Statistics and Probability Commons^™

Relative Risk Regression In Medical Research: Models, Contrasts, Estimators, And Algorithms, Thomas Lumley, Richard Kronmal, Shuangge Ma

UW Biostatistics Working Paper Series

The relative risk or prevalence ratio is a natural and familiar summary of association between a binary outcome and an exposure or intervention. For rare events, the relative risk can be approximately estimated by logistic regression. For common events estimation is more difficult. We review proposed estimation algorithms for relative risk regression. Some of these give inconsistent estimates or invalid standard errors. We show that the methods that give correct inference can be viewed as arising from a family of quasilikelihood estimating functions for the same generalized linear model, differing in their efficiency and in their robustness to outlying values …

The Combination Of Ecological And Case-Control Data, Sebastien Haneuse, Jon Wakefield

UW Biostatistics Working Paper Series

Ecological studies, in which data are available at the level of the group, rather than at the level of the individual, are susceptible to a range of biases due to their inability to characterize within-group variability in exposures and confounders. In order to overcome these biases, we propose a hybrid design in which ecological data are supplemented with a sample of individual-level case-control data. We develop the likelihood for this design and illustrate its benefits via simulation, both in bias reduction when compared to an ecological study, and in efficiency gains relative to a conventional case-control study. An interesting special …

The Combination Of Ecological And Case-Control Data, Sebastien Haneuse, Jon Wakefield

UW Biostatistics Working Paper Series

Ecological studies, in which data are available at the level of the group, rather than at the level of the individual, are susceptible to a range of biases due to their inability to characterize within-group variability in exposures and confounders. In order to overcome these biases, we propose a hybrid design in which ecological data are supplemented with a sample of individual-level case-control data. We develop the likelihood for this design and illustrate its benefits via simulation, both in bias reduction when compared to an ecological study, and in efficiency gains relative to a conventional case-control study. An interesting special …

Evaluating Causal Effect Predictiveness Of Candidate Surrogate Endpoints, Peter B. Gilbert, Michael Hudgens

UW Biostatistics Working Paper Series

Most methods for evaluating surrogate endpoints measure validity in terms of net effects (i.e., treatment effects adjusted for the biomarker measured after randomization). Frangakis and Rubin (2002, Biometrics) criticized these approaches because net effects may reflect selection bias, and suggested an alternative definition of a surrogate endpoint (a "principal" surrogate) based on causal effects. For evaluating principal surrogates we introduce a causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. The CEP surface is not identifiable in general due to missing potential outcomes. However, by incorporating …

Hierarchical Lévy Frailty Models And A Frailty Analysis Of Data On Infant Mortality In Norwegian Siblings, Tron Anders Moger, Odd O. Aalen

UW Biostatistics Working Paper Series

Distributions determined by non-negative Lévy processes, which include the power variance function (PVF) distributions among others, are commonly used as frailty distributions to model dependent survival times in family data. We present a hierarchical frailty model constructed by randomizing scale parameters, corresponding to time parameters of Lévy processes, in the Lévy frailty distributions. In its simplest form, this yields a two-model with heterogeneity the individual and family level. The family level frailty is shared within families, creating dependence. In the more complex models, it is extended to allow for several levels of dependence. This yields models with nested dependence structures …

Age- And Sex-Specific Transformations Of Health Status Measures To Incorporate Death, Ann M. Derleth, Paula Diehr

UW Biostatistics Working Paper Series

Introduction: Measures of health status and physical function do not usually include a specific code for death. This can cause problems in longitudinal studies because analyses limited to survivors may bias the results. One approach is to recode the status variables to include a reasonable value for death. One method that has been used is to replace each scale value with the estimated probability that a person with this value will be “healthy”. “Healthy” has been defined as being above a particular threshold on the variable of interest one year later, or alternatively as being in excellent, very good, or …

Integrating The Predictiveness Of A Marker With Its Performance As A Classifier, Margaret S. Pepe, Ziding Feng, Ying Huang, Gary M. Longton, Ross Prentice, Ian M. Thompson, Yingye Zheng

