Using forest plots to interpret covariate effects in pharmacometric models.

The inclusion of covariates in pharmacometric models is important due to their ability to explain variability in drug exposure and response. Clear communication of the impact of covariates is needed to support informed decision making in clinical practice and in drug development. However, effectively conveying these effects to key stakeholders and decision makers can be challenging. Forest plots have been proposed to meet these communication needs. However, forest plots for the illustration of covariate effects in pharmacometrics are complex combinations of model predictions, uncertainty estimates, tabulated results, and reference lines and intervals. The purpose of this tutorial is to outline the aspects that influence the interpretation of forest plots, recommend best practices, and offer specific guidance for a clear and transparent communication of covariate effects.

Subcutaneous Marzeptacog Alfa (Activated) for On-Demand Treatment of Bleeding Events in Subjects With Hemophilia A or B With Inhibitors.

Marzeptacog alfa (MarzAA) is under development for subcutaneous treatment of episodic bleeds in patients with hemophilia A/B and was studied in a phase III trial evaluating MarzAA compared with standard-of-care (SoC) for on-demand use. The work presented here aimed to evaluate MarzAA and SoC treatment of bleeding events on a standardized four-point efficacy scale (poor, fair, good, and excellent). Two continuous-time Markov modeling approaches were explored; a four-state model analyzing all four categories of bleeding improvement and a two-state model analyzing a binarized outcome (treatment failure (poor/fair), and treatment success (good/excellent)). Different covariates impacting improvement of bleeding episodes as well as a putative relationship between MarzAA exposure and improvement of bleeding episodes were evaluated. In the final four-state model, higher baseline diastolic blood pressure and higher age (> 33 years of age) were found to negatively and positively impact improvement of bleeding condition, respectively. Bleeding events occurring in knees and ankles were found to improve faster than bleeding events at other locations. The covariate effects had most impact on early treatment success (≤ 3 hours) whereas at later timepoints (> 12 hours), treatment success was similar for all patients indicating that these covariates might be clinically relevant for early treatment response. A statistically significant relationship between MarzAA zero-order absorption and improvement of bleedings (P < 0.05) were identified albeit with low precision. No statistically significant difference in treatment response between MarzAA and intravenous SoC was identified, indicating the potential of MarzAA for treatment of episodic bleeding events with a favorable subcutaneous administration route.

Properties of the full random-effect modeling approach with missing covariate data.

During drug development, a key step is the identification of relevant covariates predicting between-subject variations in drug response. The full random effects model (FREM) is one of the full-covariate approaches used to identify relevant covariates in nonlinear mixed effects models. Here we explore the ability of FREM to handle missing (both missing completely at random (MCAR) and missing at random (MAR)) covariate data and compare it to the full fixed-effects model (FFEM) approach, applied either with complete case analysis or mean imputation. A global health dataset (20 421 children) was used to develop a FREM describing the changes of height for age Z-score (HAZ) over time. Simulated datasets (n = 1000) were generated with variable rates of missing (MCAR) covariate data (0%-90%) and different proportions of missing (MAR) data condition on either observed covariates or predicted HAZ. The three methods were used to re-estimate model and compared in terms of bias and precision which showed that FREM had only minor increases in bias and minor loss of precision at increasing percentages of missing (MCAR) covariate data and performed similarly in the MAR scenarios. Conversely, the FFEM approaches either collapsed at ≥ $$ \ge $$ 70% of missing (MCAR) covariate data (FFEM complete case analysis) or had large bias increases and loss of precision (FFEM with mean imputation). Our results suggest that FREM is an appropriate approach to covariate modeling for datasets with missing (MCAR and MAR) covariate data, such as in global health studies.

Statistical recommendations for count, binary, and ordinal data in rare disease cross-over trials.

