Observational studies,clinical trials,and the women’s health initiative

The complementary roles fulfilled by observational studies and randomized controlled trials in the population science research agenda is illustrated using results from the Women’s Health Initiative (WHI). Comparative and joint analyses of clinical trial and observational study data can enhance observational study design and analysis choices, and can augment randomized trial implications. These concepts are described in the context of findings from the WHI randomized trials of postmenopausal hormone therapy and of a low-fat dietary pattern, especially in relation to coronary heart disease, stroke, and breast cancer. The role of biomarkers of exposure and outcome, including high-dimensional genomic and proteomic biomarkers, in the elucidation of disease associations, will also be discussed in these same contexts.     

High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics

We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical biomarkers. Based on the metaphor of statistically derived "factors" as representing biological "subpathway" structure, we explore the decomposition of fitted sparse factor models into pathway subcomponents and investigate how these components overlay multiple aspects of known biological activity. Our methodology is based on sparsity modeling of multivariate regression, ANOVA, and latent factor models, as well as a class of models that combines all components. Hierarchical sparsity priors address questions of dimension reduction and multiple comparisons, as well as scalability of the methodology. The models include practically relevant non-Gaussian/nonparametric components for latent structure, underlying often quite complex non-Gaussianity in multivariate expression patterns. Model search and fitting are addressed through stochastic simulation and evolutionary stochastic search methods that are exemplified in the oncogenic pathway studies. Supplementary supporting material provides more details of the applications, as well as examples of the use of freely available software tools for implementing the methodology.     

Risk Prediction for Prostate Cancer Recurrence Through Regularized Estimation with Simultaneous Adjustment for Nonlinear Clinical Effects

In biomedical studies, it is of substantial interest to develop risk prediction scores using high-dimensional data such as gene expression data for clinical endpoints that are subject to censoring. In the presence of well-established clinical risk factors, investigators often prefer a procedure that also adjusts for these clinical variables. While accelerated failure time (AFT) models are a useful tool for the analysis of censored outcome data, it assumes that covariate effects on the logarithm of time-to-event are linear, which is often unrealistic in practice. We propose to build risk prediction scores through regularized rank estimation in partly linear AFT models, where high-dimensional data such as gene expression data are modeled linearly and important clinical variables are modeled nonlinearly using penalized regression splines. We show through simulation studies that our model has better operating characteristics compared to several existing models. In particular, we show that there is a non-negligible effect on prediction as well as feature selection when nonlinear clinical effects are misspecified as linear. This work is motivated by a recent prostate cancer study, where investigators collected gene expression data along with established prognostic clinical variables and the primary endpoint is time to prostate cancer recurrence. We analyzed the prostate cancer data and evaluated prediction performance of several models based on the extended c statistic for censored data, showing that 1) the relationship between the clinical variable, prostate specific antigen, and the prostate cancer recurrence is likely nonlinear, i.e., the time to recurrence decreases as PSA increases and it starts to level off when PSA becomes greater than 11; 2) correct specification of this nonlinear effect improves performance in prediction and feature selection; and 3) addition of gene expression data does not seem to further improve the performance of the resultant risk prediction scores.     

A statistician's perspective on biomarkers in drug development

Biomarkers play an increasingly important role in many aspects of pharmaceutical discovery and development, including personalized medicine and the assessment of safety data, with heavy reliance being placed on their delivery. Statisticians have a fundamental role to play in ensuring that biomarkers and the data they generate are used appropriately and to address relevant objectives such as the estimation of biological effects or the forecast of outcomes so that claims of predictivity or surrogacy are only made based upon sound scientific arguments. This includes ensuring that studies are designed to answer specific and pertinent questions, that the analyses performed account for all levels and sources of variability and that the conclusions drawn are robust in the presence of multiplicity and confounding factors, especially as many biomarkers are multidimensional or may be an indirect measure of the clinical outcome. In all of these areas, as in any area of drug development, statistical best practice incorporating both scientific rigor and a practical understanding of the situation should be followed. This article is intended as an introduction for statisticians embarking upon biomarker-based work and discusses these issues from a practising statistician's perspective with reference to examples.     

Bayesian Weibull tree models for survival analysis of clinico-genomic data

An important goal of research involving gene expression data for outcome prediction is to establish the ability of genomic data to define clinically relevant risk factors. Recent studies have demonstrated that microarray data can successfully cluster patients into low- and high-risk categories. However, the need exists for models which examine how genomic predictors interact with existing clinical factors and provide personalized outcome predictions. We have developed clinico-genomic tree models for survival outcomes which use recursive partitioning to subdivide the current data set into homogeneous subgroups of patients, each with a specific Weibull survival distribution. These trees can provide personalized predictive distributions of the probability of survival for individuals of interest. Our strategy is to fit multiple models; within each model we adopt a prior on the Weibull scale parameter and update this prior via Empirical Bayes whenever the sample is split at a given node. The decision to split is based on a Bayes factor criterion. The resulting trees are weighted according to their relative likelihood values and predictions are made by averaging over models. In a pilot study of survival in advanced stage ovarian cancer we demonstrate that clinical and genomic data are complementary sources of information relevant to survival, and we use the exploratory nature of the trees to identify potential genomic biomarkers worthy of further study.     

