Physical Sciences and Mathematics Commons^™

Multiple Testing Procedures For Controlling Tail Probability Error Rates, Sandrine Dudoit, Mark J. Van Der Laan, Merrill D. Birkner

U.C. Berkeley Division of Biostatistics Working Paper Series

The present article discusses and compares multiple testing procedures (MTP) for controlling Type I error rates defined as tail probabilities for the number (gFWER) and proportion (TPPFP) of false positives among the rejected hypotheses. Specifically, we consider the gFWER- and TPPFP-controlling MTPs proposed recently by Lehmann & Romano (2004) and in a series of four articles by Dudoit et al. (2004), van der Laan et al. (2004b,a), and Pollard & van der Laan (2004). The former Lehmann & Romano (2004) procedures are marginal, in the sense that they are based solely on the marginal distributions of the test statistics, i.e., …

Multiple Testing Procedures: R Multtest Package And Applications To Genomics, Katherine S. Pollard, Sandrine Dudoit, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The Bioconductor R package multtest implements widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics. The current version of multtest provides MTPs for tests concerning means, differences in means, and regression parameters in linear and Cox proportional hazards models. Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of false positives and rejected hypotheses. These error rates include tail probabilities …

Semiparametric Regression In Capture-Recapture Modelling, O. Gimenez, C. Barbraud, Ciprian M. Crainiceanu, S. Jenouvrier, B.T. Morgan

Johns Hopkins University, Dept. of Biostatistics Working Papers

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in the survival process may be explained by incorporating relevant covariates. We develop nonparametric and semiparametric regression models for estimating survival in capture-recapture models. A fully Bayesian approach using MCMC simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adelie.

Semi-Parametric Single-Index Two-Part Regression Models, Xiao-Hua Zhou, Hua Liang

UW Biostatistics Working Paper Series

In this paper, we proposed a semi-parametric single-index two-part regression model to weaken assumptions in parametric regression methods that were frequently used in the analysis of skewed data with additional zero values. The estimation procedure for the parameters of interest in the model was easily implemented. The proposed estimators were shown to be consistent and asymptotically normal. Through a simulation study, we showed that the proposed estimators have reasonable finite-sample performance. We illustrated the application of the proposed method in one real study on the analysis of health care costs.

A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch

The University of Michigan Department of Biostatistics Working Paper Series

A goal of radiation therapy is to deliver maximum dose to the target tumor while minimizing complications due to irradiation of critical organs. Technological advances in 3D conformal radiation therapy has allowed great strides in realizing this goal, however complications may still arise. Critical organs may be adjacent to tumors or in the path of the radiation beam. Several mathematical models have been proposed that describe a relationship between dose and observed functional complication, however only a few published studies have successfully fit these models to data using modern statistical methods which make efficient use of the data. One complication …

Choice Of Monitoring Mechanism For Optimal Nonparametric Functional Estimation For Binary Data, Nicholas P. Jewell, Mark J. Van Der Laan, Stephen Shiboski

U.C. Berkeley Division of Biostatistics Working Paper Series

Optimal designs of dose levels in order to estimate parameters from a model for binary response data have a long and rich history. These designs are based on parametric models. Here we consider fully nonparametric models with interest focused on estimation of smooth functionals using plug-in estimators based on the nonparametric maximum likelihood estimator. An important application of the results is the derivation of the optimal choice of the monitoring time distribution function for current status observation of a survival distribution. The optimal choice depends in a simple way on the dose response function and the form of the functional. …

Semiparametric Binary Regression Under Monotonicity Constraints, Moulinath Banerjee, Pinaki Biswas, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to …

Deletion/Substitution/Addition Algorithm For Partitioning The Covariate Space In Prediction, Annette Molinaro, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a new method for predicting censored (and non-censored) clinical outcomes from a highly-complex covariate space. Previously we suggested a unified strategy for predictor construction, selection, and performance assessment. Here we introduce a new algorithm which generates a piecewise constant estimation sieve of candidate predictors based on an intensive and comprehensive search over the entire covariate space. This algorithm allows us to elucidate interactions and correlation patterns in addition to main effects.

