Statistical Models Commons^™

Semiparametric Quantitative-Trait-Locus Mapping: Ii. On Censored Age-At-Onset, Ying Qing Chen, Chengcheng Hu, Rongling Wu

U.C. Berkeley Division of Biostatistics Working Paper Series

In genetic studies, the variation in genotypes may not only affect different inheritance patterns in qualitative traits, but may also affect the age-at-onset as quantitative trait. In this article, we use standard cross designs, such as backcross or F2, to propose some hazard regression models, namely, the additive hazards model in quantitative trait loci mapping for age-at-onset, although the developed method can be extended to more complex designs. With additive invariance of the additive hazards models in mixture probabilities, we develop flexible semiparametric methodologies in interval regression mapping without heavy computing burden. A recently developed multiple comparison procedures is adapted …

Nonparametric Methods For Analyzing Replication Origins In Genomewide Data, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Due to the advent of high-throughput genomic technology, it has become possible to globally monitor cellular activities on a genomewide basis. With these new methods, scientists can begin to address important biological questions. One such question involves the identification of replication origins, which are regions in chromosomes where DNA replication is initiated. In addition, one hypothesis regarding replication origins is that their locations are non-random throughout the genome. In this article, we develop methods for identification of and cluster inference regarding replication origins involving genomewide expression data. We compare several nonparametric regression methods for the identification of replication origin locations. …

Mean Response Models Of Repeated Measurements In Presence Of Varying Effectiveness Onset, Ying Qing Chen, Su-Chun Cheng

U.C. Berkeley Division of Biostatistics Working Paper Series

Repeated measurements are often collected over time to evaluate treatment efficacy in clinical trials. Most of the statistical models of the repeated measurements have been focusing on their mean response as function of time. These models usually assume that the treatment has persistent effect of constant additivity or multiplicity on the mean response functions throughout the observation period of time. In reality, however, such assumption may be confounded by the potential existence of the so-called effectiveness action onset, although they are often unobserved or difficult to obtain. Instead of including nonparametric time-varying coefficients in the mean response models, we propose …

Semiparametric Methods For Identification Of Tumor Progression Genes From Microarray Data, Debashis Ghosh, Arul Chinnaiyan

The University of Michigan Department of Biostatistics Working Paper Series

The use of microarray data has become quite commonplace in medical and scientific experiments. We focus here on microarray data generated from cancer studies. It is potentially important for the discovery of biomarkers to identify genes whose expression levels correlate with tumor progression. In this article, we develop statistical procedures for the identification of such genes, which we term tumor progression genes. Two methods are considered in this paper. The first is use of a proportional odds procedure, combined with false discovery rate estimation techniques to adjust for the multiple testing problem. The second method is based on order-restricted estimation …

The False Discovery Rate: A Variable Selection Perspective, Debashis Ghosh, Wei Chen, Trivellore E. Raghuanthan

The University of Michigan Department of Biostatistics Working Paper Series

In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to …

Combining Predictors For Classification Using The Area Under The Roc Curve, Margaret S. Pepe, Tianxi Cai, Zheng Zhang

UW Biostatistics Working Paper Series

We compare simple logistic regression with an alternative robust procedure for constructing linear predictors to be used for the two state classification task. Theoritical advantages of the robust procedure over logistic regression are: (i) although it assumes a generalized linear model for the dichotomous outcome variable, it does not require specification of the link function; (ii) it accommodates case-control designs even when the model is not logistic; and (iii) it yields sensible results even when the generalized linear model assumption fails to hold. Surprisingly, we find that the linear predictor derived from the logistic regression likelihood is very robust in …

Seasonal Analyses Of Air Pollution And Mortality In 100 U.S. Cities, Roger D. Peng, Francesca Dominici, Roberto Pastor-Barriuso, Scott L. Zeger, Jonathan M. Samet