UW Biostatistics Working Paper Series

There are two popular statistical approaches to biomarker evaluation. One models the risk of disease (or disease outcome) using, for example, logistic regression. A marker is useful if it has a strong effect on risk. The second evaluates classification performance using measures such as sensitivity, specificity, predictive values and ROC curves. There is controversy about which approach is most appropriate. Moreover, the two approaches often give contradictory results on the same data. We present a new graphic, the predictiveness curve, that complements the risk modeling approach. It assesses the usefulness of a risk model when applied to the population. In …

A Marginalized Diffusion Model For Estimating Age At First Endoscopy Examination From Current Status Data, Diana Miglioretti, Elizabeth Brown

UW Biostatistics Working Paper Series

We propose an approach for estimating the age at first endoscopy examination from current status data collected via two series of cross-sectional surveys. To model the national probability of ever having an endoscopy, we incorporate birth cohort effects into a mixed-influence diffusion model. We link a state-specific model to the national-level diffusion model using a marginalized modeling approach. In future research, results from our model will be used as microsimulation model inputs to estimate the contribution of endoscopy examinations to observed changes in colorectal cancer incidence and mortality.

Reliability, Effect Size, And Responsiveness And Intraclass Correlation Of Health Status Measures Used In Randomized And Cluster-Randomized Trials, Paula Diehr, Lu Chen, Donald L. Patrick, Ziding Feng, Yutaka Yasui

UW Biostatistics Working Paper Series

Background: New health status instruments are described by psychometric properties, such as Reliability, Effect Size, and Responsiveness. For cluster-randomized trials, another important statistic is the Intraclass Correlation for the instrument within clusters. Studies using better instruments can be performed with smaller sample sizes, but better instruments may be more expensive in terms of dollars, lost opportunities, or poorer data quality due to the response burden of longer instruments. Investigators often need to estimate the psychometric properties of a new instrument, or of an established instrument in a new setting. Optimal sample sizes for estimating these properties have not been studied …

Adjusting For Covariate Effects On Classification Accuracy Using The Covariate-Adjusted Roc Curve, Holly Janes, Margaret S. Pepe

UW Biostatistics Working Paper Series

Recent scientific and technological innovations have produced an abundance of potential markers which are being investigated for their use in disease screen- ing and diagnosis. In evaluating these markers, it is often necessary to account for covariates which are associated with the marker of interest. These covariates may include subject characteristics, expertise of the test operator, test proce- dures, or aspects of specimen handling. In this paper, we propose the AROC, a covariate-adjusted measure of the classification accuracy. The AROC is the common covariate-specific ROC curve, when the covariate does not affect dis- crimination, and a weighted average of covariate-specific …

The Two-Sample Problem For Failure Rates Depending On A Continuous Mark: An Application To Vaccine Efficacy, Peter B. Gilbert, Ian W. Mckeague, Yanqing Sun

UW Biostatistics Working Paper Series

The efficacy of an HIV vaccine to prevent infection is likely to depend on the genetic variation of the exposing virus. This paper addresses the problem of using data on the HIV sequences that infect vaccine efficacy trial participants to 1) test for vaccine efficacy more powerfully than procedures that ignore the sequence data; and 2) evaluate the dependence of vaccine efficacy on the divergence of infecting HIV strains from the HIV strain that is contained in the vaccine. Because hundreds of amino acid sites in each HIV genome are sequenced, it is natural to treat the divergence (defined in …

Genome Scanning Methods For Comparing Sequences Between Groups, With Application To Hiv Vaccine Trials, Peter B. Gilbert, Chunyuan Wu, David V. Jobes

UW Biostatistics Working Paper Series

Consider a placebo-controlled preventive HIV vaccine efficacy trial. An HIV amino acid sequence is measured from each volunteer who acquires HIV, and these sequences are aligned together with the reference HIV sequence represented in the vaccine. We develop genome scanning methods to identify HIV positions at which the amino acids in sequences from infected vaccine recipients tend to be more divergent from the corresponding reference amino acid than the amino acids in sequences from infected placebo recipients. We consider five two-sample test statistics, based on Euclidean, Mahalanobis, and Kullback-Leibler divergence measures. Weights are incorporated to reflect biological information contained in …

