Physical Sciences and Mathematics Commons^™

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 …

Semiparametric Estimation Of Time-Dependent: Roc Curves For Longitudinal Marker Data, Yingye Zheng, Patrick Heagerty

UW Biostatistics Working Paper Series

One approach to evaluating the strength of association between a longitudinal marker process and a key clinical event time is through predictive regression methods such as a time-dependent covariate hazard model. For example, a time-varying covariate Cox model specifies the instantaneous risk of the event as a function of the time-varying marker and additional covariates. In this manuscript we explore a second complementary approach which characterizes the distribution of the marker as a function of both the measurement time and the ultimate event time. Our goal is to flexibly extend the standard diagnostic accuracy concepts of sensitivity and specificity to …

A Corrected Pseudo-Score Approach For Additive Hazards Model With Longitudinal Covariates Measured With Error, Xiao Song, Yijian Huang

UW Biostatistics Working Paper Series

In medical studies, it is often of interest to characterize the relationship between a time-to-event and covariates, not only time-independent but also time-dependent. Time-dependent covariates are generally measured intermittently and with error. Recent interests focus on the proportional hazards framework, with longitudinal data jointly modeled through a mixed effects model. However, approaches under this framework depend on the normality assumption of the error, and might encounter intractable numerical difficulties in practice. This motivates us to consider an alternative framework, that is, the additive hazards model, under which little has been done when time-dependent covariates are measured with error. We propose …

Adjusting For Non-Ignorable Verification Bias In Clinical Studies For Alzheimer’S Disease, Xiao-Hua Zhou, Pete Castelluccio

UW Biostatistics Working Paper Series

A common problem for comparing the relative accuracy of two screening tests for Alzheimer’s disease (D) in a two-stage design study is verification bias. If the verification bias can be assumed to be ignorable, Zhou and Higgs (2000) have proposed a maximum likelihood approach to compare the relative accuracy of screening tests in a two-stage design study. However, if the verification mechanism also depends on the unobserved disease status, the ignorable assumption does not hold. In this paper, we discuss how to use a profile likelihood approach to compare the relative accuracy of two screening tests for AD without assuming …

Design Considerations For Efficient And Effective Microarray Studies, M. Kathleen Kerr

UW Biostatistics Working Paper Series

This paper describes the theoretical and practical issues in experimental design for gene expression microarrays. Specifically, this paper (1) discusses the basic principles of design (randomization, replication, and blocking) as they pertain to microarrays, and (2) provides some general guidelines for statisticians designing microarray studies.

A New Confidence Interval For The Difference Between Two Binomial Proportions Of Paired Data, Xiao-Hua Zhou, Gengsheng Qin

UW Biostatistics Working Paper Series

Motivated by a study on comparing sensitivities and specificities of two diagnostic tests in a paired design when the sample size is small, we first derived an Edgeworth expansion for the studentized difference between two binomial proportions of paired data. The Edgeworth expansion can help us understand why the usual Wald interval for the difference has poor coverage performance in the small sample size. Based on the Edgeworth expansion, we then derived a transformation based confidence interval for the difference. The new interval removes the skewness in the Edgeworth expansion; the new interval is easy to compute, and its coverage …

Improved Confidence Intervals For The Sensitivity At A Fixed Level Of Specificity Of A Continuous-Scale Diagnostic Test, Xiao-Hua Zhou, Gengsheng Qin

UW Biostatistics Working Paper Series

For a continuous-scale test, it is an interest to construct a confidence interval for the sensitivity of the diagnostic test at the cut-off that yields a predetermined level of its specificity (eg. 80%, 90%, or 95%). IN this paper we proposed two new intervals for the sensitivity of a continuous-scale diagnostic test at a fixed level of specificity. We then conducted simulation studies to compare the relative performance of these two intervals with the best existing BCa bootstrap interval, proposed by Platt et al. (2000). Our simulation results showed that the newly proposed intervals are better than the BCa bootstrap …

Bootstrap Confidence Intervals For Medical Costs With Censored Observations, Hongyu Jiang, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Medical costs data with administratively censored observations often arise in cost-effectiveness studies of treatments for life threatening diseases. Mean of medical costs incurred from the start of a treatment till death or certain timepoint after the implementation of treatment is frequently of interest. In many situations, due to the skewed nature of the cost distribution and non-uniform rate of cost accumulation over time, the currently available normal approximation confidence interval has poor coverage accuracy. In this paper, we proposed a bootstrap confidence interval for the mean of medical costs with censored observations. In simulation studies, we showed that the proposed …

New Intervals For The Difference Between Two Independent Binomial Proportions, Xiao-Hua Zhou, Min Tsao, Gengsheng Qin

UW Biostatistics Working Paper Series

In this paper we gave an Edgeworth expansion for the studentized difference of two binomial proportions. We then proposed two new intervals by correcting the skewness in the Edgeworth expansion in a direct and an indirect way. Such the bias-correct confidence intervals are easy to compute, and their coverage probabilities converge to the nominal level at a rate of O(n-½), where n is the size of the combined samples. Our simulation results suggest tat in finite samples the new interval based on the indirect method have the similar performance to the two best existing intervals in terms of coverage accuracy …

Linear Models For Microarray Data Analysis: Hidden Similarities And Differences, M. Kathleen Kerr

UW Biostatistics Working Paper Series

In the past several years many linear models have been proposed for analyzing two-color microarray data. As presented in the literature, many of these models appear dramatically different. However, many of these models are reformulations of the same basic approach to analyzing microarray data. This paper demonstrates the equivalence of some of these models. Attention is directed at choices in microarray data analysis that have a larger impact on the results than the choice of linear model.