Johns Hopkins University, Dept. of Biostatistics Working Papers

Time series models relating short-term changes in air pollution levels to daily mortality counts typically assume that the effects of air pollution on the log relative rate of mortality do not vary with time. However, these short-term effects might plausibly vary by season. Changes in the sources of air pollution and meteorology can result in changes in characteristics of the air pollution mixture across seasons. The authors develop Bayesian semi-parametric hierarchical models for estimating time-varying effects of pollution on mortality in multi-site time series studies. The methods are applied to the updated National Morbidity and Mortality Air Pollution Study database …

Semiparametric Regression Analysis Of Mean Residual Life With Censored Survival Data, Ying Qing Chen, Su-Chun Cheng

U.C. Berkeley Division of Biostatistics Working Paper Series

As a function of time t, mean residual life is the remaining life expectancy of a subject given survival up to t. The proportional mean residual life model, proposed by Oakes & Dasu (1990), provides an alternative to the Cox proportional hazards model to study the association between survival times and covariates. In the presence of censoring, we develop semiparametric inference procedures for the regression coefficients of the Oakes-Dasu model using martingale theory for counting processes. We also present simulation studies and an application to the Veterans' Administration lung cancer data.

Nonparametric And Semiparametric Inference For Models Of Tumor Size And Metastasis, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been some recent work in the statistical literature for modelling the relationship between the size of primary cancers and the occurrences of metastases. While nonparametric methods have been proposed for estimation of the tumor size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to nonparametric and semiparametric analysis of modelling tumor size-metastasis data in this article. An equivalence between the models considered by previous authors with survival data …

Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been much work on developing statistical procedures for associating tumor size with the probability of detecting a metastasis. Recently, Ghosh (2004) developed a unified statistical framework in which equivalences with censored data structures and models for tumor size and metastasis were examined. Based on this framework, we consider model checking techniques for semiparametric regression models in this paper. The procedures are for checking the additive hazards model. Goodness of fit methods are described for assessing functional form of covariates as well as the additive hazards assumption. The finite-sample properties of the methods are assessed using simulation studies.

Binary Isotonic Regression Procedures, With Application To Cancer Biomarkers, Debashis Ghosh, Moulinath Banerjee, Pinaki Biswas

The University of Michigan Department of Biostatistics Working Paper Series

There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for …

Semiparametic Models And Estimation Procedures For Binormal Roc Curves With Multiple Biomarkers, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used for receiver operating characteristic (ROC) curve modelling when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We show that the Van der Waerden rank score …

On Corrected Score Approach For Proportional Hazards Model With Covariate Measurement Error, Xiao Song, Yijian Huang

UW Biostatistics Working Paper Series

In the presence of covariate measurement error with the proportional hazards model, several functional modeling methods have been proposed. These include the conditional score estimator (Tsiatis and Davidian, 2001), the parametric correction estimator (Nakamura, 1992) and the nonparametric correction estimator (Huang and Wang, 2000, 2003) in the order of weaker assumptions on the error. Although they are all consistent, each suffers from potential difficulties with small samples and substantial measurement error. In this article, upon noting that the conditional score and parametric correction estimators are asymptotically equivalent in the case of normal error, we investigate their relative finite sample performance …

Classification Using Generalized Partial Least Squares, Beiying Ding, Robert Gentleman

Bioconductor Project Working Papers

The advances in computational biology have made simultaneous monitoring of thousands of features possible. The high throughput technologies not only bring about a much richer information context in which to study various aspects of gene functions but they also present challenge of analyzing data with large number of covariates and few samples. As an integral part of machine learning, classification of samples into two or more categories is almost always of interest to scientists. In this paper, we address the question of classification in this setting by extending partial least squares (PLS), a popular dimension reduction tool in chemometrics, in …

Covariate Adjustment In The Analysis Of Microarray Data From Clinical Studies, Debashis Ghosh, Arul Chinnaiyan

The University of Michigan Department of Biostatistics Working Paper Series

There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for followup validation studies. We develop two approaches to the analysis of microarray data in nonrandomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic curve for the analysis of gene expression …

Regulatory Motif Finding By Logic Regression, Sunduz Keles, Mark J. Van Der Laan, Chris Vulpe