2^K Factorials In Blocks Of Size 2, With Application To Two-Color Microarray Experiments, Kathleen F. Kerr

UW Biostatistics Working Paper Series

When a two-level design must be run in blocks of size two, there is a unique blocking scheme that enables estimation of all the main effects. Unfortunately this design does not enable estimation of any two-factor interactions. When the experimental goal is to estimate all main effects and two-factor interactions, it is necessary to combine replicates of the experiment that use different blocking schemes. In this paper we identify such designs for up to eight factors that enable estimation of all main effects and two-factor interactions with the fewest number of replications. In addition, we give a construction for general …

Evaluating The Predictiveness Of A Continuous Marker, Ying Huang, Margaret S. Pepe, Ziding Feng

UW Biostatistics Working Paper Series

Consider a continuous marker for predicting a binary outcome. For example, serum concentration of prostate specific antigen (PSA) may be used to calculate the risk of finding prostate cancer in a biopsy. In this paper we argue that the predictive capacity of a marker has to do with the population distribution of risk given the marker and suggest a graphical tool, the predictiveness curve, that displays this distribution. The display provides a common meaningful scale for comparing markers that may not be comparable on their original scales. Some existing measures of predictiveness are shown to be summary indices derived from …

Different Public Health Interventions Have Varying Effects, Paula Diehr, Anne B. Newman, Liming Cai, Ann Derleth

UW Biostatistics Working Paper Series

Objective: To compare performance of one-time health interventions to those that change the probability of transitioning from one health state to another. Study Design and Setting: We used multi-state life table methods to estimate the impact of eight types of interventions on several outcomes. Results: In a cohort beginning at age 65, curing all the sick persons at baseline would increase life expectancy by 0.23 years and increase years of healthy life by .54 years. An equal amount of improvement could be obtained with a 12% decrease in the probability of getting sick, a 16% increase in the probability of …

Case-Cohort Methods For Survival Data On Families From Routine Registers, Tron Anders Moger, Yudi Pawitan, Ørnulf Borgan

UW Biostatistics Working Paper Series

In the Nordic countries, there exist several registers containing information on diseases and risk factors for millions of individuals. This information can be linked into families by use of personal identification numbers, and represent a great opportunity for studying diseases that show familial aggregation. Due to the size of the registers, it is difficult to analyze the data by using traditional methods for multivariate survival analysis, such as frailty or copula models. Since the size of the cohort is known, case-cohort methods based on pseudo-likelihoods are suitable for analyzing the data. We present methods for sampling control families both with …

Comparison Of Haplotype-Based And Tree-Based Snp Imputation In Association Studies, James Y. Dai, Ingo Ruczinski, Michael Leblanc, Charles Kooperberg

UW Biostatistics Working Paper Series

Missing single nucleotide polymorphisms (SNPs) are quite common in genetic association studies. Subjects with missing SNPs are often discarded in analyses, which may seriously undermine the inference of SNP-disease association. In this article, we compare two haplotype-based imputation approaches and one regression tree-based imputation approach for association studies. The goal is to assess the imputation accuracy, and to evaluate the impact of imputation on parameter estimation. Haplotype-based approaches build on haplotype reconstruction by the expectation-maximization (EM) algorithm or a weighted EM (WEM) algorithm, depending on whether case-control status is taken into account. The tree-based approach uses a Gibbs sampler to …

Semiparametric Approaches For Joint Modeling Of Longitudinal And Survival Data With Time Varying Coefficients, Xiao Song, C.Y. Wang

UW Biostatistics Working Paper Series

We study joint modeling of survival and longitudinal data. There are two regression models of interest. The primary model is for survival outcomes, which are assumed to follow a time varying coefficient proportional hazards model. The second model is for longitudinal data, which are assumed to follow a random effects model. Based on the trajectory of a subject's longitudinal data, some covariates in the survival model are functions of the unobserved random effects. Estimated random effects are generally different from the unobserved random effects and hence this leads to covariate measurement error. To deal with covariate measurement error, we propose …