Scalable module detection for attributed networks with applications to breast cancer

The objective of network module detection is to identify groups of nodes within a network structure that are tightly connected. Nodes in a network often have attributes (aka metadata) associated with them. It is often desirable to identify groups of nodes that are tightly connected in the network structure, but also have strong similarity in their attributes. Utilizing attribute information in module detection is a major challenge because it requires bridging the structural network with attribute data. A Weighted Fast Greedy (WFG) algorithm for attribute-based module detection is proposed. WFG utilizes logistic regression to bridge the structural and attribute spaces. The logistic function naturally emphasizes associations between attributes and network structure accordingly, and can be easily interpreted. A breast cancer application is presented that connects a protein–protein interaction network gene expression data and a survival outcome. This application demonstrates the importance of embedding attribute information into the community detection framework on a breast cancer dataset. Five modules were significant for survival and they contained known pathways and markers for cancer, including cell cycle, p53 pathway, BRCA1, BRCA2, and AURKB, among others. Whereas, neither the gene expression data nor the network structure alone gave rise to these cancer biomarkers and signatures.     

Conditional screening for ultra-high dimensional covariates with survival outcomes

Identifying important biomarkers that are predictive for cancer patients’ prognosis is key in gaining better insights into the biological influences on the disease and has become a critical component of precision medicine. The emergence of large-scale biomedical survival studies, which typically involve excessive number of biomarkers, has brought high demand in designing efficient screening tools for selecting predictive biomarkers. The vast amount of biomarkers defies any existing variable selection methods via regularization. The recently developed variable screening methods, though powerful in many practical setting, fail to incorporate prior information on the importance of each biomarker and are less powerful in detecting marginally weak while jointly important signals. We propose a new conditional screening method for survival outcome data by computing the marginal contribution of each biomarker given priorily known biological information. This is based on the premise that some biomarkers are known to be associated with disease outcomes a priori. Our method possesses sure screening properties and a vanishing false selection rate. The utility of the proposal is further confirmed with extensive simulation studies and analysis of a diffuse large B-cell lymphoma dataset. We are pleased to dedicate this work to Jack Kalbfleisch, who has made instrumental contributions to the development of modern methods of analyzing survival data.     

The additive hazards model with high-dimensional regressors

This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary cirrhosis clinical data.     

False Discovery Rate Control With Groups

In the context of large-scale multiple hypothesis testing, the hypotheses often possess certain group structures based on additional information such as Gene Ontology in gene expression data and phenotypes in genome-wide association studies. It is hence desirable to incorporate such information when dealing with multiplicity problems to increase statistical power. In this article, we demonstrate the benefit of considering group structure by presenting a p-value weighting procedure which utilizes the relative importance of each group while controlling the false discovery rate under weak conditions. The procedure is easy to implement and shown to be more powerful than the classical Benjamini-Hochberg procedure in both theoretical and simulation studies. By estimating the proportion of true null hypotheses, the data-driven procedure controls the false discovery rate asymptotically. Our analysis on one breast cancer dataset confirms that the procedure performs favorably compared with the classical method.     

Bayesian nonparametric statistics: A new toolkit for discovery in cancer research

Many commonly used statistical methods for data analysis or clinical trial design rely on incorrect assumptions or assume an over‐simplified framework that ignores important information. Such statistical practices may lead to incorrect conclusions about treatment effects or clinical trial designs that are impractical or that do not accurately reflect the investigator's goals. Bayesian nonparametric (BNP) models and methods are a very flexible new class of statistical tools that can overcome such limitations. This is because BNP models can accurately approximate any distribution or function and can accommodate a broad range of statistical problems, including density estimation, regression, survival analysis, graphical modeling, neural networks, classification, clustering, population models, forecasting and prediction, spatiotemporal models, and causal inference. This paper describes 3 illustrative applications of BNP methods, including a randomized clinical trial to compare treatments for intraoperative air leaks after pulmonary resection, estimating survival time with different multi‐stage chemotherapy regimes for acute leukemia, and evaluating joint effects of targeted treatment and an intermediate biological outcome on progression‐free survival time in prostate cancer.     

An Improved Method on Wilcoxon Rank Sum Test for Gene Selection from Microarray Experiments

Selecting a small subset out of the thousands of genes in microarray data is important for accurate classification of phenotypes. In this paper, we propose a flexible rank-based nonparametric procedure for gene selection from microarray data. In the method we propose a statistic for testing whether area under receiver operating characteristic curve (AUC) for each gene is equal to 0.5 allowing different variance for each gene. The contribution to this “single gene” statistic is the studentization of the empirical AUC, which takes into account the variances associated with each gene in the experiment. Delong et al. proposed a nonparametric procedure for calculating a consistent variance estimator of the AUC. We use their variance estimation technique to get a test statistic, and we focus on the primary step in the gene selection process, namely, the ranking of genes with respect to a statistical measure of differential expression. Two real datasets are analyzed to illustrate the methods and a simulation study is carried out to assess the relative performance of different statistical gene ranking measures. The work includes how to use the variance information to produce a list of significant targets and assess differential gene expressions under two conditions. The proposed method does not involve complicated formulas and does not require advanced programming skills. We conclude that the proposed methods offer useful analytical tools for identifying differentially expressed genes for further biological and clinical analysis.     