A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In the analysis of observational studies, propensity score subclassification has been shown to be a powerful method for adjusting unbalanced covariates for the purpose of causal inferences. One practical difficulty in carrying out such an analysis is to obtain a correct variance estimate for such inferences, while reducing bias in the estimate of the treatment effect due to an imbalance in the measured covariates. In this paper, we propose a bootstrap procedure for the inferences concerning the average treatment effect; our bootstrap method is based on an extension of Efron’s bias-corrected accelerated (BCa) bootstrap confidence interval to a two-sample problem. …

Constrained Boundary Monitoring For Group Sequential Clinical Trials, Bart E. Burington, Scott S. Emerson

UW Biostatistics Working Paper Series

Group sequential stopping rules are often used during the conduct of clinical trials in order to attain more ethical treatment of patients and to better address efficiency concerns. Because the use of such stopping rules materially affects the frequentist operating characteristics of the hypothesis test, it is necessary to choose an appropriate stopping rule during the planning of the study. It is often the case, however, that the number and timing of interim analyses are not precisely known at the time of trial design, and thus the implementation of a particular stopping rule must allow for flexible determination of the …

Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten

UW Biostatistics Working Paper Series

PCR-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive" yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity when the target number is 0). However, estimating this "sensitivity curve" is problematic since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle …

Design Of The Hiv Prevention Trials Network (Hptn) Protocol 054: A Cluster Randomized Crossover Trial To Evaluate Combined Access To Nevirapine In Developing Countries, Jim Hughes, Robert L. Goldenberg, Catherine M. Wilfert, Megan Valentine, Kasonde G. Mwinga, Laura A. Guay, Francis Mmiro, Jeffrey S. A. Stringer

UW Biostatistics Working Paper Series

HPTN054 is a cluster randomized trial designed to compare two approaches to providing single dose nevirapine to HIV-seropositive mothers and their infants to prevent mother-to-child transmission of HIV in resource limited settings. A number of challenging issues arose during the design of this trial. Most importantly, the need to achieve high participation rates among pregnant, HIV-seropositive women in selected prenatal care clinics led us to develop a method of collecting anonymous and unlinked information on a key surrogate endpoint instead of pursuing linked and identified information on a clinical endpoint. In addition, since group counseling is the standard model for …

Selecting Differentially Expressed Genes From Microarray Experiments, Margaret S. Pepe, Gary M. Longton, Garnet L. Anderson, Michel Schummer

UW Biostatistics Working Paper Series

High throughput technologies, such as gene expression arrays and protein mass spectrometry, allow one to simultaneously evaluate thousands of potential biomarkers that distinguish different tissue types. Of particular interest here is cancer versus normal organ tissues. We consider statistical methods to rank genes (or proteins) in regards to differential expression between tissues. Various statistical measures are considered and we argue that two measures related to the Receiver Operating Characteristic Curve are particularly suitable for this purpose. We also propose that sampling variability in the gene rankings be quantified and suggest using the “selection probability function”, the probability distribution of rankings …

Semiparametric Receiver Operating Characteristic Analysis To Evaluate Biomarkers For Disease, Tianxi Cai, Margaret S. Pepe

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve is a popular method for characterizing the accuracy of diagnostic tests when test results are not binary. Various methodologies for estimating and comparing ROC curves have been developed. One approach, due to Pepe, uses a parametric regression model with the baseline function specified up to a finite-dimensional parameter. In this article we extend the regression models by allowing arbitrary nonparametric baseline functions. We also provide asymptotic distribution theory and procedures for making statistical inference. We illustrate our approach with dataset from a prostate cancer biomarker study. Simulation studies suggest that the extra flexibility inherent …

Semi-Parametric Regression For The Area Under The Receiver Operating Characteristic Curve, Lori E. Dodd, Margaret S. Pepe

UW Biostatistics Working Paper Series

Medical advances continue to provide new and potentially better means for detecting disease. Such is true in cancer, for example, where biomarkers are sought for early detection and where improvements in imaging methods may pick up the initial functional and molecular changes associated with cancer development. In other binary classification tasks, computational algorithms such as Neural Networks, Support Vector Machines and Evolutionary Algorithms have been applied to areas as diverse as credit scoring, object recognition, and peptide-binding prediction. Before a classifier becomes an accepted technology, it must undergo rigorous evaluation to determine its ability to discriminate between states. Characterization of …

Estimating Disease Prevalence In Two-Phase Studies, Todd A. Alonzo, Margaret S. Pepe

UW Biostatistics Working Paper Series

Disease prevalence is ideally estimated using a “gold standard” to ascertain true disease status on all subjects in a population of interest. In practice, however, the gold standard may be too costly or invasive to be applied to all subjects, in which case a two-phase design is often employed. Phase 1 data consisting of inexpensive and non-invasive screening tests on all study subjects are used to determine the subjects that receive the gold standard in the second phase. Naïve estimates of prevalence in two-phase studies can be biased (verification bias). Imputation and re-weighting estimators are often used to avoid this …

Partial Auc Estimation And Regression, Lori E. Dodd, Margaret S. Pepe

UW Biostatistics Working Paper Series

Accurate disease diagnosis is critical for health care. New diagnostic and screening tests must be evaluated for their abilities to discriminate disease from non-diseased states. The partial area under the ROC curve (partial AUC) is a measure of diagnostic test accuracy. We present an interpretation of the partial AUC that gives rise to a new non-parametric estimator. This estimator is more robust than existing estimators, which make parametric assumptions. We show that the robustness is gained with only a moderate loss in efficiency. We describe a regression modelling framework for making inference about covariate effects on the partial AUC. Such …