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Determining causal effects in exposure-response relationships is an important but also a challenging task since confounding factors that affect both drug exposure and response often exist and lead to confounding biases in causal effect estimation. Randomized concentration control (RCC) trials are designed to eliminate or to reduce the confounding bias. However, statistical issues in the design and analysis of these trials have not been examined closely in the literature. Analysis of dose-exposure relationship may also be affected by confounding factors if they affect dose adjustments. We examined these issues and suggest methodological and practical solutions. In particular, we proposed using instrumental variables (IV) for the estimation of causal effects in both exposure-response and dose-exposure relationships. We also examined the impacts of confounded treatment heterogeneity on the IV estimate for RCC trials. We illustrated these approaches with a trial design scenario showing the importance of considering multiple practical factors that may alter the performance of the IV estimate. The performance of the IV estimates was examined by simulations for a wide range of scenarios. The results showed clear advantages for the IV estimates over routine estimates. Some situations in which the IV estimates may fail were also identified.

Hysteresis often occurs between drug exposure and response. To model the hysteresis, one approach is to combine an effect compartment with an instantaneous exposure-response model. The combined model may not be easy to fit when the exposure-response model contains random effects. Therefore, it is sometimes useful to test existence of the hysteresis without fitting the model with an effect compartment. Although the likelihood ratio test and Wald test can be implemented based on a fitted model, they do not solve problems in fitting the combined model such as nonconvergence. Fitting a model without the effect compartment is often much easier, as the model contains fewer parameters with random effects. We propose a novel yet simple test based on an instrumental model that only requires fitting an instantaneous exposure-response model. For a wide range of pharmacokinetic/pharmacodynamic (PK/PD) models, this test can be implemented using commonly used software. The test can be used based on a parametric PK model or based on a nonparametric approach such as linear interpolation. The performance of the proposed test was compared with a test based on lagged covariate models and examined by a simulation study and illustrated by implementing it to an analysis of the relationship between drug concentration and QT interval in a cardiac safety trial.

Pharmacokinetic studies of drug and metabolite concentrations in the blood are usually conducted as crossover trials, especially in phases I and II. A longitudinal series of measurements is collected on each subject within each period. However, much of the dependence among such observations, within and between periods, is generally ignored in analyzing this type of data. Usually, only a random coefficient model is fitted for the parameters in the nonlinear mean function, along with allowing the variance to depend on the mean so that it changes over time. Here, we develop models to allow more fully for the structure of the crossover study. We introduce two levels of variance components, for the subjects and for the periods within subjects, and also an autocorrelation within periods. We also retain the time-varying variance, using a separate variance function for this, different from that for the mean. We apply this model to a phase I study of the drug flosequinan and its metabolite. This drug was developed for the treatment of heart failure. Because the metabolite also exhibits an active pharmacologic effect, study of both the parent drug and the metabolite is of interest. We find that the autocorrelation is the element in the covariance structure that most improves the fit of the model but that two levels of variance components can also be necessary.

Confounding bias often occurs in the analysis of the exposure-safety relationship due to confounding factors that have impacts on both drug exposure and safety outcomes. Instrumental variable (IV) methods have been widely used to eliminate or to reduce the bias in observational studies in, for example, epidemiology. Recently applications of IV methods can also be found in clinical trials to deal with problems such as treatment non-compliance. IV methods have rarely been used in pharmacokinetic/pharmacodynamic analyses in clinical trials, although in a randomized trial with multiple dose levels dose may be a powerful IV. We consider modeling the relationship between pharmacokinetics as a measure of drug exposure and risk of adverse events with Poisson regression models and dose as an IV. We show that although IV methods for nonlinear models are in general complex, simple approaches are available for the combination of Poisson regression models and routinely used dose-exposure models. We propose two simple methods that are intuitive and easy to implement. Both methods consist of two stages with the first stage fitting the dose-exposure model; then the fitted model is used in fitting the Poisson regression model in two different ways. The properties of the two methods are compared under several practical scenarios with simulation. A numerical example is used to illustrate an application of the methods.

Sample size reestimation (SSRE) provides a useful tool to change the sample size when an interim look reveals that the original sample size is inadequate. To control the overall type I error, for testing one hypothesis, several approaches have been proposed to construct a statistic so that its distribution is independent to the SSRE under the null hypothesis. We considered a similar approach for comparisons between multiple treatment arms and placebo, allowing the change of sample sizes in all arms depending on interim information. A construction of statistics similar to that for a single hypothesis test is proposed. When the changes of sample sizes in different arms are proportional, we show that one-step and stepwise Dunnett tests can be used directly on statistics constructed in the proposed way. The approach can also be applied to clinical trials with SSRE and treatment selection at interim. The proposed approach is evaluated with simulations under different situations.

The current guidelines, ICH E14, for the evaluation of non-antiarrhythmic compounds recommends a "thorough" QT study (TQT) to be conducted during clinical development. Typically the treatment arms in the TQT study should include study drug at therapeutic and supra-therapeutic doses, placebo and a positive control such as Moxifloxacin (Avelox). The current hypothesis for assay sensitivity involves testing at pre-selected time points, where electrocardiograms (ECG) are obtained, if the mean baseline adjusted differences between positive control and placebo are greater than 5 ms. Since multiple time points are tested, the overall type I error rate should be adjusted using an appropriate multiple comparison procedure. In this article, we consider some recently proposed tests (Zhang, 2008) and explore the use of some standard global test procedures such as O'Brien's ordinary least squares (OLS) and Lauter's standardized sum (SS) tests for testing sensitivity of positive control. The powers of several test procedures are evaluated using simulation. The simulation shows that Zhang's method performs quite well in general but the OLS and SS tests have higher power when the coefficient of variations of QTc intervals have high heterogeneity.