Alleviating Linear Ecological Bias And Optimal Design With Subsample Data, Adam Glynn, Jon Wakefield, Mark Handcock, Thomas Richardson

UW Biostatistics Working Paper Series

In this paper, we illustrate that combining ecological data with subsample data in situations in which a linear model is appropriate provides three main benefits. First, by including the individual level subsample data, the biases associated with linear ecological inference can be eliminated. Second, by supplementing the subsample data with ecological data, the information about parameters will be increased. Third, we can use readily available ecological data to design optimal subsampling schemes, so as to further increase the information about parameters. We present an application of this methodology to the classic problem of estimating the effect of a college degree …

Bayesian Analysis Of Cell-Cycle Gene Expression Data, Chuan Zhou, Jon Wakefield, Linda Breeden

UW Biostatistics Working Paper Series

The study of the cell-cycle is important in order to aid in our understanding of the basic mechanisms of life, yet progress has been slow due to the complexity of the process and our lack of ability to study it at high resolution. Recent advances in microarray technology have enabled scientists to study the gene expression at the genome-scale with a manageable cost, and there has been an increasing effort to identify cell-cycle regulated genes. In this chapter, we discuss the analysis of cell-cycle gene expression data, focusing on a model-based Bayesian approaches. The majority of the models we describe …

Empirical Likelihood Inference For The Area Under The Roc Curve, Gengsheng Qin, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

For a continuous-scale diagnostic test, the most commonly used summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC) that measures the accuracy of the diagnostic test. In this paper we propose an empirical likelihood approach for the inference of AUC. We first define an empirical likelihood ratio for AUC and show that its limiting distribution is a scaled chi-square distribution. We then obtain an empirical likelihood based confidence interval for AUC using the scaled chi-square distribution. This empirical likelihood inference for AUC can be extended to stratified samples and the resulting limiting distribution …

Interval Estimation For The Ratio And Difference Of Two Lognormal Means, Yea-Hung Chen, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Health research often gives rise to data that follow lognormal distributions. In two sample situations, researchers are likely to be interested in estimating the difference or ratio of the population means. Several methods have been proposed for providing confidence intervals for these parameters. However, it is not clear which techniques are most appropriate, or how their performance might vary. Additionally, methods for the difference of means have not been adequately explored. We discuss in the present article five methods of analysis. These include two methods based on the log-likelihood ratio statistic and a generalized pivotal approach. Additionally, we provide and …

Inferences In Censored Cost Regression Models With Empirical Likelihood, Xiao-Hua Zhou, Gengsheng Qin, Huazhen Lin, Gang Li

UW Biostatistics Working Paper Series

In many studies of health economics, we are interested in the expected total cost over a certain period for a patient with given characteristics. Problems can arise if cost estimation models do not account for distributional aspects of costs. Two such problems are 1) the skewed nature of the data and 2) censored observations. In this paper we propose an empirical likelihood (EL) method for constructing a confidence region for the vector of regression parameters and a confidence interval for the expected total cost of a patient with the given covariates. We show that this new method has good theoretical …

Confidence Intervals For Predictive Values Using Data From A Case Control Study, Nathaniel David Mercaldo, Xiao-Hua Zhou, Kit F. Lau

UW Biostatistics Working Paper Series

The accuracy of a binary-scale diagnostic test can be represented by sensitivity (Se), specificity (Sp) and positive and negative predictive values (PPV and NPV). Although Se and Sp measure the intrinsic accuracy of a diagnostic test that does not depend on the prevalence rate, they do not provide information on the diagnostic accuracy of a particular patient. To obtain this information we need to use PPV and NPV. Since PPV and NPV are functions of both the intrinsic accuracy and the prevalence of the disease, constructing confidence intervals for PPV and NPV for a particular patient in a population with …

Optimal Feature Selection For Nearest Centroid Classifiers, With Applications To Gene Expression Microarrays, Alan R. Dabney, John D. Storey

