.83  70.7  98  
Medium  0.23  66.91  97.3  
High  5.68  64.54  96.5  
Perfect  1.52  58.06  97.4 
Figure S1: Relative bias of each randomeffect PK parameter estimate under complete schedule designs with different sample sizes (m = 60, 120, and 240). , , and are the variances of the random effects for CL, Q, and , respectively. , , and are the covariances between the respective random effects. and are the proportional and additive error variances, respectively.
Figure S2: Relative root mean squared errors of each randomeffect PK parameter estimate under complete schedule designs with different sample sizes (m = 60, 120, and 240). , , and are the variances of the random effects for CL, Q, and , respectively. , , and are the covariances between the respective random effects. and are the proportional and additive error variances, respectively.
Figure S3: Shrinkage estimates under complete schedule design scenarios. , , and are the random effects for CL, Q, and , respectively.
Figure S4: Relative bias of each randomeffect PK parameter estimate under coarsened schedule designs with m = 240 compared to the complete schedule design with m = 120. , , and are the variances of the random effects for CL, Q, and , respectively. , , and are the covariances between the respective random effects. and are the proportional and additive error variances, respectively.
Figure S5: Relative root mean squared errors of each randomeffect PK parameter estimate under coarsened schedule designs with m = 240 compared to the complete schedule design with m = 120. , , and are the variances of the random effects for CL, Q, and , respectively. , , and are the covariances between the respective random effects. and are the proportional and additive error variances, respectively.
Figure S6: Shrinkage estimates under coarsened schedule designs with m = 240 compared to the complete schedule design with m = 120. The ‘First half’ design samples the first 11 timepoints (excluding time 0) out of the total 22 complete schedule timepoints. The ‘Mixed half’ design samples timepoints after every other infusion. The ‘Trough only’ design samples only trough timepoints. All 3 coarsened schedule designs always include the 5day post infusion timepoint. , , and are the random effects for CL, Q, and , respectively.
See pages 1 of Visit_Scheduling_and_Coding_and_Appendix