Operating characteristics of stepwise covariate selection in pharmacometric modeling

Covariate Model Selection Approaches for Population Pharmacokinetics: A Systematic Review of Existing Methods, From SCM to AI

A growing number of covariate modeling methods have been proposed in the field of popPK modeling, but limited information exists on how they all compare. The objective of this study was to perform a systematic review of all popPK covariate modeling methods, focusing on assessing the existing knowledge on their performances. For each method of each article included in this review, evaluation setting, performance metrics along with their associated values, and relative computational times were reported when available. Evaluation settings report was done for uncertainty assessment of communicated results. Results showed that EBEs-based ML methods stood out as the best covariate selection methods. AALASSO, a hybrid genetic algorithm, FREM with a clinical significance criterion and SCM+ with stagewise filtering were the best covariate model selection techniques-AALASSO being the very best one. Results also showed a lack of consensus on how to benchmark simulated datasets of different scenarios when evaluating method performances, but also on which metrics to use for method evaluation. We propose to systematically report TPR (sensitivity), FPR (Type I error), FNR (Type II error), TNR (specificity), covariate parameter error bias (MPE) and precision (RMSE), clinical relevance, and model fitness by means of BIC, concentration prediction error bias (MPE), and precision (RMSE) of new proposed methods and compare them with SCM. We propose to systematically combine covariate selection techniques to SCM or FFEM to allow for comparison with SCM. We also highlight the need for an open-source benchmark of simulated datasets on a representative set of scenarios.

Population pharmacokinetics and dosing optimization of imipenem in Chinese elderly patients

Objectives

To assess the pharmacokinetics and pharmacodynamics of imipenem in a retrospective cohort of hospitalized Chinese older patients.

Methods

A population pharmacokinetic (PPK) model was constructed utilizing a nonlinear mixed-effects modeling approach. The final model underwent evaluation through bootstrap resampling and visual predictive checks. Additionally, a population pharmacokinetic and pharmacodynamic analysis was conducted employing Monte Carlo simulations to investigate the impact of commonly used dosing regimens (0.25 g every 6 h, 0.5 g every 6 h, 0.5 g every 8 h, 1 g every 6 h, 1 g every 8 h, and 1 g every 12 h) on the likelihood of achieving the target therapeutic outcomes.

Results

A total of 370 observations available from 142 patients were incorporated in the PPK model. A two-compartment PPK model with linear elimination best predicted the imipenem plasma concentrations, with the creatinine clearance as a significant covariate of clearance. Typical estimates for clearance, inter-compartmental clearance, central and peripheral volume were 13.1 L·h-1, 11.9 L·h-1, 11.7 L, 29.3 L, respectively.

Conclusion

The pharmacokinetics of imipenem in elderly patients were effectively characterized by the established PPK model, which includes creatinine clearance as a key covariate. This research will enhance our understanding of imipenem elimination and support precision dosing in this patient demographic.

Impact of covariate model building methods on their clinical relevance evaluation in population pharmacokinetic analyses: comparison of the full model, stepwise covariate model (SCM) and SCM+ approaches

Covariate analysis in population pharmacokinetics is key for adjusting doses for patients. The main objective of this work was to compare the adequacy of various modeling approaches on covariate clinical relevance decision-making. The full model, stepwise covariate model (SCM) and SCM+ PsN algorithms were compared in a clinical trial simulation of a 383-patient population pharmacokinetic study mixing rich and sparse designs. A one-compartment model with first-order absorption was used. A base model including a body weight effect on CL/F and V/F and a covariate model including 4 additional covariates-parameters relationships were simulated. As for forest plots, ratios between covariates at a specific value and that of a typical individual were calculated with their 90% confidence interval (CI90) using standard errors. Covariates on CL, V and KA were considered relevant if their CI90 fell completely outside the reference area [0.8-1.2]. All approaches provided unbiased covariate ratio estimates. For covariates with a simulated effect, the 3 approaches correctly identify their clinical relevance. However, significant covariates were missed in up to 15% of cases with SCM/SCM+. For covariate with no simulated effects, the full model mainly identified them as non-relevant or with insufficient information while SCM/SCM+ mainly did not select them. SCM/SCM+ assume that non-selected covariates are non-relevant when it could be due to insufficient information, whereas the full model does not make this assumption and is faster. This study must be extended to other methods and completed by a more complex high-dimensional simulation framework.

