Confirmatory analysis for phase III population pharmacokinetics

Population pharmacokinetics (POPPK) has many important uses at various stages of drug development and approval. At the phase III stage, one of the major uses of POPPK is to identify covariate influences on human pharmacokinetics, which is important for potential dose adjustment and drug labeling. One common analysis approach is nonlinear mixed‐effect modeling, which typically involves time‐consuming extensive search for best fits among a large number of possible models. We propose that the analysis goal can be better achieved with a more standard confirmatory statistical analysis approach, which uses a prespecified primary analysis and additional sensitivity analyses. We illustrate this approach using a phase III study data set and compare the result with that calculated using the common exploratory approach. We argue that the confirmatory approach not only substantially reduces analysis time but also yields more accurate and interpretable results. Some aspects of this confirmatory approach may also be extended to data analysis in earlier stages of clinical drug development, i.e. phase II and phase I. Copyright © 2009 John Wiley & Sons, Ltd.     

Multiple outliers detection in sparse high-dimensional regression

The presence of outliers would inevitably lead to distorted analysis and inappropriate prediction, especially for multiple outliers in high-dimensional regression, where the high dimensionality of the data might amplify the chance of an observation or multiple observations being outlying. Noting that the detection of outliers is not only necessary but also important in high-dimensional regression analysis, we, in this paper, propose a feasible outlier detection approach in sparse high-dimensional linear regression model. Firstly, we search a clean subset by use of the sure independence screening method and the least trimmed square regression estimates. Then, we define a high-dimensional outlier detection measure and propose a multiple outliers detection approach through multiple testing procedures. In addition, to enhance efficiency, we refine the outlier detection rule after obtaining a relatively reliable non-outlier subset based on the initial detection approach. By comparison studies based on Monte Carlo simulation, it is shown that the proposed method performs well for detecting multiple outliers in sparse high-dimensional linear regression model. We further illustrate the application of the proposed method by empirical analysis of a real-life protein and gene expression data.     

A Comparison of Multiple Outlier Detection Methods for Regression Data

The problem of outliers in statistical data has attracted many researchers for a long time. Consequently, numerous outlier detection methods have been proposed in the statistical literature. However, no consensus has emerged as to which method is uniformly better than the others or which one is recommended for use in practical situations. In this article, we perform an extensive comparative Monte Carlo simulation study to assess the performance of the multiple outlier detection methods that are either recently proposed or frequently cited in the outlier detection literature. Our simulation experiments include a wide variety of realistic and challenging regression scenarios. We give recommendations on which method is superior to others under what conditions.     

Assessing goodness-of-fit for evaluation of dose-proportionality

For the clinical development of a new drug, the determination of dose-proportionality is an essential part of the pharmacokinetic evaluations, which may provide early indications of non-linear pharmacokinetics and may help to identify sub-populations with divergent clearances. Prior to making any conclusions regarding dose-proportionality, the goodness-of-fit of the model must be assessed to evaluate the model performance. We propose the use of simulation-based visual predictive checks to improve the validity of dose-proportionality conclusions for complex designs. We provide an illustrative example and include a table to facilitate review by regulatory authorities.     

A comparison of models using removal effort to estimate animal abundance

This paper compares methods for modeling the probability of removal when variable amounts of removal effort are present. A hierarchical modeling framework can produce estimates of animal abundance and detection from replicated removal counts taken at different locations in a region of interest. A common method of specifying variation in detection probabilities across locations or replicates is with a logistic model that incorporates relevant detection covariates. As an alternative to this logistic model, we propose using a catch–effort (CE) model to account for heterogeneity in detection when a measure of removal effort is available for each removal count. This method models the probability of detection as a nonlinear function of removal effort and a removal probability parameter that can vary spatially. Simulation results demonstrate that the CE model can effectively estimate abundance and removal probabilities when average removal rates are large but both the CE and logistic models tend to produce biased estimates as average removal rates decrease. We also found that the CE model fits better than logistic models when estimating wild turkey abundance using harvest and hunter counts collected by the Minnesota Department of Natural Resources during the spring turkey hunting season.     

Bayesian scale space analysis of temporal changes in satellite images

We consider the detection of land cover changes using pairs of Landsat ETM+ satellite images. The images consist of eight spectral bands and to simplify the multidimensional change detection task, the image pair is first transformed to a one-dimensional image. When the transformation is non-linear, the true change in the images may be masked by complex noise. For example, when changes in the Normalized Difference Vegetation Index is considered, the variance of noise may not be constant over the image and methods based on image thresholding can be ineffective. To facilitate detection of change in such situations, we propose an approach that uses Bayesian statistical modeling and simulation-based inference. In order to detect both large and small scale changes, our method uses a scale space approach that employs multi-level smoothing. We demonstrate the technique using artificial test images and two pairs of real Landsat ETM+satellite images.     