BACKGROUND: Recommendations for statistical methods in rare disease trials are scarce, especially for cross-over designs. As a result various state-of-the-art methodologies were compared as neutrally as possible using an illustrative data set from epidermolysis bullosa research to build recommendations for count, binary, and ordinal outcome variables. For this purpose, parametric (model averaging), semiparametric (generalized estimating equations type [GEE-like]) and nonparametric (generalized pairwise comparisons [GPC] and a marginal model implemented in the R package nparLD) methods were chosen by an international consortium of statisticians. RESULTS: It was found that there is no uniformly best method for the aforementioned types of outcome variables, but in particular situations, there are methods that perform better than others. Especially if maximizing power is the primary goal, the prioritized unmatched GPC method was able to achieve particularly good results, besides being appropriate for prioritizing clinically relevant time points. Model averaging led to favorable results in some scenarios especially within the binary outcome setting and, like the GEE-like semiparametric method, also allows for considering period and carry-over effects properly. Inference based on the nonparametric marginal model was able to achieve high power, especially in the ordinal outcome scenario, despite small sample sizes due to separate testing of treatment periods, and is suitable when longitudinal and interaction effects have to be considered. CONCLUSION: Overall, a balance has to be found between achieving high power, accounting for cross-over, period, or carry-over effects, and prioritizing clinically relevant time points.

Machine Learning and Pharmacometrics for Prediction of Pharmacokinetic Data: Differences, Similarities and Challenges Illustrated with Rifampicin.

Pharmacometrics (PM) and machine learning (ML) are both valuable for drug development to characterize pharmacokinetics (PK) and pharmacodynamics (PD). Pharmacokinetic/pharmacodynamic (PKPD) analysis using PM provides mechanistic insight into biological processes but is time- and labor-intensive. In contrast, ML models are much quicker trained, but offer less mechanistic insights. The opportunity of using ML predictions of drug PK as input for a PKPD model could strongly accelerate analysis efforts. Here exemplified by rifampicin, a widely used antibiotic, we explore the ability of different ML algorithms to predict drug PK. Based on simulated data, we trained linear regressions (LASSO), Gradient Boosting Machines, XGBoost and Random Forest to predict the plasma concentration-time series and rifampicin area under the concentration-versus-time curve from 0-24 h (AUC0-24h) after repeated dosing. XGBoost performed best for prediction of the entire PK series (R2: 0.84, root mean square error (RMSE): 6.9 mg/L, mean absolute error (MAE): 4.0 mg/L) for the scenario with the largest data size. For AUC0-24h prediction, LASSO showed the highest performance (R2: 0.97, RMSE: 29.1 h·mg/L, MAE: 18.8 h·mg/L). Increasing the number of plasma concentrations per patient (0, 2 or 6 concentrations per occasion) improved model performance. For example, for AUC0-24h prediction using LASSO, the R2 was 0.41, 0.69 and 0.97 when using predictors only (no plasma concentrations), 2 or 6 plasma concentrations per occasion as input, respectively. Run times for the ML models ranged from 1.0 s to 8 min, while the run time for the PM model was more than 3 h. Furthermore, building a PM model is more time- and labor-intensive compared with ML. ML predictions of drug PK could thus be used as input into a PKPD model, enabling time-efficient analysis.

Exposure-response analyses for the MET inhibitor tepotinib including patients in the pivotal VISION trial: support for dosage recommendations.

PURPOSE: Tepotinib is a highly selective MET inhibitor approved for treatment of non-small cell lung cancer (NSCLC) harboring METex14 skipping alterations. Analyses presented herein evaluated the relationship between tepotinib exposure, and efficacy and safety outcomes. METHODS: Exposure-efficacy analyses included data from an ongoing phase 2 study (VISION) investigating 500 mg/day tepotinib in NSCLC harboring METex14 skipping alterations. Efficacy endpoints included objective response, duration of response, and progression-free survival. Exposure-safety analyses included data from VISION, plus four completed studies in advanced solid tumors/hepatocellular carcinoma (30-1400 mg). Safety endpoints included edema, serum albumin, creatinine, amylase, lipase, alanine aminotransferase, aspartate aminotransferase, and QT interval corrected using Fridericia's method (QTcF). RESULTS: Tepotinib exhibited flat exposure-efficacy relationships for all endpoints within the exposure range observed with 500 mg/day. Tepotinib also exhibited flat exposure-safety relationships for all endpoints within the exposure range observed with 30-1400 mg doses. Edema is the most frequently reported adverse event and the most frequent cause of tepotinib dose reductions and interruptions; however, the effect plateaued at low exposures. Concentration-QTc analyses using data from 30 to 1400 mg tepotinib resulted in the upper bounds of the 90% confidence interval being less than 10 ms for the mean exposures at the therapeutic (500 mg) and supratherapeutic (1000 mg) doses. CONCLUSIONS: These analyses provide important quantitative pharmacologic support for benefit/risk assessment of the 500 mg/day dosage of tepotinib as being appropriate for the treatment of NSCLC harboring METex14 skipping alterations. REGISTRATION NUMBERS: NCT01014936, NCT01832506, NCT01988493, NCT02115373, NCT02864992.