Trilaciclib dosage in Chinese patients with extensive-stage small cell lung cancer: a pooled pharmacometrics analysis

This study aimed to analyze potential ethnic disparities in the dose-exposure-response relationships of trilaciclib, a first-in-class intravenous cyclin-dependent kinase 4/6 inhibitor for treating chemotherapy-induced myelosuppression in patients with extensive-stage small cell lung cancer (ES-SCLC). This investigation focused on characterizing these relationships in both Chinese and non-Chinese patients to further refine the dosing regimen for trilaciclib in Chinese patients with ES-SCLC. Population pharmacokinetic (PopPK) and exposure-response (E-R) analyses were conducted using pooled data from four randomized phase 2/3 trials involving Chinese and non-Chinese patients with ES-SCLC. PopPK analysis revealed that trilaciclib clearance in Chinese patients was approximately 17% higher than that in non-Chinese patients with ES-SCLC. Sex and body surface area influenced trilaciclib pharmacokinetics in both populations but did not exert a significant clinical impact. E-R analysis demonstrated that trilaciclib exposure increased with a dosage escalation from 200 to 280 mg/m2, without notable changes in myeloprotective or antitumor efficacy. However, the incidence of infusion site reactions, headaches, and phlebitis/thrombophlebitis rose with increasing trilaciclib exposure in both Chinese and non-Chinese patients with ES-SCLC. These findings suggest no substantial ethnic disparities in the dose-exposure-response relationship between Chinese and non-Chinese patients. They support the adoption of a 240-mg/m2 intravenous 3-day or 5-day dosing regimen for trilaciclib in Chinese patients with ES-SCLC.

Machine-Learning Assisted Screening of Correlated Covariates: Application to Clinical Data of Desipramine

Stepwise covariate modeling (SCM) has a high computational burden and can select the wrong covariates. Machine learning (ML) has been proposed as a screening tool to improve the efficiency of covariate selection, but little is known about how to apply ML on actual clinical data. First, we simulated datasets based on clinical data to compare the performance of various ML and traditional pharmacometrics (PMX) techniques with and without accounting for highly-correlated covariates. This simulation step identified the ML algorithm and the number of top covariates to select when using the actual clinical data. A previously developed desipramine population-pharmacokinetic model was used to simulate virtual subjects. Fifteen covariates were considered with four having an effect included. Based on the F1 score (an accuracy measure), ridge regression was the most accurate ML technique on 200 simulated datasets (F1 score = 0.475 ± 0.231), a performance which almost doubled when highly-correlated covariates were accounted for (F1 score = 0.860 ± 0.158). These performances were better than forwards selection with SCM (F1 score = 0.251 ± 0.274 and 0.499 ± 0.381 without/with correlations respectively). In terms of computational cost, ridge regression (0.42 ± 0.07 seconds/simulated dataset, 1 thread) was ~20,000 times faster than SCM (2.30 ± 2.29 hours, 15 threads). On the clinical dataset, prescreening with the selected ML algorithm reduced SCM runtime by 42.86% (from 1.75 to 1.00 days) and produced the same final model as SCM only. In conclusion, we have demonstrated that accounting for highly-correlated covariates improves ML prescreening accuracy. The choice of ML method and the proportion of important covariates (unknown a priori) can be guided by simulations.

Go beyond the limits of genetic algorithm in daily covariate selection practice

Covariate identification is an important step in the development of a population pharmacokinetic/pharmacodynamic model. Among the different available approaches, the stepwise covariate model (SCM) is the most used. However, SCM is based on a local search strategy, in which the model-building process iteratively tests the addition or elimination of a single covariate at a time given all the others. This introduces a heuristic to limit the searching space and then the computational complexity, but, at the same time, can lead to a suboptimal solution. The application of genetic algorithms (GAs) for covariate selection has been proposed as a possible solution to overcome these limitations. However, their actual use during model building is limited by the extremely high computational costs and convergence issues, both related to the number of models being tested. In this paper, we proposed a new GA for covariate selection to address these challenges. The GA was first developed on a simulated case study where the heuristics introduced to overcome the limitations affecting currently available GA approaches resulted able to limit the selection of redundant covariates, increase replicability of results and reduce convergence times. Then, we tested the proposed GA on a real-world problem related to remifentanil. It obtained good results both in terms of selected covariates and fitness optimization, outperforming the SCM.