A review of cancer screening evaluation techniques, with some particular examples in breast cancer screening

Summary.  The instigation of mass screening for breast cancer has, over the last three decades, raised various statistical issues and led to the development of new statistical approaches. Initially, the design of screening trials was the main focus of research but, as the evidence in favour of population-based screening programmes mounts, a variety of other applications have also been identified. These include administrative and quality control tasks, for monitoring routine screening services, as well as epidemiological modelling of incidence and mortality. We review the commonly used methods of cancer screening evaluation, highlight some current issues in breast screening and, using examples from randomized trials and established screening programmes, illustrate the role that statistical science has played in the development of clinical research in this field.     

Markov chain models for multivariate repeated binary data analysis

Repeated categorical outcomes frequently occur in clinical trials. Muenz and Rubinstein (1985) presented Markov chain models to analyze binary repeated data in a breast cancer study. We extend their method to the setting when more than one repeated outcome variable is of interest. In a randomized clinical trial of breast cancer, we investigate the dependency of toxicities on predictor variables and the relationship among multiple toxic effects.     

Clustering microarray data using model-based double K-means

The microarray technology allows the measurement of expression levels of thousands of genes simultaneously. The dimension and complexity of gene expression data obtained by microarrays create challenging data analysis and management problems ranging from the analysis of images produced by microarray experiments to biological interpretation of results. Therefore, statistical and computational approaches are beginning to assume a substantial position within the molecular biology area. We consider the problem of simultaneously clustering genes and tissue samples (in general conditions) of a microarray data set. This can be useful for revealing groups of genes involved in the same molecular process as well as groups of conditions where this process takes place. The need of finding a subset of genes and tissue samples defining a homogeneous block had led to the application of double clustering techniques on gene expression data. Here, we focus on an extension of standard K-means to simultaneously cluster observations and features of a data matrix, namely double K-means introduced by Vichi (2000). We introduce this model in a probabilistic framework and discuss the advantages of using this approach. We also develop a coordinate ascent algorithm and test its performance via simulation studies and real data set. Finally, we validate the results obtained on the real data set by building resampling confidence intervals for block centroids.     

A new test for high-dimensional regression coefficients in partially linear models

Partially linear regression models are semiparametric models that contain both linear and nonlinear components. They are extensively used in many scientific fields for their flexibility and convenient interpretability. In such analyses, testing the significance of the regression coefficients in the linear component is typically a key focus. Under the high-dimensional setting, i.e., “large p, small n,” the conventional F-test strategy does not apply because the coefficients need to be estimated through regularization techniques. In this article, we develop a new test using a U-statistic of order two, relying on a pseudo-estimate of the nonlinear component from the classical kernel method. Using the martingale central limit theorem, we prove the asymptotic normality of the proposed test statistic under some regularity conditions. We further demonstrate our proposed test's finite-sample performance by simulation studies and by analyzing some breast cancer gene expression data.     

Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling

ABSTRACT

We introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from 97 breast cancer patients; moreover some simulations reveal that the proposed test is more powerful than its competitors previously discussed in literature.     

Ratio index variables or ANCOVA? Fisher's cats revisited

Over 60 years ago Ronald Fisher demonstrated a number of potential pitfalls with statistical analyses using ratio variables. Nonetheless, these pitfalls are largely overlooked in contemporary clinical and epidemiological research, which routinely uses ratio variables in statistical analyses. This article aims to demonstrate how very different findings can be generated as a result of less than perfect correlations among the data used to generate ratio variables. These imperfect correlations result from measurement error and random biological variation. While the former can often be reduced by improvements in measurement, random biological variation is difficult to estimate and eliminate in observational studies. Moreover, wherever the underlying biological relationships among epidemiological variables are unclear, and hence the choice of statistical model is also unclear, the different findings generated by different analytical strategies can lead to contradictory conclusions. Caution is therefore required when interpreting analyses of ratio variables whenever the underlying biological relationships among the variables involved are unspecified or unclear. Copyright © 2009 John Wiley & Sons, Ltd.     

Simultaneous Bayesian modeling of longitudinal and survival data in breast cancer patients

Abstract

Using simultaneous Bayesian modeling, an attempt is made to analyze data on the size of lymphedema occurring in the arms of breast cancer patients after breast cancer surgery (as the longitudinal data) and the time interval for disease progression (as the time-to-event occurrence). A model based on a multivariate skew t distribution is shown to provide the best fit. This outcome was confirmed by simulation studies too.