A quantitative approach to the choice of number of samples for percentile estimation in bootstrap and visual predictive check analyses.

Understanding the uncertainty in parameter estimates or in derived secondary variables is important in all data analysis activities. In pharmacometrics, this is often done based on the standard errors from the variance-covariance matrix of the estimates. Confidence intervals derived in this way are by definition symmetrical, which may lead to implausible outcomes, and will require translation to generate uncertainties in derived variables. An often-used alternative is numerical percentile estimation by, for example, nonparametric bootstraps to circumvent these issues. Visual predictive checks (VPCs), which is a commonly used model diagnostic tool in pharmacometric analyses, also rely on the estimation of percentiles through numerical approaches. Given the cost in terms of run times and processing times for these methods, it is important to consider the trade-off between the number of bootstrap samples or simulated data sets in the VPCs, to the increase in precision related to a large number of bootstrap samples or simulated data sets. The objective with this tutorial is to provide a quantitative framework for assessing the precision in estimated percentile limits in bootstrap and visual predictive checks analyses to facilitate an informed choice of confidence interval width, number of bootstrap samples/simulated data sets, and required level of precision.

An introduction to the full random effects model.

The full random-effects model (FREM) is a method for determining covariate effects in mixed-effects models. Covariates are modeled as random variables, described by mean and variance. The method captures the covariate effects in estimated covariances between individual parameters and covariates. This approach is robust against issues that may cause reduced performance in methods based on estimating fixed effects (e.g., correlated covariates where the effects cannot be simultaneously identified in fixed-effects methods). FREM covariate parameterization and transformation of covariate data records can be used to alter the covariate-parameter relation. Four relations (linear, log-linear, exponential, and power) were implemented and shown to provide estimates equivalent to their fixed-effects counterparts. Comparisons between FREM and mathematically equivalent full fixed-effects models (FFEMs) were performed in original and simulated data, in the presence and absence of non-normally distributed and highly correlated covariates. These comparisons show that both FREM and FFEM perform well in the examined cases, with a slightly better estimation accuracy of parameter interindividual variability (IIV) in FREM. In addition, FREM offers the unique advantage of letting a single estimation simultaneously provide covariate effect coefficient estimates and IIV estimates for any subset of the examined covariates, including the effect of each covariate in isolation. Such subsets can be used to apply the model across data sources with different sets of available covariates, or to communicate covariate effects in a way that is not conditional on other covariates.

Sensitivity of Pegfilgrastim Pharmacokinetic and Pharmacodynamic Parameters to Product Differences in Similarity Studies.

In this work, a previously developed pegfilgrastim (PG) population pharmacokinetic-pharmacodynamic (PKPD) model was used to evaluate potential factors of importance in the assessment of PG PK and PD similarity. Absolute neutrophil count (ANC) was the modelled PD variable. A two-way cross-over study was simulated where a reference PG and a potentially biosimilar test product were administered to healthy volunteers. Differences in delivered dose amounts or potency between the products were simulated. A different baseline absolute neutrophil count (ANC) was also considered. Additionally, the power to conclude PK or PD similarity based on areas under the PG concentration-time curve (AUC) and ANC-time curve (AUEC) were calculated. Delivered dose differences between the products led to a greater than dose proportional differences in AUC but not in AUEC, respectively. A 10% dose difference from a 6 mg dose resulted in 51% and 7% differences in AUC and AUEC, respectively. These differences were more pronounced with low baseline ANC. Potency differences up to 50% were not associated with large differences in either AUCs or AUECs. The power to conclude PK similarity was affected by the simulated dose difference; with a 4% dose difference from 6 mg the power was approximately 29% with 250 subjects. The power to conclude PD similarity was high for all delivered dose differences and sample sizes.

