Clinical Epidemiology Commons^™

Evaluating Subject-Level Incremental Values Of New Markers For Risk Classification Rule, Tianxi Cai, Lu Tian, Donald M. Lloyd-Jones, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Comparison Of Methods For Estimating The Causal Effect Of A Treatment In Randomized Clinical Trials Subject To Noncompliance, Rod Little, Qi Long, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Adjusting For Covariates In Studies Of Diagnostic, Screening, Or Prognostic Markers: An Old Concept In A New Setting, Holly Janes, Margaret Pepe

UW Biostatistics Working Paper Series

The concept of covariate adjustment is well established in therapeutic and etiologic studies. However, it has received little attention in the growing area of medical research devoted to the development of markers for disease diagnosis, screening, or prognosis, where classification accuracy, rather than association, is of primary interest. In this paper, we demonstrate the need for covariate adjustment in studies of classification accuracy, discuss methods for adjusting for covariates, and distinguish covariate adjustment from several other related but fundamentally different uses for covariates. We draw analogies and contrasts throughout with studies of association.

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. …

Insights Into Latent Class Analysis, Margaret S. Pepe, Holly Janes

UW Biostatistics Working Paper Series

Latent class analysis is a popular statistical technique for estimating disease prevalence and test sensitivity and specificity. It is used when a gold standard assessment of disease is not available but results of multiple imperfect tests are. We derive analytic expressions for the parameter estimates in terms of the raw data, under the conditional independence assumption. These expressions indicate explicitly how observed two- and three-way associations between test results are used to infer disease prevalence and test operating characteristics. Although reasonable if the conditional independence model holds, the estimators have no basis when it fails. We therefore caution against using …

Standardizing Markers To Evaluate And Compare Their Performances, Margaret S. Pepe, Gary M. Longton

UW Biostatistics Working Paper Series

Introduction: Markers that purport to distinguish subjects with a condition from those without a condition must be evaluated rigorously for their classification accuracy. A single approach to statistically evaluating and comparing markers is not yet established.

Methods: We suggest a standardization that uses the marker distribution in unaffected subjects as a reference. For an affected subject with marker value Y, the standardized placement value is the proportion of unaffected subjects with marker values that exceed Y.

Results: We apply the standardization to two illustrative datasets. In patients with pancreatic cancer placement values calculated for the CA 19-9 marker are smaller …

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

UW Biostatistics Working Paper Series

No single biomarker for cancer is considered adequately sensitive and specific for cancer screening. It is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification. Typically the objective function that is optimized for combining markers is the likelihood function. In this paper we consider an alternative objective function -- the area under the empirical receiver operating characteristic curve (AUC). We note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function. Like logistic regression it yields …

Semiparametric Methods For The Binormal Model With Multiple Biomarkers, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Abstract: 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 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 also discuss adjustment for covariates in this class of models and provide a simple …

A Marginal Model Approach For Analysis Of Multi-Reader Multi-Test Receiver Operating Characteristic (Roc) Data, Xiao Song, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve is a popular tool to characterize the capabilities of diagnostic tests with continuous or ordinal responses. One common design for assessing the accuracy of diagnostic tests is to have each patient examined by multiple readers with multiple tests; this design is most commonly used in a radiology setting, where the results of diagnostic tests depend on a radiologist's subjective interpretation. The most widely used approach for analyzing data from such a study is the Dorfman-Berbaum-Metz (DBM) method (Dorfman, Berbaum and Metz, 1992) which utilizes a standard analysis of variance (ANOVA) model for the jackknife …

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 …

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 …

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 …

Evaluating Markers For Selecting A Patient's Treatment, Xiao Song, Margaret S. Pepe

UW Biostatistics Working Paper Series

Selecting the best treatment for a patient's disease may be facilitated by evaluating clinical characteristics or biomarker measurements at diagnosis. We consider how to evaluate the potential of such measurements to impact on treatment selection algorithms. For example, magnetic resonance neurographic imaging is potentially useful for deciding whether a patient should be treated surgically for carpal tunnel syndrome or if he/she should receive less invasive conservative therapy. We propose a graphical display, the selection impact (SI) curve, that shows the population response rate as a function of treatment selection criteria based on the marker. The curve can be useful for …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

The Analysis Of Placement Values For Evaluating Discriminatory Measures, Margaret S. Pepe, Tianxi Cai

UW Biostatistics Working Paper Series

The idea of using measurements such as biomarkers, clinical data, or molecular biology assays for classification and prediction is popular in modern medicine. The scientific evaluation of such measures includes assessing the accuracy with which they predict the outcome of interest. Receiver operating characteristic curves are commonly used for evaluating the accuracy of diagnostic tests. They can be applied more broadly, indeed to any problem involving classification to two states or populations (D = 0 or D = 1). We show that the ROC curve can be interpreted as a cumulative distribution function for the discriminatory measure Y in the …

The Association Of Fluid Intake With Total Natural-Cause Mortality, Coronary Heart Disease And Fatal Stroke, Jacqueline Chung Lun Chan

Loma Linda University Electronic Theses, Dissertations & Projects

Hypohydration may be more widespread than realized since it does not always arouse a sense of thirst. When thirst is felt, it is often ignored, or satisfied before euhydration is achieved. There is growing evidence indicating that hypohydration contributes to acute and chronic illnesses, and to rheological factors associated with coronary heart disease (CHD) and stroke. Therefore the relationship of fluid intake with risk of total natural-cause mortality, CHD and stroke death was examined using data on 34,192 white, non-Hispanic participants in the Adventist Health Study.

Among the 27,342 reporting no CHD, stroke or diabetes at baseline, during six years …

Assessing The Accuracy Of A New Diagnostic Test When A Gold Standard Does Not Exist, Todd A. Alonzo, Margaret S. Pepe

UW Biostatistics Working Paper Series

Often the accuracy of a new diagnostic test must be assessed when a perfect gold standard does not exist. Use of an imperfect test biases the accuracy estimates of the new test. This paper reviews existing approaches to this problem including discrepant resolution and latent class analysis. Deficiencies with these approaches are identified. A new approach is proposed that combines the results of several imperfect reference tests to define a better reference standard. We call this the composite reference standard (CRS). Using the CRS, accuracy can be assessed using multistage sampling designs. Maximum likelihood estimates of accuracy and expressions for …