Akifumi Yafune

Bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters. I: a use of bootstrap standard error

In population pharmacokinetic studies, one of the main objectives is to estimate population pharmacokinetic parameters specifying the population distributions of pharmacokinetic parameters. Confidence intervals for population pharmacokinetic parameters are generally estimated by assuming the asymptotic normality, which is a large-sample property, that is, a property which holds for the cases where sample sizes are large enough. In actual clinical trials, however, sample sizes are limited and not so large in general. Likelihood functions in population pharmacokinetic modelling include a multiple integral and are quite complicated. We hence suspect that the sample sizes of actual trials are often not large enough for assuming the asymptotic normality and that the asymptotic confidence intervals underestimate the uncertainties of the estimates of population pharmacokinetic parameters. As an alternative to the asymptotic normality approach, we can employ a bootstrap approach. This paper proposes a bootstrap standard error approach for constructing confidence intervals for population pharmacokinetic parameters. Comparisons between the asymptotic and bootstrap confidence intervals are made through applications to a simulated data set and an actual phase I trial.

Treatment of thoracic esophageal carcinoma invading adjacent structures

T4 esophageal cancer is defined as the tumor invading adjacent structures, using tumor–node–metastasis (TNM) staging. For clinically T4 thoracic esophageal carcinoma, multimodality therapy, that is, neoadjuvant chemoradiotherapy (CRT) followed by surgery or definitive CRT, has generally been performed. However, the prognosis of patients with these tumors remains poor. Another strategy is needed to achieve curative treatment. In the present article, the treatment strategies employed to date are reviewed. Furthermore, the strategies for these malignancies are reassessed, based on our experiences. R1/2 and R0 resections are regarded as those with residual and no tumor after surgery. The present data show that patients who underwent R1/2 resection after neoadjuvant CRT experienced little survival benefit, while complete response (CR) cases after definitive CRT had comparatively better results. Therefore, curative surgery should not be attempted without down‐staging, and definitive CRT should be the initial treatment. Then surgery is indicated for the eradication of residual cancer cells. Close surveillance is essential for early detection of relapse even after CR, because the operation will gradually become increasingly difficult due to post‐CRT fibrosis. In conclusion, multimodality therapy consists of definitive CRT followed by R0 resection, which can be the treatment of choice for T4 esophageal carcinoma. These challenging treatments have the potential to constitute the most effective therapeutic strategy. (Cancer Sci 2007; 98: 937–942)

A use of Monte Carlo integration for population pharmacokinetics with multivariate population distribution.

This paper describes a use of Monte Carlo integration for population pharmacokinetics with multivariate population distribution. In the proposed approach, a multivariate lognormal distribution is assumed for a population distribution of pharmacokinetic (PK) parameters. The maximum likelihood method is employed to estimate the population means, variances, and correlation coefficients of the multivariate lognormal distribution. Instead of a first-order Taylor series approximation to a nonlinear PK model, the proposed approach employs a Monte Carlo integration for the multiple integral in maximizing the log likelihood function. Observations below the lower limit of detection, which are usually included in Phase 1 PK data, are also incorporated into the analysis. Applications are given to a simulated data set and an actual Phase 1 trial to show how the proposed approach works in practice.

Bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters. II : A bootstrap modification of standard two-stage (STS) method for phase I trial

For population pharmacokinetics in phase I trials, the standard two-stage (STS) method is quite appealing, especially to non-statisticians, because the method is theoretically and computationally simple. The method, however, does not take into account the uncertainty in estimating individual-specific parameters and gives biased estimates for population variances of pharmacokinetic parameters. This is one of the main reasons why the STS method is not generally recommended. This paper proposes a simple bootstrap modification of the STS method for estimating confidence intervals of population means and standard deviations of pharmacokinetic parameters in phase I trials. The proposed approach adopts a bootstrap bias correction in estimating population variances of pharmacokinetic parameters. Applications are given to a simulated data set and an actual phase I trial to show how the proposed approach works in practice.

Evaluation of Bayesian estimation of pharmacokinetic parameters

The validity of pharmacokinetic parameters estimated by the maximum a posteriori probability (MAP) Bayesian method was investigated by simulation studies. A 1-compartment model with bolus intravenous administration was used as a pharmacokinetic model, and the coefficients of variation for the parameters and residual error were set at 30% and 10%, respectively. The accuracy of the posterior modes of pharmacokinetic parameters estimated by the MAP Bayesian method was assessed by the difference between the true value and the estimated value. The results showed that the accuracy of the Bayesian estimation depended on sampling times and on the differences between the prior means and individual true parameter values. For assessing the reliability and accuracy of the Bayesian estimation, the authors suggest using the whole posterior distribution of the pharmacokinetic parameters to describe the 95th percentile range for predicted blood concentration profiles. The authors believe that the proposed procedures provide helpful information for evaluating the Bayesian estimation of pharmacokinetic profiles.

A Note on Sample Size Determination for Akaike Information Criterion (AIC) Approach to Clinical Data Analysis

ABSTRACT Because of its flexibility and usefulness, Akaike Information Criterion (AIC) has been widely used for clinical data analysis. In general, however, AIC is used without paying much attention to sample size. If sample sizes are not large enough, it is possible that the AIC approach does not lead us to the conclusions which we seek. This article focuses on the sample size determination for AIC approach to clinical data analysis. We consider a situation in which outcome variables are dichotomous and propose a method for sample size determination under this situation. The basic idea is also applicable to the situations in which outcome variables have more than two categories or outcome variables are continuous. We present simulation studies and an application to an actual clinical trial.

Kullback-leibler information approach to the optimum measurement point for bayesian estimation

When an appropriate parametric model and a prior distribution of its parameters are given to describe clinical time courses of a dynamic biological process, Bayesian approaches allow us to estimate the entire profiles from a few or even a single observation per subject. The goodness of the estimation depends on the measurement points at which the observations were made. The number of measurement points per subject is generally limited to one or two. The limited measurement points have to be selected carefully. This paper proposes an approach to the selection of the optimum measurement point for Bayesian estimations of clinical time courses. The selection is made among given candidates, based on the goodness of estimation evaluated by the Kullback-Leibler information. This information measures the discrepancy of an estimated time course from the true one specified by a given appropriate model. The proposed approach is applied to a pharmacokinetic analysis, which is a typical clinical example where the sele...

Profile Likelihood-Based Confidence Intervals Using Monte Carlo Integration for Population Pharmacokinetic Parameters

ABSTRACT Population pharmacokinetic (PPK) analysis usually employs nonlinear mixed effects models using first-order linearization methods. It is well known that linearization methods do not always perform well in actual situations. To avoid linearization, the Monte Carlo integration method has been proposed. Moreover, we generally utilize asymptotic confidence intervals for PPK parameters based on Fisher information. It is known that likelihood-based confidence intervals are more accurate than those from the usual asymptotic confidence intervals. We propose profile likelihood-based confidence intervals using Monte Carlo integration. We have evaluated the performance of the proposed method through a simulation study, and analyzed the erythropoietin concentration data set by the method.

Observation of Time-Dependent Adverse Events and the Influence of Drop-Out Thereon in Long-Term Safety Studies—Simulation Study Under the Current Practice of Post-marketing Safety Evaluation in Japan

Abstract Safety assessment of a new drug should be continuously carried out in the premarketing phase as well as in the postmarketing phase. Considering the actual conditions and problems of postmarketing safety studies in Japan, i.e., the lack of attention to the extent of patients’ exposure to the drug (duration and the number of patients), we simulated the number of adverse events to be observed after specified intervals of exposure. This was done by applying different sets of hazard functions for a Weibull distribution under the circumstances that a certain number of patients has dropped out, focusing on rare and delayed adverse events associated with chronically used drugs. By using the result of these simulations, we point out potential problems of underestimating adverse event rates in situations where the hazard rate of the event escalates over time. Patients drop-out from the study also deteriorates the ability to observe such time-dependent adverse events. The simulation can also serve as a useful tool to examine the necessary sample size and the duration of exposure in order to observe and characterize potentially expected adverse events. It is important to take the two key factors into consideration: the change of hazard function over time and the effect of drop-out in designing, analyzing, and evaluating safety studies for new drugs.

A note on population pharmacokinetic studies with a single sampling design.

The choice of sampling time point in a population pharmacokinetic study with severe limitation on the number of samples per study subject (single sampling design) is critical in obtaining reliable parameter estimates. The authors have investigated the relationship between the timing as well as the degree of distribution of a sampling point among study subjects and the reliability of the estimates of pharmacokinetic parameters in a population pharmacokinetic study. This was achieved through a simulation, assuming an intravenously administered drug whose pharmacokinetic profile follows a 1-compartment model. The convergence rate of the NLMIXED procedure as well as the values of bias and MSE for the estimated parameters showed great variability depending on the sampling schedules. The results indicate that, in the case of a single sampling design, the sampling points should be distributed as widely as possible over a time range along the concentration-time profile to obtain reliable parameter estimates.