U.C. Berkeley Division of Biostatistics Working Paper Series

Multiple transcription factors coordinately control transcriptional regulation of genes in eukaryotes. Although multiple computational methods consider the identification of individual transcription factor binding sites (TFBSs), very few focus on the interactions between these sites. We consider finding transcription factor binding sites and their context specific interactions using microarray gene expression data. We devise a hybrid approach called LogicMotif composed of a TFBS identification method combined with the new regression methodology logic regression of Ruczinski et al. (2003). LogicMotif has two steps: First potential binding sites are identified from transcription control regions of genes of interest. Various available methods can be …

A Statistical Method For Constructing Transcriptional Regulatory Networks Using Gene Expression And Sequence Data , Biao Xing, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Transcriptional regulation is one of the most important means of gene regulation. Uncovering transcriptional regulatory network helps us to understand the complex cellular process. In this paper, we describe a comprehensive statistical approach for constructing the transcriptional regulatory network using data of gene expression, promoter sequence, and transcription factor binding sites. Our simulation studies show that the overall and false positive error rates in the estimated transcriptional regulatory network are expected to be small if the systematic noise in the constructed feature matrix is small. Our analysis based on 658 microarray experiments on yeast gene expression programs and 46 transcription …

Error Models For Microarray Intensities, Wolfgang Huber, Anja Von Heydebreck, Martin Vingron

Bioconductor Project Working Papers

We derive the additive-multiplicative error model for microarray intensities, and describe two applications. For the detection of differentially expressed genes, we obtain a statistic whose variance is approximately independent of the mean intensity. For the post hoc calibration (normalization) of data with respect to experimental factors, we describe a method for parameter estimation.

A Bayesian Hierarchical Approach To Multirater Correlated Roc Analysis, Tim Johnson, Valen Johnson

The University of Michigan Department of Biostatistics Working Paper Series

In a common ROC study design, several readers are asked to rate diagnostics of the same cases processed under different modalities. We describe a Bayesian hierarchical model that facilitates the analysis of this study design by explicitly modeling the three sources of variation inherent to it. In so doing, we achieve substantial reductions in the posterior uncertainty associated with estimates of the differences in areas under the estimated ROC curves and corresponding reductions in the mean squared error (MSE) of these estimates. Based on simulation studies, both the widths of confidence intervals and MSE of estimates of differences in the …

Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …

A Bayesian Chi-Squared Test For Goodness Of Fit, Valen Johnson

The University of Michigan Department of Biostatistics Working Paper Series

This article describes an extension of classical x 2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involvesevaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptoti-cally distributed as a x2 random variable on K-1 degrees of freedom, indepen-dently of the dimension of the underlying parameter vector. By averaging over the posterior distribution of this statistic, a global goodness-of-fit diagnostic is obtained. Advantages of this diagnostic{which may be interpreted as the area under an ROC curve{include ease of interpretation, computational conve-nience, and favorable power properties. The proposed …

Individual Prediction In Prostate Cancer Studies Using A Joint Longitudinal-Survival-Cure Model, Menggang Yu, Jeremy Taylor, Howard M. Sandler

The University of Michigan Department of Biostatistics Working Paper Series

For monitoring patients treated for prostate cancer, Prostate Specific Antigen (PSA) is measured periodically after they receive treatment. Increases in PSA are suggestive of recurrence of the cancer and are used in making decisions about possible new treatments. The data from studies of such patients typically consist of longitudinal PSA measurements, censored event times and baseline covariates. Methods for the combined analysis of both longitudinal and survival data have been developed in recent years, with the main emphasis being on modeling and estimation. We analyze data from a prostate cancer study that has been extended by adding a mixture structure …

Mixture Models For Assessing Differential Expression In Complex Tissues Using Microarray Data, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

The use of DNA microarrays has become quite popular in many scientific and medical disciplines, such as in cancer research. One common goal of these studies is to determine which genes are differentially expressed between cancer and healthy tissue, or more generally, between two experimental conditions. A major complication in the molecular profiling of tumors using gene expression data is that the data represent a combination of tumor and normal cells. Much of the methodology developed for assessing differential expression with microarray data has assumed that tissue samples are homogeneous. In this article, we outline a general framework for determining …