Multiple Testing And Data Adaptive Regression: An Application To Hiv-1 Sequence Data, Merrill D. Birkner, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Analysis of viral strand sequence data and viral replication capacity could potentially lead to biological insights regarding the replication ability of HIV-1. Determining specific target codons on the viral strand will facilitate the manufacturing of target specific antiretrovirals. Various algorithmic and analysis techniques can be applied to this application. We propose using multiple testing to find codons which have significant univariate associations with replication capacity of the virus. We also propose using a data adaptive multiple regression algorithm to obtain multiple predictions of viral replication capacity based on an entire mutant/non-mutant sequence profile. The data set to which these techniques …

Data Adaptive Estimation Of The Treatment Specific Mean, Yue Wang, Oliver Bembom, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

An important problem in epidemiology and medical research is the estimation of the causal effect of a treatment action at a single point in time on the mean of an outcome, possibly within strata of the target population defined by a subset of the baseline covariates. Current approaches to this problem are based on marginal structural models, i.e., parametric models for the marginal distribution of counterfactural outcomes as a function of treatment and effect modifiers. The various estimators developed in this context furthermore each depend on a high-dimensional nuisance parameter whose estimation currently also relies on parametric models. Since misspecification …

Cholesky Residuals For Assessing Normal Errors In A Linear Model With Correlated Outcomes: Technical Report, E. Andres Houseman, Louise Ryan, Brent Coull

Harvard University Biostatistics Working Paper Series

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and …

Censored Linear Regression For Case-Cohort Studies, Bin Nan, Menggang Yu, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

Right censored data from a classical case-cohort design and a stratified case-cohort design are considered. In the classical case-cohort design, the subcohort is obtained as a simple random sample of the entire cohort, whereas in the stratified design, the subcohort is selected by independent Bernoulli sampling with arbitrary selection probabilities. For each design and under a linear regression model, methods for estimating the regression parameters are proposed and analyzed. These methods are derived by modifying the linear ranks tests and estimating equations that arise from full-cohort data using methods that are similar to the "pseudo-likelihood" estimating equation that has been …

Semiparametric Methods For Semi-Competing Risks Problem With Censoring And Truncation, Hongyu Jiang, Jason Fine, Richard J. Chappell

Harvard University Biostatistics Working Paper Series

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator …

Estimating The Retransformed Mean In A Heteroscedastic Two-Part Model, Alan H. Welsh, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Two distribution free estimators are proposed to estimate the mean of a dependent variable after fitting a semiparametric two-part heteroscedastic regression model to a transformation of the dependent variable. We show that the proposed estimators are consistent and have asymptotic normal distributions. We also compare their finite-sample performance in a simulation study. Finally, we illustrate the proposed methods in a real-world example of predicting in-patient health care costs.

History-Adjusted Marginal Structural Models And Statically-Optimal Dynamic Treatment Regimes, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at a final time point. However, the utility of these models for some applications has been limited by their inability to incorporate modification of the causal effect of treatment by time-varying covariates. …

A Hypothesis Test For The End Of A Common Source Outbreak, Ron Brookmeyer, Xiaojun You

Johns Hopkins University, Dept. of Biostatistics Working Papers

The objective of this paper is to develop a hypothesis testing procedure to determine whether a common source outbreak has ended. We do not assume that the calendar date of exposure to the pathogen is known. We assume an underlying parametric model for the incubation period distribution of a 2-paramter exponential model with a guarantee time, although the parameters are not assumed to be known. The hypothesis testing procedure is based on the spacings between ordered calendar dates of disease onset of the cases. A simulation study was performed to evaluate the robustness of the methods to a lognormal model …

Nonparametric Confidence Intervals For The One- And Two-Sample Problems, Xiao-Hua Zhou, Phillip Dinh