Outlier detection in contingency tables using decomposable graphical models

For high-dimensional data, it is a tedious task to determine anomalies such as outliers. We present a novel outlier detection method for high-dimensional contingency tables. We use the class of decomposable graphical models to model the relationship among the variables of interest, which can be depicted by an undirected graph called the interaction graph. Given an interaction graph, we derive a closed-form expression of the likelihood ratio test (LRT) statistic and an exact distribution for efficient simulation of the test statistic. An observation is declared an outlier if it deviates significantly from the approximated distribution of the test statistic under the null hypothesis. We demonstrate the use of the LRT outlier detection framework on genetic data modeled by Chow–Liu trees.     

Two-stage Adaptive Designs in Nonlinear Mixed Effects Models: Application to Pharmacokinetics in Children

Nonlinear mixed effects models (NLMEM) are used in pharmacokinetics to analyse concentrations of patients during drug development, particularly for pediatric studies. Approaches based on the Fisher information matrix can be used to optimize their design. Local design needs some a priori parameter values which might be difficult to guess. Therefore, two-stage adaptive designs are useful to provide some flexibility. We implemented in the R function PFIM the Fisher matrix for two-stage designs in NLMEM. We evaluated, with simulations, the impact of one-stage and two-stage designs on the precision of parameter estimation when the true and a priori parameters are different.     

Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

We review and discuss numerical inversion of the characteristic function as a tool for obtaining cumulative distribution functions. With the availability of high-speed computing and symbolic computation software, the method is ideally suited for instructional purposes, particularly in the illustration of the inversion theorems covered in graduate probability courses. The method is also available as an alternative to asymptotic approximations, Monte Carlo, or bootstrap techniques when analytic expressions for the distribution function are not available. We illustrate the method with several examples, including one which is concerned with the detection of possible clusters of disease in an epidemiologic study.     

A geometric characterization of optimal designs for regression models with correlated observations

We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics.     

Multivariate outbreak detection

Online monitoring is needed to detect outbreaks of diseases such as influenza. Surveillance is also needed for other kinds of outbreaks, in the sense of an increasing expected value after a constant period. Information on spatial location or other variables might be available and may be utilized. We adapted a robust method for outbreak detection to a multivariate case. The relation between the times of the onsets of the outbreaks at different locations (or some other variable) was used to determine the sufficient statistic for surveillance. The derived maximum-likelihood estimator of the outbreak regression was semi-parametric in the sense that the baseline and the slope were non-parametric while the distribution belonged to the one-parameter exponential family. The estimator was used in a generalized-likelihood ratio surveillance method. The method was evaluated with respect to robustness and efficiency in a simulation study and applied to spatial data for detection of influenza outbreaks in Sweden.     

Outlier detection using difference-based variance estimators in multiple regression

In this article, we propose an outlier detection approach in a multiple regression model using the properties of a difference-based variance estimator. This type of a difference-based variance estimator was originally used to estimate error variance in a non parametric regression model without estimating a non parametric function. This article first employed a difference-based error variance estimator to study the outlier detection problem in a multiple regression model. Our approach uses the leave-one-out type method based on difference-based error variance. The existing outlier detection approaches using the leave-one-out approach are highly affected by other outliers, while ours is not because our approach does not use the regression coefficient estimator. We compared our approach with several existing methods using a simulation study, suggesting the outperformance of our approach. The advantages of our approach are demonstrated using a real data application. Our approach can be extended to the non parametric regression model for outlier detection.     

Maximin efficient design of experiment for exponential regression models

In this paper robust and efficient designs are derived for several exponential decay models. These models are widely used in chemistry, pharmacokinetics or microbiology. We propose a maximin approach, which determines the optimal design such that a minimum of the D-efficiencies (taken over a certain range) becomes maximal. Analytic solutions are derived if optimization is performed in the class of minimal supported designs. In general the optimal designs with respect to the maximin criterion have to be determined numerically and some properties of these designs are also studied. We also illustrate the benefits of our approach by reanalysing a data example from the literature.     

Nonparametric Estimation of the Number of Drug Users in Hong Kong Using Repeated Multiple Lists

We update a previous approach to the estimation of the size of an open population when there are multiple lists at each time point. Our motivation is 35 years of longitudinal data on the detection of drug users by the Central Registry of Drug Abuse in Hong Kong. We develop a two‐stage smoothing spline approach. This gives a flexible and easily implemented alternative to the previous method which was based on kernel smoothing. The new method retains the property of reducing the variability of the individual estimates at each time point. We evaluate the new method by means of a simulation study that includes an examination of the effects of variable selection. The new method is then applied to data collected by the Central Registry of Drug Abuse. The parameter estimates obtained are compared with the well known Jolly–Seber estimates based on single capture methods.     