Overlap Bias In The Case-Crossover Design, With Application To Air Pollution Exposures, Holly Janes, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

The case-crossover design uses cases only, and compares exposures just prior to the event times to exposures at comparable control, or “referent” times, in order to assess the effect of short-term exposure on the risk of a rare event. It has commonly been used to study the effect of air pollution on the risk of various adverse health events. Proper selection of referents is crucial, especially with air pollution exposures, which are shared, highly seasonal, and often have a long term time trend. Hence, careful referent selection is important to control for time-varying confounders, and in order to ensure that …

Robust Likelihood-Based Analysis Of Multivariate Data With Missing Values, Rod Little, An Hyonggin

The University of Michigan Department of Biostatistics Working Paper Series

The model-based approach to inference from multivariate data with missing values is reviewed. Regression prediction is most useful when the covariates are predictive of the missing values and the probability of being missing, and in these circumstances predictions are particularly sensitive to model misspecification. The use of penalized splines of the propensity score is proposed to yield robust model-based inference under the missing at random (MAR) assumption, assuming monotone missing data. Simulation comparisons with other methods suggest that the method works well in a wide range of populations, with little loss of efficiency relative to parametric models when the latter …

Uncertainty And The Value Of Diagnostic Information With Application To Axillary Lymph Node Dissection In Breast Cancer, Giovanni Parmigiani

Johns Hopkins University, Dept. of Biostatistics Working Papers

In clinical decision making, it is common to ask whether, and how much, a diagnostic procedure is contributing to subsequent treatment decisions. Statistically, quantification of the value of the information provided by a diagnostic procedure can be carried out using decision trees with multiple decision points, representing both the diagnostic test and the subsequent treatments that may depend on the test's results. This article investigates probabilistic sensitivity analysis approaches for exploring and communicating parameter uncertainty in such decision trees. Complexities arise because uncertainty about a model's inputs determines uncertainty about optimal decisions at all decision nodes of a tree. We …

Marginalized Transition Models For Longitudinal Binary Data With Ignorable And Nonignorable Dropout, Brenda F. Kurland, Patrick J. Heagerty

UW Biostatistics Working Paper Series

We extend the marginalized transition model of Heagerty (2002) to accommodate nonignorable monotone dropout. Using a selection model, weakly identified dropout parameters are held constant and their effects evaluated through sensitivity analysis. For data missing at random (MAR), efficiency of inverse probability of censoring weighted generalized estimating equations (IPCW-GEE) is as low as 40% compared to a likelihood-based marginalized transition model (MTM) with comparable modeling burden. MTM and IPCW-GEE regression parameters both display misspecification bias for MAR and nonignorable missing data, and both reduce bias noticeably by improving model fit

Marginal Modeling Of Multilevel Binary Data With Time-Varying Covariates, Diana Miglioretti, Patrick Heagerty

UW Biostatistics Working Paper Series

We propose and compare two approaches for regression analysis of multilevel binary data when clusters are not necessarily nested: a GEE method that relies on a working independence assumption coupled with a three-step method for obtaining empirical standard errors; and a likelihood-based method implemented using Bayesian computational techniques. Implications of time-varying endogenous covariates are addressed. The methods are illustrated using data from the Breast Cancer Surveillance Consortium to estimate mammography accuracy from a repeatedly screened population.

Survival Model Predictive Accuracy And Roc Curves, Patrick Heagerty, Yingye Zheng

UW Biostatistics Working Paper Series

The predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model, or R^2, commonly used for continuous response models, or using extensions of sensitivity and specificity which are commonly used for binary response models.

In this manuscript we propose new time-dependent accuracy summaries based on time-specific versions of sensitivity and specificity calculated over risk sets. We connect the accuracy summaries to a previously proposed global concordance measure which is a variant of Kendall's tau. In addition, we show how standard Cox regression output can be used to obtain estimates of …

Partly Conditional Survival Models For Longitudinal Data, Yingye Zheng, Patrick Heagerty

UW Biostatistics Working Paper Series

It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript we decouple the time scale for modeling the hazard from the time scale for accrual …