UW Biostatistics Working Paper Series

Confidence intervals for the mean of one sample and the difference in means of two independent samples based on the ordinary-t statistic suffer deficiencies when samples come from skewed distributions. In this article, we evaluate several existing techniques and propose new methods to improve coverage accuracy. The methods examined include the ordinary-t, the bootstrap-t, the biased-corrected acceleration (BCa) bootstrap, and three new intervals based on transformation of the t-statistic. Our study shows that our new transformation intervals and the bootstrap-t intervals give best coverage accuracy for a variety of skewed distributions; and that our new transformation intervals have shorter interval …

Effect Of Misreported Family History On Mendelian Mutation Prediction Models, Hormuzd A. Katki

Johns Hopkins University, Dept. of Biostatistics Working Papers

People with familial history of disease often consult with genetic counselors about their chance of carrying mutations that increase disease risk. To aid them, genetic counselors use Mendelian models that predict whether the person carries deleterious mutations based on their reported family history. Such models rely on accurate reporting of each member's diagnosis and age of diagnosis, but this information may be inaccurate. Commonly encountered errors in family history can significantly distort predictions, and thus can alter the clinical management of people undergoing counseling, screening, or genetic testing. We derive general results about the distortion in the carrier probability estimate …

Estimating A Survival Distribution With Current Status Data And High-Dimensional Covariates, Mark J. Van Der Laan, Aad Van Der Vaart

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider the inverse problem of estimating a survival distribution when the survival times are only observed to be in one of the intervals of a random bisection of the time axis. We are particularly interested in the case that high-dimensional and/or time-dependent covariates are available, and/or the survival events and censoring times are only conditionally independent given the covariate process. The method of estimation consists of regularizing the survival distribution by taking the primitive function or smoothing, estimating the regularized parameter by using estimating equations, and finally recovering an estimator for the parameter of interest.

Estimation Of Treatment Effects In Randomized Trials With Noncompliance And A Dichotomous Outcome , Mark J. Van Der Laan, Alan E. Hubbard, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non-compliance. Recent articles by Vansteelandt and Goethebeur (2003) and Robins and Rotnitzky (2004) have presented consistent and asymptotically linear estimators of a causal odds ratio, which rely, beyond correct specification of a model for the causal odds ratio, on a correctly specified model for a potentially high dimensional nuisance parameter. In this article we propose consistent, asymptotically linear and locally efficient estimators of a causal relative risk and a new parameter -- …

Studying Effects Of Primary Care Physicians And Patients On The Trade-Off Between Charges For Primary Care And Specialty Care Using A Hierarchical Multivariate Two-Part Model, John W. Robinson, Scott L. Zeger, Christopher B. Forrest

Johns Hopkins University, Dept. of Biostatistics Working Papers

Objective. To examine effects of primary care physicians (PCPs) and patients on the association between charges for primary care and specialty care in a point-of-service (POS) health plan.

Data Source. Claims from 1996 for 3,308 adult male POS plan members, each of whom was assigned to one of the 50 family practitioner-PCPs with the largest POS plan member-loads.

Study Design. A hierarchical multivariate two-part model was fitted using a Gibbs sampler to estimate PCPs' effects on patients' annual charges for two types of services, primary care and specialty care, the associations among PCPs' effects, and within-patient associations between charges for …

A Hierarchical Multivariate Two-Part Model For Profiling Providers' Effects On Healthcare Charges, John W. Robinson, Scott L. Zeger, Christopher B. Forrest

Johns Hopkins University, Dept. of Biostatistics Working Papers

Procedures for analyzing and comparing healthcare providers' effects on health services delivery and outcomes have been referred to as provider profiling. In a typical profiling procedure, patient-level responses are measured for clusters of patients treated by providers that in turn, can be regarded as statistically exchangeable. Thus, a hierarchical model naturally represents the structure of the data. When provider effects on multiple responses are profiled, a multivariate model rather than a series of univariate models, can capture associations among responses at both the provider and patient levels. When responses are in the form of charges for healthcare services and sampled …