Population Kinetics of 0.9% Saline Distribution in Hemorrhaged Awake and Isoflurane-anesthetized Volunteers.

BACKGROUND: Population-based, pharmacokinetic modeling can be used to describe variability in fluid distribution and dilution between individuals and across populations. The authors hypothesized that dilution produced by crystalloid infusion after hemorrhage would be larger in anesthetized than in awake subjects and that population kinetic modeling would identify differences in covariates. METHODS: Twelve healthy volunteers, seven females and five males, mean age 28 ± 4.3 yr, underwent a randomized crossover study. Each subject participated in two separate sessions, separated by four weeks, in which they were assigned to an awake or an anesthetized arm. After a baseline period, hemorrhage (7 ml/kg during 20 min) was induced, immediately followed by a 25 ml/kg infusion during 20 min of 0.9% saline. Hemoglobin concentrations, sampled every 5 min for 60 min then every 10 min for an additional 120 min, were used for population kinetic modeling. Covariates, including body weight, sex, and study arm (awake or anesthetized), were tested in the model building. The change in dilution was studied by analyzing area under the curve and maximum plasma dilution. RESULTS: Anesthetized subjects had larger plasma dilution than awake subjects. The analysis showed that females increased area under the curve and maximum plasma dilution by 17% (with 95% CI, 1.08 to 1.38 and 1.07 to 1.39) compared with men, and study arm (anesthetized increased area under the curve by 99% [0.88 to 2.45] and maximum plasma dilution by 35% [0.71 to 1.63]) impacted the plasma dilution whereas a 10-kg increase of body weight resulted in a small change (less than1% [0.93 to 1.20]) in area under the curve and maximum plasma dilution. Mean arterial pressure was lower in subjects while anesthetized (P < 0.001). CONCLUSIONS: In awake and anesthetized subjects subjected to controlled hemorrhage, plasma dilution increased with anesthesia, female sex, and lower body weight. Neither study arm nor body weight impact on area under the curve or maximum plasma dilution were statistically significant and therefore no effect can be established.

Analysis of opioid consumption in clinical trials: a simulation based analysis of power of four approaches.

Inconsistent trial design and analysis is a key reason that few advances in postoperative pain management have been made from clinical trials analyzing opioid consumption data. This study aimed to compare four different approaches to analyze opioid consumption data. A repeated time-to-event (RTTE) model in NONMEM was used to simulate clinical trials of morphine consumption with and without a hypothetical adjuvant analgesic in doses equivalent to 15-62% reduction in morphine consumption. Trials were simulated with duration of 24-96 h. Monte Carlo simulation and re-estimation were performed to determine sample size required to demonstrate efficacy with 80% power using t test, Mann-Whitney rank sum test, time-to-event (TTE) modeling and RTTE modeling. Precision of efficacy estimates for RTTE models were evaluated in 500 simulations. A sample size of 50 patients was required to detect 37% morphine sparing effect with at least 80% power in a 24 h trial with RTTE modeling whereas the required sample size was 200 for Mann-Whitney, 180 for t-test and 76 for TTE models. Extending the trial duration from 24 to 96 h reduced the required sample size by 3.1 fold with RTTE modeling. Precise estimate of potency was obtained with a RTTE model accounting for both morphine effects and time-varying covariates on opioid consumption. An RTTE analysis approach proved better suited for demonstrating efficacy of opioid sparing analgesics than traditional statistical tests as a lower sample size was required due the ability to account for time-varying factors including PK.

Exposure-Response Analyses Supporting Ticagrelor Dosing Recommendation in Patients With Prior Myocardial Infarction.

