Recent Advances in Biostatistics

The following sections are included:

• Contents

• Foreword

• Preface

• Overview

Benjamini, Krieger and Yekutieli (BKY, 2006) have given an adaptive method of controlling the false discovery rate (FDR) by incorporating an estimate of n₀, the number of true null hypotheses, into the FDR controlling method of Benjamini and Hochberg (BH, 1995). The BKY method improves the BH method in terms of the FDR control and power. Benjamini, Krieger and Yekutieli have proved that their method controls the FDR when the p-values are independent and provided numerical evidence showing that the control over the FDR continues to hold when the p-values have some type of positive dependence. In this paper, we propose an alternative adaptive method via a different estimate of n₀. Like the BKY method, this new method controls the FDR under the independence, and can maintain a control over the FDR, as shown numerically, under the same type of positive dependence of the p-values. More importantly, as our simulations indicate, the proposed method can often outperform the BKY method in terms of the FDR control and power, particularly when the correlation between the test statistics is moderately low or the proportion of true null hypotheses is very high. When applied to a real microarray data, the new method is seen to pick up a few more significant genes than the BKY method.

In multiple testing, the unknown proportion of true null hypotheses among all null hypotheses that are tested often plays an important role. In adaptive procedures this proportion is estimated and then used to derive more powerful multiple testing procedures. Hochberg and Benjamini (1990) first presented adaptive Holm and Hochberg procedures for controlling the familywise error rate (FWER). However, until now, no mathematical proof has been provided to demonstrate that these procedures control the FWER in finite samples. In this paper, we present new adaptive Holm and Hochberg procedures and prove they can control the FWER in finite samples under some common types of positive dependence. Through a small simulation study, we illustrate that these adaptive procedures are more powerful than the corresponding non-adaptive procedures.

Almost all multiple comparison and multiple endpoint procedures applied in experimental settings are designed to control the Family Wise Error Rate (FWER) at a prespecified level of α. Benjamini and Hochberg (1995) argued that in certain settings, requiring strict control of the FWER can be overly conservative. They suggested controlling the False Discovery Rate (FDR), defined as the expected proportion of true (null) hypotheses that are incorrectly rejected. When one or more of the hypotheses being tested uses a categorical data endpoint, it is possible to further increase the power of both FWER and FDR controlling procedures. Methods proposed by Tarone (1990) for FWER control and Gilbert (2005) for FDR control have increased power by using the discreteness in the distribution of the test statistic to essentially reduce the effective number of hypotheses considered for the multiplicity adjustment. A modified fully discrete FDR sequential procedure is introduced that uses the exact conditional distribution of potential study outcomes. The FDR control, and the potential gains in power were estimated using simulation. An application of the proposed FDR procedure in the setting of genetic data analysis is reviewed, and other potential uses of the method are discussed.

This paper studies the kernel assisted conditional Nelson-Aalen and Kaplan-Meier estimators. The presented results improve the existing ones in two aspects: (1) the asymptotic properties (uniform consistency, rate of convergence and almost sure iid representation) are extended to the entire support of the covariates by use of Müller-Wang boundary kernel; and (2) the order of the remainder terms in the iid representation is improved from (log n/(nh^d))^3/4 to log n/(nh^d) thanks to the exponential inequality for U-statistics of order two. These results are useful for semiparametric estimation based on a first stage nonparametric estimation.

We use a mixture model or cure model to simultaneously model the probability of a patient who will never experience the failure and the risk of death or onset of the disease for those at risk of eventual failure. The former is modeled through a nonstandard logistic regression model and the latter is modeled using a nonstandard Cox model. We allow the regression coefficients in the both models to change according to the unknown thresholds of covariates. We develop the semiparametric maximum likelihood estimation procedures through the EM algorithm. We also formulate the test statistics to test the existence of a change point in the covariate effects and its location for the latency survival model as well for the cure probability. A simulation study is conducted to check the performance of the proposed estimation and testing procedures. The procedure is demonstrated through an application to the melanoma survival study.

In this paper we present a fully Bayesian approach to model survival data using the piecewise exponential model (PEM) with random time grid. We assume a joint noninformative improper prior distribution for the time grid and the failure rates of the PEM, and show how the clustering structure of the product partition model can be adapted to accommodate improper prior distributions in the framework of the PEM. Properties of the model are discussed and the use of the proposed methodology is exemplified through the the analysis of a real data set. For comparison purposes, the results obtained are compared with those provided by other methods existing in the literature.