Detection of Change Point in Nonparametric Function with Unit-Root Noise by Wavelet

A wavelet method is proposed to detect jumps in a function which is observed with unit-root noise. We obtain critical values at any scale and prove the consistency of wavelet detection when the nonparametric function is smooth. It shows that the estimation of the number and locations of change points are consistent when there are change points in the nonparametric function. Simulation study supports our method.     

Block bootstrap testing for changes in persistence with heavy-tailed innovations

This article considers the detection of changes in persistence in heavy-tailed series. We adopt a Dickey–Fuller-type ratio statistic and derive its null asymptotic distribution of test statistic. We find that the asymptotic distribution depends on the stable index, which is often typically unknown and difficult to estimate. Therefore, the block bootstrap method is proposed to detect changes without estimating κ. The empirical sizes and power values are investigated to show that the block bootstrap test is valid. Finally, the validity of the method is demonstrated by analyzing the exchange rate of RMB and US dollars.     

A simple diagnostic method of outlier detection for stationary Gaussian time series

In this paper we present a "model free' method of outlier detection for Gaussian time series by using the autocorrelation structure of the time series. We also present a graphic diagnostic method in order to distinguish an additive outlier (AO) from an innovation outlier (IO). The test statistic for detecting the outlier has a χ ² distribution with one degree of freedom. We show that this method works well when the time series contain either one type of the outliers or both additive and innovation type outliers, and this method has the advantage that no time series model needs to be estimated from the data. Simulation evidence shows that different types of outliers can be graphically distinguished by using the techniques proposed.     

Detection and Diagnosis of Distribution Changes of Degree Ratio in Complex Networks

The detection and diagnosis problems of distribution changes of degree ratio in complex networks are studied in this paper. We not only give the asymptotic expressions of the in-control and out-of-control average run lengths in detecting the distribution change by the cumulative sum chart, but also provide an effective and practicable method to transform the detection problem of the high dimensional Markov chain into a one-dimensional problem. Moreover, three multi-charts each based on the reference transition probabilities, the principal components, and the entropy statistics are presented to deal with the diagnosis problem. Finally, a real financial network which describes the dynamics and random correlations among 90 assets is investigated to demonstrate the detection and diagnosis performance of both the reference-free Cuscore chart and the multi-chart based on the entropy statistics.     

LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation

Parametric nonlinear mixed effects models (NLMEs) are now widely used in biometrical studies, especially in pharmacokinetics research and HIV dynamics models, due to, among other aspects, the computational advances achieved during the last years. However, this kind of models may not be flexible enough for complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been proposed as an extension of NLMEs. These models are a good compromise and retain nice features of both parametric and nonparametric models resulting in more flexible models than standard parametric NLMEs. However, SNMMs are complex models for which estimation still remains a challenge. Previous estimation procedures are based on a combination of log-likelihood approximation methods for parametric estimation and smoothing splines techniques for nonparametric estimation. In this work, we propose new estimation strategies in SNMMs. On the one hand, we use the Stochastic Approximation version of EM algorithm (SAEM) to obtain exact ML and REML estimates of the fixed effects and variance components. On the other hand, we propose a LASSO-type method to estimate the unknown nonlinear function. We derive oracle inequalities for this nonparametric estimator. We combine the two approaches in a general estimation procedure that we illustrate with simulations and through the analysis of a real data set of price evolution in on-line auctions.     

An online copy number variant detection method for short sequencing reads

The availability of the next generation sequencing (NGS) technology in today's biomedical research has provided new opportunities in scientific discovery of genetic information. The high-throughput NGS technology, especially DNA-seq, is particularly useful in profiling a genome for the analysis of DNA copy number variants (CNVs). The read count (RC) data resulting from NGS technology are massive and information rich. How to exploit the RC data for accurate CNV detection has become a computational and statistical challenge. We provide a statistical online change point method to help detect CNVs in the sequencing RC data in this paper. This method uses the idea of online searching for change point (or breakpoint) with a Markov chain assumption on the breakpoints loci and an iterative computing process via a Bayesian framework. We illustrate that an online change-point detection method is particularly suitable for identifying CNVs in the RC data. The algorithm is applied to the publicly available NCI-H2347 lung cancer cell line sequencing reads data for locating the breakpoints. Extensive simulation studies have been carried out and results show the good behavior of the proposed algorithm. The algorithm is implemented in R and the codes are available upon request.