Evaluation of the effect of erenumab on migraine-specific questionnaire in patients with chronic and episodic migraine

Erenumab is a fully human anti-canonical calcitonin gene-related peptide receptor monoclonal antibody approved for migraine prevention. The Migraine-Specific Quality-of-Life Questionnaire (MSQ) is a 14-item patient-reported outcome instrument that measures the impact of migraine on health-related quality of life. Erenumab data from four phase II/III clinical trials were used to develop an item response theory (IRT) model within a nonlinear mixed effects framework, (i) evaluate the MSQ item information with respect to patient disability, (ii) characterize the longitudinal progression of the MSQ, and (iii) quantify the effect of erenumab on the MSQ in patients with migraine. The majority (80%) of information was found to be contained in 9 out of 14 items, extending the current knowledge on the reliability of the MSQ as a psychometric tool. Simulations across three MSQ domains show significant improvement from baseline, exceeding minimally important differences. Overall, the IRT model platform developed herein allows for systematic quantification of the effect of erenumab on the MSQ in patients with migraine.

Operational characteristics of full random effects modelling ('frem') compared to stepwise covariate modelling ('scm')

An adequate covariate selection is a key step in population pharmacokinetic modelling. In this study, the automated stepwise covariate modelling technique ('scm') was compared to full random effects modelling ('frem'). We evaluated the power to identify a 'true' covariate (covariate with highest correlation to the pharmacokinetic parameter), precision, and accuracy of the parameter-covariate estimates. Furthermore, the predictive performance of the final models was assessed. The scenarios varied in covariate effect sizes, number of individuals (n = 20-500) and covariate correlations (0-90% cov-corr). The PsN 'frem' routine provides a 90% confidence intervals around the covariate effects. This was used to evaluate its operational characteristics for a statistical backward elimination procedure, defined as 'frem_posthoc' and to facilitate the comparison to 'scm'. 'Frem_posthoc' had a higher power to detect the true covariate with lower bias in small n studies compared to 'scm', applied with commonly used settings (forward p < 0.05, backward p < 0.01). This finding was vice versa in a statistically similar setting. For 'frem_posthoc', power, precision and accuracy of the covariate coefficient increased with higher number of individuals and covariate effect magnitudes. Without a backward elimination step 'frem' models provided unbiased coefficients with highly imprecise coefficients in small n datasets. Yet, precision was superior to final 'scm' model precision obtained using common settings. We conclude that 'frem_posthoc' is also a suitable method to guide covariate selection, although intended to serve as a full model approach. However, a deliberated selection of automated methods is essential for the modeller and using those methods in small datasets needs to be taken with caution.

Population Pharmacokinetics of Tenecteplase in Patients With Acute Myocardial Infarction and Application to Patients With Acute Ischemic Stroke

The pharmacokinetics (PK) of tenecteplase in patients with acute ischemic stroke has not been extensively studied. This study aimed to describe PK characteristics of tenecteplase in patients with acute myocardial infarction (AMI) using a population PK approach and to assess applicability of the findings to patients with acute ischemic stroke by means of external validation. A population PK model was developed using nonlinear mixed-effects modeling based on the phase II TIMI 10B study in patients with AMI (785 PK observations from 103 patients). The statistical and clinical impact of selected covariates on PK parameters were evaluated by a stepwise covariate modeling procedure and simulations, respectively. The performance of the final model was evaluated for patients with acute ischemic stroke using summary statistics of tenecteplase concentrations of 75 patients from investigator-initiated study N1811s. Tenecteplase PK was well described by a 2-compartment linear model, incorporating allometric scaling of clearance and volume parameters and weight-normalized creatinine clearance on clearance. Simulations showed that the identified covariates (weight and creatinine clearance) were of limited influence on exposure at the intended dosing regimen for patients with acute ischemic stroke. The model overpredicted mean tenecteplase plasma concentrations from N1811s by 39%, but 72% of the distribution from N1811s was within the 90% prediction interval of the model predictions. The PK characteristics of tenecteplase in patients with AMI were well described by the final model. Simulations from the model indicated that no specific dose recommendations based on covariates are warranted for patients with AMI.

Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations

Pharmacometrics is a multidisciplinary field utilizing mathematical models of physiology, pharmacology, and disease to describe and quantify the interactions between medication and patient. As these models become more and more advanced, the need for advanced data analysis tools grows. Recently, there has been much interest in the adoption of machine learning (ML) algorithms. These algorithms offer strong function approximation capabilities and might reduce the time spent on model development. However, ML tools are not yet an integral part of the pharmacometrics workflow. The goal of this work is to discuss how ML algorithms have been applied in four stages of the pharmacometrics pipeline: data preparation, hypothesis generation, predictive modelling, and model validation. We will also discuss considerations before the use of ML algorithms with respect to each topic. We conclude by summarizing applications that hold potential for adoption by pharmacometricians.

Population Pharmacokinetics and Dosing Regimen of Lithium in Chinese Patients With Bipolar Disorder

Background: Lithium is an effective medication approved for the treatment of bipolar disorder (BD). It has a narrow therapeutic index (TI) and requires therapeutic drug monitoring. This study aimed to conduct a population pharmacokinetics (PPK) analysis of lithium and investigate the appropriateness of the dosing regimen according to different patient characteristics.

Methods: A total of 476 lithium concentrations from 268 patients with bipolar disorder were analyzed using nonlinear mixed-effects modeling. Monte Carlo simulations were employed to investigate the influence of covariates, such as weight, creatinine clearance, and daily doses of lithium concentrations, and to determine the individualized dosing regimens for patients.

Results: Lithium PK was described by a one-compartment model with first-order absorption and elimination processes. The typical estimated apparent clearance was 0.909 L/h⁻¹ with 16.4% between-subject variability in the 62 kg patients with 116 ml/min creatinine clearance and 600 mg daily doses. To achieve a target trough concentration (0.4–0.8 mmol/L) in the maintenance phase, the regimen of 500 mg than 750 mg daily dose was recommended for patients with renal insufficiency and weighing 100 kg.

Conclusion: A PPK model for lithium was developed to determine the influence of patient characteristics on lithium pharmacokinetics. Weight, creatinine clearance, and total daily dose of lithium can affect the drug’s clearance. These results demonstrate the nonlinear renal excretion of lithium; hence, dosage adjustments are recommended for patients with renal insufficiency.

Population Pharmacokinetic Properties of Omecamtiv Mecarbil in Healthy Subjects and Patients with Heart Failure with Reduced Ejection Fraction

ABSTRACT

Omecamtiv mecarbil is a small molecule that has been shown to improve cardiac function in patients with heart failure with reduced ejection fraction and is currently being developed as an oral modified release (MR) tablet for subjects with chronic HF. The objectives of this study were to analyze the pharmacokinetic (PK) properties of omecamtiv mecarbil and to investigate the effects of potential covariates on pertinent PK parameters using population PK modeling of data from 3 clinical trials in healthy subjects (N=85) and 3 clinical trials in patients with heart failure (N=4261). The population PK analysis was performed using a non-linear mixed effects modeling approach. Omecamtiv mecarbil has a clearance of 11.7 L/hr (0.701 % RSE [relative standard error]) and a central volume of distribution of 275 L (2.12% RSE). The estimated half-life of omecamtiv mecarbil was 33 hours. Body weight and estimated glomerular filtration rate (eGFR) were significant covariates, but their effect on exposure was modest and lacked clinical relevance. Additional covariates including sex, race, bilirubin, albumin, concomitant medications, New York Heart Association Functional Classification, N-terminal-pro hormone B-type natriuretic peptide (NT-proBNP), troponin I, creatine kinase MB, serum hemoglobin, tablet formulation, aspartate aminotransferase, and serum urea was tested and found to have no impact on omecamtiv mecarbil exposures. The results of this integrated evaluation of the impact of covariates on the systemic exposure of omecamtiv mecarbil suggest dose adjustment is not required for the studied subpopulations of patients with heart failure.

Population Pharmacokinetic and Concentration-QTc Analysis of Delamanid in Pediatric Participants with Multidrug-Resistant Tuberculosis

A population pharmacokinetic analysis of delamanid and its major metabolite DM-6705 was conducted to characterize the pharmacokinetics of delamanid and DM-6705 in pediatric participants with multidrug-resistant tuberculosis (MDR-TB). Data from participants between the ages of 0.67 and 17 years, enrolled in 2 clinical trials, were utilized for the analysis. The final data set contained 634 delamanid and 706 DM-6705 valid plasma concentrations from 37 children. A transit model with three compartments best described the absorption of delamanid. Two-compartment models for each component with linear elimination were selected to characterize the dispositions of delamanid and DM-6705, respectively. The covariates included in the model were body weight on the apparent volume of distribution and apparent clearance (for both delamanid and DM-6705); formulation (dispersible versus film-coated tablet) on the mean absorption time; age, formulation, and dose on the bioavailability of delamanid; and age on the fraction of delamanid metabolized to DM-6705. Based on the simulations, doses for participants within different age/weight groups that result in delamanid exposure comparable to that in adults following the approved adult dose were calculated. By concentration-QTc (QTcB [QT corrected by Bazett’s formula]) analysis, a significant positive correlation was detected with concentrations of DM-6705. However, the model-predicted upper bounds of the 90% confidence intervals of ΔQTc values were <10 ms at the simulated maximum concentration (C_max) of DM-6705 following the administration of the maximum doses simulated. This suggests that the effect on the QT interval following the proposed dosing is unlikely to be clinically meaningful in children with MDR-TB who receive delamanid.

A Disease Progression Model to Quantify the Nonmotor Symptoms of Parkinson's Disease in Participants With Leucine-Rich Repeat Kinase 2 Mutation

Leucine-rich repeat kinase 2 (LRRK2) inhibitors are currently in clinical development as interventions to slow progression of Parkinson's disease (PD). Understanding the rate of progression in PD as measured by both motor and nonmotor features is particularly important in assessing the potential therapeutic effect of LRRK2 inhibitors in clinical development. Using standardized data from the Critical Path for Parkinson's Unified Clinical Database, we quantified the rate of progression of the Movement Disorder Society-sponsored revision of the Unified Parkinson's Disease Rating Scale (MDS-UPDRS) Part I (nonmotor aspects of experiences of daily living) in 158 participants with PD who were carriers and 598 participants with PD who were noncarriers of at least one of three different LRRK2 gene mutations (G2019S, R1441C/G, or R1628P). Age and disease duration were found to predict baseline disease severity, while presence of at least one of these three LRRK2 mutations was a predictor of the rate of MDS-UPDRS Part I progression. The estimated progression rate in MDS-UPDRS Part I was 0.648 (95% confidence interval: 0.544, 0.739) points per year in noncarriers of a LRRK2 mutation and 0.259 (95% confidence interval: 0.217, 0.295) points per year in carriers of a LRRK2 mutation. This analysis demonstrates that the rate of progression based on MDS-UPDRS Part I is ~ 60% lower in carriers as compared with noncarriers of LRRK2 gene mutations.

Population pharmacokinetics of the anti-PD-1 antibody camrelizumab in patients with multiple tumor types and model-informed dosing strategy

Camrelizumab, a programmed cell death 1 (PD-1) inhibitor, has been approved for the treatment of patients with relapsed or refractory classical Hodgkin lymphoma, nasopharyngeal cancer and non-small cell lung cancer. The aim of this study was to perform a population pharmacokinetic (PK) analysis of camrelizumab to quantify the impact of patient characteristics and to investigate the appropriateness of a flat dose in the dosing regimen. A total of 3092 camrelizumab concentrations from 133 patients in four clinical trials with advanced melanoma, relapsed or refractory classical Hodgkin lymphoma and other solid tumor types were analyzed using nonlinear mixed effects modeling. The PKs of camrelizumab were properly described using a two-compartment model with parallel linear and nonlinear clearance. Then, covariate model building was conducted using stepwise forward addition and backward elimination. The results showed that baseline albumin had significant effects on linear clearance, while actual body weight affected intercompartmental clearance. However, their impacts were limited, and no dose adjustments were required. The final model was further evaluated by goodness-of-fit plots, bootstrap procedures, and visual predictive checks and showed satisfactory model performance. Moreover, dosing regimens of 200 mg every 2 weeks and 3 mg/kg every 2 weeks provided similar exposure distributions by model-based Monte Carlo simulation. The population analyses demonstrated that patient characteristics have no clinically meaningful impact on the PKs of camrelizumab and present evidence for no advantage of either the flat dose or weight-based dose regimen for most patients with advanced solid tumors.