In many biomedical studies, each patient can experience events that can occur repeatedly over time. Modeling techniques have been developed to analyze recurrent time-to-event data assuming independent censoring, i.e., the censoring process is unrelated to the event failure process conditional on the covariates. However, this assumption may not hold in general. This would happen if, for instance, the subjects who are at higher risks of recurrent events tend to withdraw from the stud earlier. Another form of dependent censoring could occur due to terminal events, such as death. Two methods were recently proposed to account for dependent censoring with the marginal rate models for analysis of recurrent event data. This paper overviews these approaches and critically compare them through extensive simulation studies. The simulation results showed that the approaches are effective for handling dependent censoring when the source of informative censoring is correctly specified. Further research is still needed for more complex situations.

We here propose different Gibbs sampling algorithms in the context of the binary response regression models under the skew-probit link. We use latent variables, which is a technique widely use to attainment of the full posterior conditional distributions. Analytical expressions for the full conditional posterior distributions are obtained and presented. These algorithms are compared through two measures of efficiency, the average Euclidean update distance between interactions and the effective sample size. We conclude that the new algorithms are more efficient than the usual Gibbs sampling, where one of them leads to around 160% of improvement in the effective sample size measure. The developed procedures are illustrated with an application to a medical data set.

In many applications it is common to encounter data which depart from various modeling assumptions such as homogeneity of variances. The problem is further complicated by the existence of potential outliers and inuential observations. In such situations results based on ordinary least squares (OLS) and model based maximum likelihood (ML) methods may be inappropriate and even misleading. In this study a robust M-estimation based methodology for heteroscedastic nonlinear regression models is considered. An M-estimator is proposed and its asymptotic properties, including asymptotic normality, are studied under suitable regularity conditions. The proposed methodology is illustrated using a real example from toxicology.

We propose an inverse censoring weighted estimator of a survival function when the data are doubly censored but the left censoring variable is always observed. The proposed estimator reduces to the standard inverse censoring weighted estimator for right censored data, where there is no left censoring, and in that sense may be viewed as an extension of the latter estimator to the special double censoring scenario considered in this paper. However, the equivalence exhibited by the Kaplan–Meier and inverse censoring weighted estimators in the case of right censoring does not apply any more for the scenario studied here. Specifically, a Kaplan–Meier approach based on a modified risk set and the proposed inverse censoring approach lead to different estimators. Furthermore, when both censoring variables are always observed, as in the case of an AIDS clinical trial data set analyzed in this paper, an alternative inverse censoring weighted estimator can be computed using the additional available censoring information. We present the results of a numerical comparison study between the Kaplan–Meier type and the two inverse censoring weighted estimators.

As competing risks occur commonly in medical research, increased attention has been paid to competing risks data in recent years. In this article, we review fundamentals of cumulative incidence function, Gray test, and Fine and Gray model and illustrate competing risks data analysis using clinical datasets of hematopoietic stem cell transplantation. In addition, we present limitations o Fine and Gray model, model selection in competing risks regression analysis, power calculation, and computing tools.

Comparative genomic analyses of homologous protein sequences provide insight to molecular evolution of amino acid residues within species and across species. Here, we review our method of identifying statistically related amino acid positions from multiple sequence alignments of nonolfactory human G protein-coupled receptors. We apply the same algorithm to the homeodomain of homeobox proteins from different species. The method uncovers statistically related amino acid positions that may potentially be important for its structure and/or function.

One of the main applications of Positron Emission Tomography (PET) is to estimate the density of a neuroreceptor at each location throughout the brain by measuring the concentration of a radiotracer over time and modeling its kinetics. Several statistical approaches to modeling the kinetics have been proposed in the literature. In this article, we will first briefly review the PET imaging acquisition process and then focus on reviewing several kinetic models for PET data, including compartment models, graphical models , and Basis Pursuit. We will also briefly discuss how to model the plasma function (input function) and how to use metabolites to correct the input function.

Medical signs, symptoms and tests are usually imperfect, as is diagnosis (which depends on these signs, symptoms, and tests.) Latent class analysis is a statistical method that allows evaluation of these indicators, as well as diagnosis, without a gold standard. This chapter discusses latent class analysis and its extensions, and applies them in medical contexts.

When several treatment regimens are possible candidates for a large phase III study, but too few resources are available to evaluate each relative to a standard, conducting a multi-arm randomized selection trial is a useful strategy to remove inferior treatments from further consideration. When the study has a relatively quick endpoint, frequent interim monitoring of the trial becomes ethically and practically appealing. In this paper, we propose a class of sequential procedures designed to select a subset of treatments that offer clinically meaningful improvements over the control group, or to declare that no such subset exists. The proposed procedures are easy to implement, allow sequential elimination of inferior treatments and sequential recruitment of promising treatments while preserving the type I error rate, and can be applied on a flexible monitoring schedule in terms of calendar time.

The following sections are included:

• Index