The relationships between drug exposure and the composite risk of cardiovascular (CV) death, myocardial infarction (MI), and stroke as well as the risk of TIMI major bleeding were estimated following long-term treatment with ticagrelor 60 or 90 mg twice daily in 20,942 patients with prior MI. These analyses support the primary reported efficacy and safety evaluations by showing that there were clear separations from placebo early in treatment with both doses, regardless of ticagrelor exposure, for both endpoints. In addition, the exposure-response analyses provided new insight into the contribution of individual exposure levels, rather than dose, as a predictor of events and accounted for differences in the baseline risk between patients. The predicted risks of CV death/MI/stroke were similar despite an increase in the median predicted ticagrelor average steady-state concentration from 606 nmol/L with ticagrelor 60 mg to 998 nmol/L with ticagrelor 90 mg (hazard ratios vs placebo of 0.83 and 0.81, respectively). The corresponding predicted risk of TIMI major bleeding slightly increased (hazard ratios vs placebo of 2.4 and 2.6, respectively). Apart from Japanese patients, showing a lower risk of CV death/MI/stroke, the response to ticagrelor was consistent across the study population, as supported by the combination of relatively flat exposure-response relationships in the studied exposure range, similar sensitivity to ticagrelor exposure, and small exposure differences. Consequently, the present analyses support the selection of the 60-mg dose for all demographic subgroups of patients studied.

The effect of Fisher information matrix approximation methods in population optimal design calculations.

With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

A Pharmacokinetic-Pharmacodynamic Model of Morphine Exposure and Subsequent Morphine Consumption in Postoperative Pain.

PURPOSE: To characterize the pharmacokinetic-pharmacodynamic (PK-PD) relationship between exposure of morphine and subsequent morphine consumption and to develop simulation tools for model validation. METHODS: Dose, formulation and time of morphine administration was available from a published study in 63 patients receiving intravenous, oral immediate release or oral controlled release morphine on request after hip surgery. The PK-PD relationship between predicted exposure of morphine and morphine consumption was modeled using repeated time to event (RTTE) modeling in NONMEM. To validate the RTTE model, a visual predictive check method was developed with simulated morphine consumption given the exposure of preceding morphine administration. RESULTS: The probability of requesting morphine was found to be significantly related to the exposure of morphine as well as night/day. Oral controlled release morphine was more effective than intravenous and oral immediate release formulations at equivalent average concentrations. Maximum effect was obtained for 8 h by oral controlled release doses ≥ 15 mg, where probability of requesting a new dose was reduced to 20% for a typical patient. CONCLUSION: This study demonstrates the first quantitative link between exposure of morphine and subsequent morphine consumption and introduces an efficient visual predictive check approach with simulation of adaptive dosing.

Inter occasion variability in individual optimal design.

Inter occasion variability (IOV) is of importance to consider in the development of a design where individual pharmacokinetic or pharmacodynamic parameters are of interest. IOV may adversely affect the precision of maximum a posteriori (MAP) estimated individual parameters, yet the influence of inclusion of IOV in optimal design for estimation of individual parameters has not been investigated. In this work two methods of including IOV in the maximum a posteriori Fisher information matrix (FIMMAP) are evaluated: (i) MAP occ-the IOV is included as a fixed effect deviation per occasion and individual, and (ii) POP occ-the IOV is included as an occasion random effect. Sparse sampling schedules were designed for two test models and compared to a scenario where IOV is ignored, either by omitting known IOV (Omit) or by mimicking a situation where unknown IOV has inflated the IIV (Inflate). Accounting for IOV in the FIMMAP markedly affected the designs compared to ignoring IOV and, as evaluated by stochastic simulation and estimation, resulted in superior precision in the individual parameters. In addition MAPocc and POP occ accurately predicted precision and shrinkage. For the investigated designs, the MAP occ method was on average slightly superior to POP occ and was less computationally intensive.

Population pharmacokinetics of edoxaban in patients with symptomatic deep-vein thrombosis and/or pulmonary embolism--the Hokusai-VTE phase 3 study.