Estimation Of Direct And Indirect Causal Effects In Longitudinal Studies, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is mediated by a given intermediate variable (the indirect effect of the treatment), and the component that is not mediated by that intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Under the assumption of no-unmeasured confounders, Robins & Greenland (1992) and Pearl (2000), develop two identifiability results for direct and indirect causal effects. They define an …

Linear Life Expectancy Regression With Censored Data, Ying Qing Chen, Su-Chun Cheng

U.C. Berkeley Division of Biostatistics Working Paper Series

Life expectancy, i.e., mean residual life function, has been of important practical and scientific interests to characterise the distribution of residual life. Regression models are often needed to model the association between life expectancy and its covariates. In this article, we consider a linear mean residual life model and further developed some inference procedures in presence of censoring. The new model and proposed inference procedure will be demonstrated by numerical examples and application to the well-known Stanford heart transplant data. Additional semiparametric efficiency calculation and information bound are also considered.

Non-Parametric Estimation Of Roc Curves In The Absence Of A Gold Standard, Xiao-Hua Zhou, Pete Castelluccio, Chuan Zhou

UW Biostatistics Working Paper Series

In evaluation of diagnostic accuracy of tests, a gold standard on the disease status is required. However, in many complex diseases, it is impossible or unethical to obtain such the gold standard. If an imperfect standard is used as if it were a gold standard, the estimated accuracy of the tests would be biased. This type of bias is called imperfect gold standard bias. In this paper we develop a maximum likelihood (ML) method for estimating ROC curves and their areas of ordinal-scale tests in the absence of a gold standard. Our simulation study shows the proposed estimates for the …

The Optimal Confidence Region For A Random Parameter, Hajime Uno, Lu Tian, L.J. Wei

Harvard University Biostatistics Working Paper Series

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide …

A Note On Empirical Likelihood Inference Of Residual Life Regression, Ying Qing Chen, Yichuan Zhao

U.C. Berkeley Division of Biostatistics Working Paper Series

Mean residual life function, or life expectancy, is an important function to characterize distribution of residual life. The proportional mean residual life model by Oakes and Dasu (1990) is a regression tool to study the association between life expectancy and its associated covariates. Although semiparametric inference procedures have been proposed in the literature, the accuracy of such procedures may be low when the censoring proportion is relatively large. In this paper, the semiparametric inference procedures are studied with an empirical likelihood ratio method. An empirical likelihood confidence region is constructed for the regression parameters. The proposed method is further compared …

Semiparametric Quantitative-Trait-Locus Mapping: I. On Functional Growth Curves, Ying Qing Chen, Rongling Wu

U.C. Berkeley Division of Biostatistics Working Paper Series

The genetic study of certain quantitative traits in growth curves as a function of time has recently been of major scientific interest to explore the developmental evolution processes of biological subjects. Various parametric approaches in the statistical literature have been proposed to study the quantitative-trait-loci (QTL) mapping of the growth curves as multivariate outcomes. In this article, we view the growth curves as functional quantitative traits and propose some semiparametric models to relax the strong parametric assumptions which may not be always practical in reality. Appropriate inference procedures are developed to estimate the parameters of interest which characterise the possible …

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 …

Quantification And Visualization Of Ld Patterns And Identification Of Haplotype Blocks, Yan Wang, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Classical measures of linkage disequilibrium (LD) between two loci, based only on the joint distribution of alleles at these loci, present noisy patterns. In this paper, we propose a new distance-based LD measure, R, which takes into account multilocus haplotypes around the two loci in order to exploit information from neighboring loci. The LD measure R yields a matrix of pairwise distances between markers, based on the correlation between the lengths of shared haplotypes among chromosomes around these markers. Data analysis demonstrates that visualization of LD patterns through the R matrix reveals more deterministic patterns, with much less noise, than …