Semi-Mechanistic Pharmacokinetic Model to Guide the Dose Selection of Nimotuzumab in Patients with Autosomal Dominant Polycystic Kidney Disease

Autosomal dominant polycystic kidney disease (ADPKD) is a genetic disease characterized by an overexpression of epidermal growth factor receptor (EGFR). Nimotuzumab is a recombinant humanized monoclonal antibody against human EGFR. The aim of this study was to develop a population pharmacokinetic model for nimotuzumab and to identify demographic and clinical predictive factors of the pharmacokinetic variability. The population pharmacokinetics (PopPK) of nimotuzumab was characterized using a nonlinear mixed-effect modeling approach with NONMEM^®. A total of 422 log-transformed concentration-versus-time datapoints from 20 patients enrolled in a single-center phase I clinical trial were used. Quasi steady state approximation of the full TMDD (target-mediated drug disposition) model with constant target concentration best described the concentration-time profiles. A turnover mediator was included which stimulates the non-specific clearance of mAb in the central compartment in order to explain the reduced levels at higher doses. Covariates had no influence on the PK (pharmacokinetics) parameters. The model was able to detect that the maximum effective dose in ADPKD subjects is 100 mg. The developed PopPK model may be used to guide the dose selection for nimotuzumab during routine clinical practice in patients with polycystic kidney disease. The model will further support the ongoing investigations of the PK/PD relationships of nimotuzumab to improve its therapeutic use in other disease areas.

Evaluation of ABC gene polymorphisms on the pharmacokinetics and pharmacodynamics of capecitabine in colorectal patients: Implications for dosing recommendations

AIMS

The aims are to develop a population pharmacokinetic model of capecitabine (CAP) and its main metabolites after the oral administration of CAP in colorectal cancer patients with different polymorphisms of the ATP-binding cassette (ABC) gene and a population pharmacokinetic/pharmacodynamic model capable of accounting for the neutropenic effects, and to optimize the dosing strategy based on the polymorphisms of the ABC gene and/or the administration regimen as a single agent or in combination.

METHODS

Forty-eight patients diagnosed with colorectal cancer were included, with 432 plasma levels of CAP, 5'-desoxi-5-fluorouridine (5'-DFUR) and 5-fluorouracil (5-FU), and 370 neutrophil observations. Capecitabine doses ranged from 1250 to 2500 mg/m² /24 h. Plasma measurements of CAP, 5'-DFUR and 5-FU were obtained at 1, 2 and 3 hours post administration. Neutrophil levels were measured between day 15 and day 24 post administration.

RESULTS

The pharmacokinetic model incorporates oxaliplatin as a covariate on absorption lag time, rs6720173 (ABCG5 gene) on clearance of 5'-DFUR (182% increase for mutated rs6720173) and rs2271862 (ABCA2 gene) on clearance of 5-FU (184% increase for mutated rs2271862). System- (Circ₀ = 3.54 × 10⁹ cells/mL, MTT = 204 hours and γ = 6.0 × 10^-2 ) and drug-related (slope [SLP] = 3.1 × 10^-2 mL/mg). Co-administration of oxaliplatin resulted in a 2.84-fold increase in SLP. The predicted exposure thresholds to G3/4 neutropenia in combination and monotherapy were 26 and 70 mg·h/L, respectively.

CONCLUSIONS

The population pharmacokinetic/pharmacodynamic model characterized the time course of capecitabine and its metabolites in plasma. Dose recommendations of capecitabine in patients with mutated and wild allele for single nucleotide polymorphisms rs2271862 of ≤3000 and ≤2400 mg/m² /24 h in monotherapy and ≤1750 and ≤600 mg/m² /24 h in combination with oxaliplatin, respectively, have been proposed.

Development of a Disease Progression Model for Leucine-Rich Repeat Kinase 2 in Parkinson's Disease to Inform Clinical Trial Designs

A quantitative assessment of Parkinson's disease (PD) progression is critical for optimizing clinical trials design. Disease progression model was developed using pooled data from the Progression Marker Initiative study and the Incidence of Cognitive Impairment in Cohorts with Longitudinal Evaluation in Parkinson's Disease study. Age, gender, concomitant medication, and study arms were predictors of baseline. A mutation in the leucine-rich repeat kinase 2 (LRRK2) encoding gene was associated with the disease progression rate. The progression rate in subjects with PD who carried LRRK2 mutation was slightly slower (~0.170 points/month) than that in PD subjects without the mutation (~0.222 points/month). For a nonenriched placebo-controlled clinical trial, approximately 70 subjects/arm would be required to detect a drug effect of 50% reduction in the progression rate with 80% probability, whereas 85, 93, and 100 subjects/arm would be required for an enriched clinical trial with 30%, 50%, and 70% subjects with LRRK2 mutations, respectively.