Showing papers by "Pranab Kumar Sen published in 2013"

Robust Analysis of High Throughput Screening (HTS) Assay Data

Abstract: Quantitative high throughput screening (qHTS) assays use cells or tissues to screen thousands of compounds in a short period of time Data generated from qHTS assays are then evaluated using nonlinear regression models, such as the Hill model, and decisions regarding toxicity are made using the estimates of the parameters of the model For any given compound, the variability in the observed response may either be constant across dose groups (homoscedasticity) or vary with dose (heteroscedasticity) Since thousands of compounds are simultaneously evaluated in a qHTS assay, it is not practically feasible for an investigator to perform residual analysis to determine the variance structure before performing statistical inferences on each compound Since it is well known that the variance structure plays an important role in the analysis of linear and nonlinear regression models, it is therefore important to have practically useful and easy to interpret methodology that is robust to the variance structure Fur

Supplementary Material: Robust Analysis of High Throughput Screening (HTS) Assay Data

Abstract: This is supplementary material for the article Robust Analysis of High Throughput Screening (HTS) Assay Data.

U-tests for variance components in linear mixed models

Abstract: We propose a U-statistics-based test for null variance components in linear mixed models and obtain its asymptotic distribution (for increasing number of units) under mild regularity conditions that include only the existence of the second moment for the random effects and of the fourth moment for the conditional errors. We employ contiguity arguments to derive the distribution of the test under local alternatives assuming additionally the existence of the fourth moment of the random effects. Our proposal is easy to implement and may be applied to a wide class of linear mixed models. We also consider a simulation study to evaluate the behaviour of the U-test in small and moderate samples and compare its performance with that of exact F-tests and of generalized likelihood ratio tests obtained under the assumption of normality. A practical example in which the normality assumption is not reasonable is included as illustration.

Robust nonlinear regression in applications

Abstract: Robust statistical methods, such as M-estimators, are needed for nonlinear regression models because of the presence of outliers/influential observations and heteroscedasticity. Outliers and influential observations are commonly observed in many applications, especially in toxicology and agricultural experiments. For example, dose response studies, which are routinely conducted in toxicology and agriculture, sometimes result in potential outliers, especially in the high dose groups. This is because response to high doses often varies among experimental units (e.g., animals). Consequently, this may result in outliers (i.e., very low values) in that group. Unlike the linear models, in nonlinear models the outliers not only impact the point estimates of the model parameters but can also severely impact the estimate of the information matrix. Note that, the information matrix in a nonlinear model is a function of the model parameters. This is not the case in linear models. In addition to outliers, heteroscedasticity is a major concern when dealing with nonlinear models. Ignoring heteroscedasticity may lead to inaccurate coverage probabilities and Type I error rates. Robustness to outliers/influential observations and to heteroscedasticity is even more important when dealing with thousands of nonlinear regression models in quantitative high throughput screening assays. Recently, these issues have been studied very extensively in the literature (references are provided in this paper), where the proposed estimator is robust to outliers/influential observations as well as to heteroscedasticity. The focus of this paper is to provide the theoretical underpinnings of robust procedures developed recently.

Rank Tests for Corrupted Linear Models

Abstract: For some variants of regression models, including partial, measurement error or error-in-variables, latent effects, semi-parametric and otherwise corrupted linear models, the classical parametric tests generally do not perform well. Various modifications and generalizations considered extensively in the literature rests on stringent regularity assumptions which are not likely to be tenable in many applications. However, in such non-standard cases, rank based tests can be adapted better, and further, incorporation of rank analysis of covariance tools enhance their power-efficiency. Numerical studies and a real data illustration show the superiority of rank based inference in such corrupted linear models.

On Nonparametric Estimation of the Density of a Non-Negative Function of Observations

Abstract: Let {X1, ..., Xn} be a random sample from a continuous distribution F defined on the k−dimensional Euclidean space Rk, for some k ≥ 1. In many statistical applications we are interested in statistical properties of a function h(X1, ..., Xm) of m ≥ 1 observations. Frees (1994, J. Amer. Stat. Assoc.) considered estimating the density function g associated with the distribution function G(t) = P ( h(X1, ..., Xm) ≤ t ) using the kernel method. In many applications, though, the functions of interest are non-negative where the usual symmetric kernels applied in the kernel density estimation are not appropriate. This paper adapts the alternative density estimator developed in Chaubey and Sen (1996, Statistics and Decisions) by smoothing the so called empirical kernel distribution function:

Some Statistical Perspectives of Growth Models in Health Care Plans

Abstract: Growth (and wear) curve models, having genesis in epidemiology and system biology, have cropped up in every walk of life and science. In statistics, such growth curve models have led to an evolution of multivariate analysis with better performance characteristics and enhanced scope of applications in many interdisciplinary field of research. Recent advances in bioinformatics and genomic science have opened the Pandora’s box with high-dimensional data models, often with relatively smaller sample sizes. Growth curve models are especially useful in such contexts. There are also other areas where growth curve model-based analyses are in high demand. In this vein, the scope and perspectives of growth models are appraised with special emphasis on some health care and health study plans.

A hierarchical functional data analytic approach for analyzing physiologically based pharmacokinetic models

Abstract: Ordinary differential equation (ODE) based models find application in a wide variety of biological and physiological phenomena. For instance, they arise in the description of gene regulatory networks, study of viral dynamics and other infectious diseases, etc. In the field of toxicology, they are used in physiologically based pharmacokinetic (PBPK) models for describing absorption, distribution, metabolism and excretion (ADME) of a chemical in-vivo. Knowledge about the model parameters is important for understanding the mechanism of action of a chemical and are often estimated using non-linear least squares methodology. However, there are several challenges associated with the usual methodology. Using functional data analytic methodology, in this article we develop a general framework for drawing inferences on parameters in models described by a system of differential equations. The proposed methodology takes into account variability between and within experimental units. The performance of the proposed methodology is evaluated using a simulation study and data obtained from a benzene inhalation study. We also describe a R-based software developed towards this purpose.

On Nonparametric Estimators of the Density of aNon-negative Function of Observations

Abstract: Let {X1, ..., Xn} be a random sample from a continuous distribution F defined on the k−dimensional Euclidean space Rk, for some k ≥ 1. In many statistical applications we are interested in statistical properties of a function q(X1, ..., Xm) of m ≥ 1 observations. Frees (1994, J. Amer. Stat. Assoc.) considered estimating the density function g associated with the distribution function G(t) = P ( h(X1, ..., Xm) ≤ t ) using the kernel method. In many applications, though, the functions of interest are non-negative where the usual symmetric kernels applied in the kernel density estimation are not appropriate. This paper adapts the alternative density estimator developed in Chaubey and Sen (1996, Statistics and Decisions) by smoothing the so called empirical kernel distribution function: