This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA. We make the distinction between fixed and random effects models and show how these models can easily be fitted using modern software. Issues with fitting and testing for a difference in carry-over effects are described and the use of baseline measurements is discussed. Simple methods for testing for a treatment difference when the data are binary are also described. Various designs with two or more treatments but with three or four periods are then described and compared. These include the balanced and partially balanced designs for three or more treatments and designs for factorial treatment combinations. Also described are nearly balanced and nearly strongly balanced designs. Random subject-effects models for the designs with two or more treatments are described and methods for analysing non-normal data are also given. The chapter concludes with a description of the use of cross-over designs in the testing of bioequivalence.

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Design and Analysis of Cross-Over Trials

Therapeutic drug monitoring (TDM) is the quantification and interpretation of drug concentrations in blood to optimize pharmacotherapy. It considers the interindividual variability of pharmacokinetics and thus enables personalized pharmacotherapy. In psychiatry and neurology, patient populations that may particularly benefit from TDM are children and adolescents, pregnant women, elderly patients, individuals with intellectual disabilities, patients with substance abuse disorders, forensic psychiatric patients or patients with known or suspected pharmacokinetic abnormalities. Non-response at therapeutic doses, uncertain drug adherence, suboptimal tolerability, or pharmacokinetic drug-drug interactions are typical indications for TDM. However, the potential benefits of TDM to optimize pharmacotherapy can only be obtained if the method is adequately integrated in the clinical treatment process. To supply treating physicians and laboratories with valid information on TDM, the TDM task force of the Arbeitsgemeinschaft fur Neuropsychopharmakologie und Pharmakopsychiatrie (AGNP) issued their first guidelines for TDM in psychiatry in 2004. After an update in 2011, it was time for the next update. Following the new guidelines holds the potential to improve neuropsychopharmacotherapy, accelerate the recovery of many patients, and reduce health care costs.

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Consensus Guidelines for Therapeutic Drug Monitoring in Neuropsychopharmacology: Update 2017.

INTRODUCTION Regulatory Requirement Basic Considerations Procedures for Sample Size Calculation Aims and Structure of the Book CONSIDERATIONS PRIOR TO SAMPLE SIZE CALCULATION Confounding and Interaction One-Sided Test Versus Two-Sided Test Crossover Design Versus Parallel Design Subgroup/Interim Analyses Data Transformation Practical Issues COMPARING MEANS One-Sample Design Two-Sample Parallel Design Two-Sample Crossover Design Multiple-Sample One-Way ANOVA Multiple-Sample Williams Design Practical Issues LARGE SAMPLE TESTS FOR PROPORTIONS One-Sample Design Two-Sample Parallel Design Two-Sample Crossover Design One-Way Analysis of Variance Williams Design Relative Risk - Parallel Design Relative Risk - Crossover Design Practical Issues EXACT TESTS FOR PROPORTIONS Binomial Test Fisher's Exact Test Optimal Multiple-Stage Designs for Single Arm Trials Flexible Designs for Multiple-Arm Trials Remarks TESTS FOR GOODNESS-OF-FIT AND CONTINGENCY TABLES Tests for Goodness-of-Fit Test for Independence -Single Stratum Test for Independence -Multiple Strata Test for Categorical Shift Carry-Over Effect Test Practical Issues COMPARING TIME-TO-EVENT DATA Basic Concepts Exponential Model Cox's Proportional Hazards Model Weighted Log-Rank Test Practical Issues GROUP SEQUENTIAL METHODS Pocock's Test O'Brien and Fleming's Test Wang and Tsiatis' Test Inner Wedge Test Binary Variables Time-to-Event Data Alpha Spending Function Sample Size Re-Estimation Conditional Power Practical Issues COMPARING VARIABILITIES Comparing Intra-Subject Variabilities Comparing Intra-Subject CVs Comparing Inter-Subject Variabilities Comparing Total Variabilities Practical Issues BIOEQUIVALENCE TESTING Bioequivalence Criteria Average Bioequivalence Population Bioequivalence Individual Bioequivalence In Vitro Bioequivalence NONPARAMETRICS Violation of Assumptions One-Sample Location Problem Two-Sample Location Problem Test for Independence Practical Issues SAMPLE SIZE CALCULATION IN OTHER AREAS Dose Response Studies ANOVA with Repeated Measures Quality of Life Bridging Studies Vaccine Clinical Trials Appendix: Tables of Quantiles References Index