UW Biostatistics Working Paper Series

Nearest centroid classifiers have recently been successfully employed in high-dimensional applications. A necessary step when building a classifier for high-dimensional data is feature selection. Feature selection is typically carried out by computing univariate statistics for each feature individually, without consideration for how a subset of features performs as a whole. For subsets of a given size, we characterize the optimal choice of features, corresponding to those yielding the smallest misclassification rate. Furthermore, we propose an algorithm for estimating this optimal subset in practice. Finally, we investigate the applicability of shrinkage ideas to nearest centroid classifiers. We use gene-expression microarrays for …

A New Approach To Intensity-Dependent Normalization Of Two-Channel Microarrays, Alan R. Dabney, John D. Storey

UW Biostatistics Working Paper Series

A two-channel microarray measures the relative expression levels of thousands of genes from a pair of biological samples. In order to reliably compare gene expression levels between and within arrays, it is necessary to remove systematic errors that distort the biological signal of interest. The standard for accomplishing this is smoothing "MA-plots" to remove intensity-dependent dye bias and array-specific effects. However, MA methods require strong assumptions. We review these assumptions and derive several practical scenarios in which they fail. The "dye-swap" normalization method has been much less frequently used because it requires two arrays per pair of samples. We show …

Estimating A Treatment Effect With Repeated Measurements Accounting For Varying Effectiveness Duration, Ying Qing Chen, Jingrong Yang, Su-Chun Cheng

UW Biostatistics Working Paper Series

To assess treatment efficacy in clinical trials, certain clinical outcomes are repeatedly measured for same subject over time. They can be regarded as function of time. The difference in their mean functions between the treatment arms usually characterises a treatment effect. Due to the potential existence of subject-specific treatment effectiveness lag and saturation times, erosion of treatment effect in the difference may occur during the observation period of time. Instead of using ad hoc parametric or purely nonparametric time-varying coefficients in statistical modeling, we first propose to model the treatment effectiveness durations, which are the varying time intervals between the …

Is The Number Of Sick Persons In A Cohort Constant Over Time?, Paula Diehr, Ann Derleth, Anne Newman, Liming Cai

UW Biostatistics Working Paper Series

Objectives: To estimate the number of persons in a cohort who are sick, over time.

Methods: We calculated the number of sick persons in the Cardiovascular Health Study (CHS), a cohort study of older adults followed up to 14 years, using eight definitions of “healthy” and “sick”. We projected the number in each health state over time for a birth cohort.

Results: The number of sick persons in CHS was approximately constant for 14 years, for all definitions of “sick”. The estimated number of sick persons in the birth cohort was approximately constant from ages 55-75, after which it decreased. …

Marginal Regression Modeling Under Irregular, Biased Sampling, Petra Buzkova, Thomas Lumley

UW Biostatistics Working Paper Series

In longitudinal studies observations are often obtained at continuous subject-specific times. Frequently the availability of outcome data may be related to the outcome measure or other covariates that are related to the outcome measure. Under such biased sampling designs unadjusted regression analysis yield biased estimates. Building on the work of Lin & Ying (2001) that integrates counting processes techniques with longitudinal data settings we propose a class of estimators that can handle biased sampling. We call those estimators ``inverse--intensity--rate--ratio--weighted'' (IIRR) estimators. Of major focus is a mean--response model where we examine the marginal effect of the covariate X at time …

Longitudinal Data Analysis For Generalized Linear Models Under Irregular, Biased Sampling: Situations With Follow-Up Dependent On Outcome Or Auxiliary Outcome-Related Variables, Petra Buzkova, Thomas Lumley

UW Biostatistics Working Paper Series

In longitudinal studies, observations are often obtained at subject-specific observation times. Those times can be continuous times, not at a set of prespecified times. Frequently the observation times may be related to the outcome measure or other auxiliary variables that are related to the outcome measure but undesirable to condition upon in the regression model for outcome. Regression analysis unadjusted for such sampling designs yield biased estimates. Based on estimating equations, we propose a class of estimators in generalized linear regression models that can handle biased sampling under continuous observation times. We call those estimators ``inverse--intensity rate--ratio--weighted'' (IIRR) estimators. The …