The likelihood ratio test for the Hill model.

The Hill model is used to describe many biological phenomena to specify the dose-response relationship in clinical trials and other applications. When testing the null hypothesis of no curve versus the Hill model, the likelihood ratio test (LRT) does not exhibit the appropriate Type I error rate. We describe the reason for the failure of the LRT and then proceed to show that a chi-squared approximation with about 1.6 degrees of freedom works well. We then extend the results to analyses of data from published literature.

Pharmacodynamic models: parameterizing the hill equation, Michaelis-Menten, the logistic curve, and relationships among these models.

The Hill equation is often used in dose-response or exposure-response modeling. Aliases for the Hill model include the Emax model, and the Michaelis-Menten model. There is confusion about the appropriate parameterization, how to interpret the parameters, what the meaning is of the various parameterizations found in the literature, and which parameterization best approximates the statistical inferences produced when fitting the Hill equation to data. In this paper, we present several equivalent versions of the Hill model; show that they are equivalent in terms of yielding the same prediction for a given dose, and are equivalent to the four-parameter logistic model in this same sense; and deduce which parameterization is optimal in the sense of having the least statistical curvature and preferable multicollinearity.

Sequentially Determined Measures of Interobserver Agreement (Kappa) in Clinical Trials May Vary Independent of Changes in Observer Performance.

BACKGROUND: Cohen's kappa is a statistic that estimates interobserver agreement. It was originally introduced to help develop diagnostic tests. Interpretative readings of 2 observers, for example, of a mammogram or other imaging, were compared at a single point in time. It is known that kappa depends on the prevalence of disease and that, therefore, kappas across different settings are hard to compare. METHODS: Using simulation, we examine an analogous situation, not previously described, that occurs in clinical trials where sequential measurements are obtained to evaluate disease progression or clinical improvement over time. RESULTS: We show that weighted kappa, used for multilevel outcomes, changes during the trial even if we keep the performance of the observer constant. CONCLUSIONS: Kappa and closely related measures can therefore only be used with great difficulty, if at all, in quality assurance in clinical trials.

Sequentially Determined Measures of Interobserver Agreement (Kappa) in Clinical Trials May Vary Independent of Changes in Observer Performance.

BACKGROUND: Cohen's kappa is a statistic that estimates interobserver agreement. It was originally introduced to help develop diagnostic tests. Interpretative readings of 2 observers, for example, of a mammogram or other imaging, were compared at a single point in time. It is known that kappa depends on the prevalence of disease and that, therefore, kappas across different settings are hard to compare. METHODS: Using simulation, we examine an analogous situation, not previously described, that occurs in clinical trials where sequential measurements are obtained to evaluate disease progression or clinical improvement over time. RESULTS: We show that weighted kappa, used for multilevel outcomes, changes during the trial even if we keep the performance of the observer constant. CONCLUSIONS: Kappa and closely related measures can therefore only be used with great difficulty, if at all, in quality assurance in clinical trials.

Confidence interval of difference of proportions in logistic regression in presence of covariates.

Comparison of treatment differences in incidence rates is an important objective of many clinical trials. However, often the proportion is affected by covariates, and the adjustment of the predicted proportion is made using logistic regression. It is desirable to estimate the treatment differences in proportions adjusting for the covariates, similarly to the comparison of adjusted means in analysis of variance. Because of the correlation between the point estimates in the different treatment groups, the standard methods for constructing confidence intervals are inadequate. The problem is more difficult in the binary case, as the comparison is not uniquely defined, and the sampling distribution more difficult to analyze. Four procedures for analyzing the data are presented, which expand upon existing methods and generalize the link function. It is shown that, among the four methods studied, the resampling method based on the exact distribution function yields a coverage rate closest to the nominal.

Pharmacokinetic equivalence, comparable safety, and immunogenicity of an adalimumab biosimilar product (M923) to Humira in healthy subjects.