Sample Size Calculations in Clinical Research

Therapeutic drug monitoring (TDM), i. e., the quantification of serum or plasma concentrations of medications for dose optimization, has proven a valuable tool for the patient-matched psychopharmacotherapy. Uncertain drug adherence, suboptimal tolerability, non-response at therapeutic doses, or pharmacokinetic drug-drug interactions are typical situations when measurement of medication concentrations is helpful. Patient populations that may predominantly benefit from TDM in psychiatry are children, pregnant women, elderly patients, individuals with intelligence disabilities, forensic patients, patients with known or suspected genetically determined pharmacokinetic abnormalities or individuals with pharmacokinetically relevant comorbidities. However, the potential benefits of TDM for optimization of pharmacotherapy can only be obtained if the method is adequately integrated into the clinical treatment process. To promote an appropriate use of TDM, the TDM expert group of the Arbeitsgemeinschaft fur Neuropsychopharmakologie und Pharmakopsychiatrie (AGNP) issued guidelines for TDM in psychiatry in 2004. Since then, knowledge has advanced significantly, and new psychopharmacologic agents have been introduced that are also candidates for TDM. Therefore the TDM consensus guidelines were updated and extended to 128 neuropsychiatric drugs. 4 levels of recommendation for using TDM were defined ranging from “strongly recommended” to “potentially useful”. Evidence-based “therapeutic reference ranges” and “dose related reference ranges” were elaborated after an extensive literature search and a structured internal review process. A “laboratory alert level” was introduced, i. e., a plasma level at or above which the laboratory should immediately inform the treating physician. Supportive information such as cytochrome P450 substrate- and inhibitor properties of medications, normal ranges of ratios of concentrations of drug metabolite to parent drug and recommendations for the interpretative services are given. Recommendations when to combine TDM with pharmacogenetic tests are also provided. Following the guidelines will help to improve the outcomes of psychopharmacotherapy of many patients especially in case of pharmacokinetic problems. Thereby, one should never forget that TDM is an interdisciplinary task that sometimes requires the respectful discussion of apparently discrepant data so that, ultimately, the patient can profit from such a joint effort.

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AGNP Consensus Guidelines for Therapeutic Drug Monitoring in Psychiatry: Update 2011

The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug-receptor relationships. Many pharmacokinetic-pharmacodynamic models have used the Hill equation to describe nonlinear drug dose-response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill's original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences.

The Hill equation: a review of its capabilities in pharmacological modelling

The concept of interchangeable pharmaceutical products has been examined in great detail in the literature. Anderson and Hauck proposed a statistical random coefficient model to study 'switchability', and coined the phrase 'individual bioequivalence' which they defined with a probability-based inequality. Since that paper there has been considerable work and discussion. The Food and Drug Administration has recommended the introduction of individual bioequivalence (IBE) and population bioequivalence (PBE) methods in a draft guidance document. The proposal in the draft guidance includes criteria for IBE and PBE and recommends the use of non-parametric bootstrap 95 per cent upper confidence intervals for the conclusion of either IBE or PBE. However, this method requires intensive computations. We have developed an alternative confidence interval procedure to assess IBE by the FDA recommended criteria. This method utilizes Howe's approximation I to a Cornish-Fisher expansion. Our proposed method is applicable to balanced or unbalanced data in a broad class of extended cross-over designs, and can be easily programmed using readily available software.

A small sample confidence interval approach to assess individual bioequivalence.

Clozapine plasma levels were monitored in 16 patients during a series of three consecutive treatments (single dose-multiple dose-single dose). Each patient received a single 75-mg dose (3 x 25 mg) with clozapine tablets, and serial plasma samples were collected over 48 hr after the dose. At 48 hr, a multiple-dose regimen was started, consisting of an initial dose escalation period followed by dosing at a constant regimen for at least 6 days. After the last dose, serial plasma samples were again obtained over 72 hr. Drug was then withheld for at least 7 days, a final single 75-mg dose was given, and plasma sampling was repeated. A subset of the patient population (N = 7) was used to test for a food effect during the single-dose treatments. The pharmacokinetic parameters between the initial and the final single dose periods were not significantly different. Similarly, there were no differences within patients when given the dose after fasting (fed 1 hr after dose) or with a meal. In contrast, the terminal elimination rate differed between the single-dose and the multiple-dose treatments (t1/2 m3 = 7.9 hr single dose and 14.2 hr multiple dose) (P less than 0.05) and the dose-normalized area under the plasma concentration/time curves increased 27% with multiple dosing. Since a previous study in patients (Choc et al., Pharm. Res. 4:402-405, 1987) showed dose proportionality of clozapine plasma concentrations during multiple-dose regimens, the present results cannot be described by Michaelis-Menten kinetics.

Single- vs multiple-dose pharmacokinetics of clozapine in psychiatric patients

We propose an adaptive procedure for dose-finding in clinical trials when the primary efficacy endpoint is continuous. We model the mean of the efficacy endpoint, given the dose, as a four-parameter logistic function. The efficacy endpoint at each dose is distributed according to either a normal or a gamma distribution. We consider the cases of fixed variance and fixed coefficient of variation assuming them to be both known and unknown. The analytic formulae for the Fisher information matrix are obtained, which are used to build the locally and adaptive D-optimal designs.

Adaptive designs for dose-finding studies based on sigmoid Emax model.

SUMMARY In comparative bioavailability trials, the focus in the determination of bioequivalence has been to show that the average bioavailability on a test formulation is similar to the average bioavailability on a reference formulation. It has been argued that this is not adequate to insure interchangeability of formulations. We introduce a moment-based criterion which ensures interchangeability for at least a certain proportion of the population. An algorithm is given for determining the constant in the criterion. An example is used to illustrate how the criterion may be applied.

Francis Hsuan

Papers

A small sample confidence interval approach to assess individual bioequivalence.

Single- vs multiple-dose pharmacokinetics of clozapine in psychiatric patients

Adaptive designs for dose-finding studies based on sigmoid Emax model.

Moment-based criteria for determining bioequivalence

The {2}-inverse with applications in statistics