AIMS: This study characterized the population pharmacokinetics of edoxaban in patients with symptomatic deep-vein thrombosis and/or pulmonary embolism in the Hokusai-VTE phase 3 study. The impact of the protocol-specified 50% dose reductions applied to patients with body weight ≤ 60 kg, creatinine clearance (CL(cr)) of 30 to 50 ml min(-1) or concomitant P-glycoprotein inhibitor on edoxaban exposure was assessed using simulations. METHODS: The sparse data from Hokusai-VTE, 9531 concentrations collected from 3707 patients, were pooled with data from 13 phase 1 studies. In the analysis, the covariate relationships used for dose reductions were estimated and differences between healthy subjects and patients as well as additional covariate effects of age, race and gender were explored based on statistical and clinical significance. RESULTS: A linear two-compartment model with first order absorption preceded by a lag time best described the data. Allometrically scaled body weight was included on disposition parameters. Apparent clearance was parameterized as non-renal and renal. The latter increased non-linearly with increasing CL(cr). Compared with healthy volunteers, inter-compartmental clearance and the CL(cr) covariate effect were different in patients (+64.6% and +274%). Asian patients had a 22.6% increased apparent central volume of distribution. The effect of co-administration of P-glycoprotein inhibitors seen in phase 1 could not be confirmed in the phase 3 data. Model-based simulations revealed lower exposure in dose-reduced compared with non-dose-reduced patients. CONCLUSIONS: The adopted dose-reduction strategy resulted in reduced exposure compared with non-dose-reduced, thereby overcompensating for covariate effects. The clinical impact of these differences on safety and efficacy remains to be evaluated.

Methods and software tools for design evaluation in population pharmacokinetics-pharmacodynamics studies.

Population pharmacokinetic (PK)-pharmacodynamic (PKPD) models are increasingly used in drug development and in academic research; hence, designing efficient studies is an important task. Following the first theoretical work on optimal design for nonlinear mixed-effects models, this research theme has grown rapidly. There are now several different software tools that implement an evaluation of the Fisher information matrix for population PKPD. We compared and evaluated the following five software tools: PFIM, PkStaMp, PopDes, PopED and POPT. The comparisons were performed using two models, a simple-one compartment warfarin PK model and a more complex PKPD model for pegylated interferon, with data on both concentration and response of viral load of hepatitis C virus. The results of the software were compared in terms of the standard error (SE) values of the parameters predicted from the software and the empirical SE values obtained via replicated clinical trial simulation and estimation. For the warfarin PK model and the pegylated interferon PKPD model, all software gave similar results. Interestingly, it was seen, for all software, that the simpler approximation to the Fisher information matrix, using the block diagonal matrix, provided predicted SE values that were closer to the empirical SE values than when the more complicated approximation was used (the full matrix). For most PKPD models, using any of the available software tools will provide meaningful results, avoiding cumbersome simulation and allowing design optimization.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Optimizing disease progression study designs for drug effect discrimination.

Investigate the possibility to directly optimize a clinical trial design for statistical power to detect a drug effect and compare to optimal designs that focus on parameter precision. An improved statistic derived from the general formulation of the Wald approximation was used to predict the statistical power for given trial designs of a disease progression study. The predicted value was compared, together with the classical Wald statistic, to a type I error-corrected model-based power determined via clinical trial simulations. In a second step, a study design for maximal power was determined by directly maximizing the new statistic. The resulting power-optimal designs and their corresponding performance based on empirical power calculations were compared to designs focusing on parameter precision. Comparisons of empirically determined power and the newly developed statistic, showed excellent agreement across all scenarios investigated. This was in contrast to the classical Wald statistic, which consistently over-predicted the reference power with deviations of up to 90 %. Designs maximized using the proposed metric differed from traditional optimal designs and showed equal or up to 20 % higher power in the subsequent clinical trial simulations. Furthermore, the proposed method was used to minimize the number of individuals required to achieve 80 % power through a simultaneous optimization of study size and study design. The targeted power of 80 % was confirmed in subsequent simulation study. A new statistic was developed, allowing for the explicit optimization of a clinical trial design with respect to statistical power.