The aims of this randomized, double-blind, three-arm, single-dose study were to demonstrate pharmacokinetic (PK) equivalence of the adalimumab biosimilar M923 (hereafter referred to as "M923") to each of 2 reference products, and to assess M923's safety and immunogenicity. Primary PK endpoints were maximum observed concentration (Cmax ), area under the curve (AUC) from time 0 extrapolated to infinity (AUC0-inf ), and AUC from time 0 to 336 hours (AUC0-336 ). Secondary endpoints included safety and immunogenicity assessments. Healthy subjects were randomized 1:1:1 to receive a 40-mg dose of M923 (n = 107); adalimumab US Humira (n = 105), hereafter referred to as "US Humira"; or adalimumab EU Humira (n = 103), hereafter referred to as "EU Humira." PK equivalence was demonstrated for all primary PK endpoints. Geometric least squares means ratios (GMRs) for Cmax , AUC0-inf , and AUC0-336 were 99.4, 100.9, and 100.5, respectively, between the M923 and EU Humira arms and 102.6, 104.2, and 102.9 between the M923 and US Humira arms. The 90% confidence intervals of the GMRs for all PK endpoints were within prespecified confidence bounds of 80%-125%. Adverse event rates were similar across the M923 (47.7%), US Humira (50.9%), and EU Humira (53.3%) arms and were generally mild (73.7%) or moderate (22.0%). The proportion of subjects with a confirmed antidrug antibody (ADA) response was similar across study arms. This study demonstrated bioequivalent PK among M923, US Humira, and EU Humira and demonstrated that the PK parameters were consistent with similar safety and tolerability profile and ADA response rates.

Efficacy and tolerability exposure-response relationship of retigabine (ezogabine) immediate-release tablets in patients with partial-onset seizures.

BACKGROUND: Retigabine (international nonproprietary name)/ezogabine (United States adopted name) is an antiepileptic drug (AED) that enhances KCNQ (Kv7) potassium channel activity. OBJECTIVES: The aim of this study was to explore the relationship between retigabine/ezogabine systemic exposure and efficacy and adverse events (AEs) of retigabine/ezogabine from Phase III clinical trials. METHODS: Data were combined from Studies 301 and 302, which were both randomized, double-blind, placebo-controlled, multicenter, parallel-group studies with similar inclusion and exclusion criteria. All patients had partial-onset seizures and were receiving 1 to 3 concomitant AEDs. Systemic exposure was predicted for each patient as the average steady-state AUC0-τ during the 12-week maintenance phase, based on a population pharmacokinetic model developed for retigabine/ezogabine. Efficacy end points included reduction in total partial-seizure frequency from baseline and probability of ≥50% reduction from baseline in seizure frequency. The probabilities of occurrence of 6 AEs were also evaluated. RESULTS: AUC0-τ values increased linearly over the 600- to 1200-mg/d dose range. Over the entire AUC0-τ range, the probability of efficacy was greater than that for any AE. The slopes of the exposure-response relationship for probability of dizziness and abnormal coordination were similar to that for efficacy, whereas the slopes for dysarthria, somnolence, tremor, and blurred vision were shallower, indicating that the probability of these events occurring was less affected than the probability of efficacy by increases in retigabine/ezogabine AUC0-τ. CONCLUSIONS: Based on the summary statistics of pharmacokinetic parameters, systemic exposure to retigabine/ezogabine increased linearly with dose (600-1200 mg/d). Population pharmacokinetics and pharmacodynamics showed that the probability of efficacy and AEs increased with increasing systemic retigabine/ezogabine exposure, and the probability of efficacy was higher than the probability of any of the AEs. The 35%-50% between-patient variability and overlap between retigabine/ezogabine dose levels in AUC0-τ values indicate that, as with other AEDs, doses should be individually titrated based on a balance between efficacy and tolerability.

Rheumatoid Arthritis Disease Progression Modeling.

Time progression models provide a significant advantage in developing clinical trials and can also be used to elicit comparisons among therapeutic agents. The authors performed a meta-analysis to construct a time progression model for rheumatoid arthritis (RA), an area of significant interest for pharmaceutical development, using the ACR20 end point. Compounds studied were chiefly monoclonal antibodies that were used in conjunction with methotrexate. The study shows that an exponential time response model adequately fits the data. From the modeling, a distribution of effects for biological RA therapies can be provided.

Assessing individual bioequivalence with high-order cross-over designs: a unified procedure.

The U.S. FDA's newly issued guidance on bioequivalence recommends the use of individual bioequivalence (IBE) for highly variable drugs and possibly for modified release dosage forms. The recommended approach to the analysis is to follow the methodology of Hyslop, Hsuan and Holder (HHH), based on a linear mixed model. A limitation of the HHH method is that it works only for uniform designs, such as RTRT/TRTR. In this paper, we present an alternative approach based on a multivariate model. The multivariate model is shown to be a strict superset of the linear mixed model and can successfully model data where the mixed model fails. Our multivariate approach coincides with the HHH method where the HHH method applies, but generalizes to any high-order cross-over design, such as the Balaam design, RTR/TRT, and TRSS/RSTT/STRR. We present numerical examples to demonstrate the proposed method, and examine its properties with a simulation study.