Combining biomarkers to detect disease with application to prostate cancer

In early detection of disease, combinations of biomarkers promise improved discrimination over diagnostic tests based on single markers. An example of this is in prostate cancer screening, where additional markers have been sought to improve the specificity of the conventional Prostate-Specific Antigen (PSA) test. A marker of particular interest is the percent free PSA. Studies evaluating the benefits of percent free PSA reflect the need for a methodological approach that is statistically valid and useful in the clinical setting. This article presents methods that address this need. We focus on and-or combinations of biomarker results that we call logic rules and present novel definitions for the ROC curve and the area under the curve (AUC) that are applicable to this class of combination tests. Our estimates of the ROC and AUC are amenable to statistical inference including comparisons of tests and regression analysis. The methods are applied to data on free and total PSA levels among prostate cancer cases and matched controls enrolled in the Physicians' Health Study.     

Combining diagnostic test results to increase accuracy

When multiple diagnostic tests are performed on an individual or multiple disease markers are available it may be possible to combine the information to diagnose disease. We consider how to choose linear combinations of markers in order to optimize diagnostic accuracy. The accuracy index to be maximized is the area or partial area under the receiver operating characteristic (ROC) curve. We propose a distribution-free rank-based approach for optimizing the area under the ROC curve and compare it with logistic regression and with classic linear discriminant analysis (LDA). It has been shown that the latter method optimizes the area under the ROC curve when test results have a multivariate normal distribution for diseased and non-diseased populations. Simulation studies suggest that the proposed non-parametric method is efficient when data are multivariate normal.The distribution-free method is generalized to a smooth distribution-free approach to: (i) accommodate some reasonable smoothness assumptions; (ii) incorporate covariate effects; and (iii) yield optimized partial areas under the ROC curve. This latter feature is particularly important since it allows one to focus on a region of the ROC curve which is of most relevance to clinical practice. Neither logistic regression nor LDA necessarily maximize partial areas. The approaches are illustrated on two cancer datasets, one involving serum antigen markers for pancreatic cancer and the other involving longitudinal prostate specific antigen data.     

Estimation of the ROC Curve under Verification Bias

The ROC (receiver operating characteristic) curve is the most commonly used statistical tool for describing the discriminatory accuracy of a diagnostic test. Classical estimation of the ROC curve relies on data from a simple random sample from the target population. In practice, estimation is often complicated due to not all subjects undergoing a definitive assessment of disease status (verification). Estimation of the ROC curve based on data only from subjects with verified disease status may be badly biased. In this work we investigate the properties of the doubly robust (DR) method for estimating the ROC curve under verification bias originally developed by Rotnitzky, Faraggi and Schisterman (2006) for estimating the area under the ROC curve. The DR method can be applied for continuous scaled tests and allows for a non‐ignorable process of selection to verification. We develop the estimator's asymptotic distribution and examine its finite sample properties via a simulation study. We exemplify the DR procedure for estimation of ROC curves with data collected on patients undergoing electron beam computer tomography, a diagnostic test for calcification of the arteries.     

A Parametric ROC Model‐Based Approach for Evaluating the Predictiveness of Continuous Markers in Case–Control Studies

Summary The predictiveness curve shows the population distribution of risk endowed by a marker or risk prediction model. It provides a means for assessing the model's capacity for stratifying the population according to risk. Methods for making inference about the predictiveness curve have been developed using cross‐sectional or cohort data. Here we consider inference based on case–control studies, which are far more common in practice. We investigate the relationship between the ROC curve and the predictiveness curve. Insights about their relationship provide alternative ROC interpretations for the predictiveness curve and for a previously proposed summary index of it. Next the relationship motivates ROC based methods for estimating the predictiveness curve. An important advantage of these methods over previously proposed methods is that they are rank invariant. In addition they provide a way of combining information across populations that have similar ROC curves but varying prevalence of the outcome. We apply the methods to prostate‐specific antigen (PSA), a marker for predicting risk of prostate cancer.     

Bivariate Marker Measurements and ROC Analysis

Summary This article considers receiver operating characteristic (ROC) analysis for bivariate marker measurements. The research interest is to extend tools and rules from univariate marker to bivariate marker setting for evaluating predictive accuracy of markers using a tree‐based classification rule. Using an and–or classifier, an ROC function together with a weighted ROC function (WROC) and their conjugate counterparts are proposed for examining the performance of bivariate markers. The proposed functions evaluate the performance of and–or classifiers among all possible combinations of marker values, and are ideal measures for understanding the predictability of biomarkers in target population. Specific features of ROC and WROC functions and other related statistics are discussed in comparison with those familiar properties for univariate marker. Nonparametric methods are developed for estimating ROC‐related functions (partial) area under curve and concordance probability. With emphasis on average performance of markers, the proposed procedures and inferential results are useful for evaluating marker predictability based on a single or bivariate marker (or test) measurements with different choices of markers, and for evaluating different and–or combinations in classifiers. The inferential results developed in this article also extend to multivariate markers with a sequence of arbitrarily combined and–or classifier.     

The contribution of prostatic acid phosphatase and prostatic specific antigen in the diagnosis of prostatic cancer

Prostatic acid phosphatase (PAP) and prostatic specific antigen (PSA) were measured by immunochemical methods using test preparations from two different companies. In 66 patients with benign hyperplasia of the prostate a good correlation was found only between PSA levels (orthogonal regression analysis: y = 1.77 x -0.68; r = 0.995). Discrimination analysis between benign hyperplasia and new prostatic cancer (28 patients), using ROC curves, revealed a sensitivity for prostatic cancer of about 30 percent using both PAP methods and of about 58 percent using both PSA methods at the 95-percentile of benign hyperplasia. The PSA methods were both more sensitive in detecting prostatic cancer than the PAP methods.     

Advances in proteomic prostate cancer biomarker discovery

Prostate cancer is the most common non-cutaneous cancer in men in the United States. For reasons largely unknown, the incidence of prostate cancer has increased in the last two decades, in spite or perhaps because of a concomitant increase in serum prostate-specific antigen (PSA) screening. While PSA is acknowledged not to be an ideal biomarker for prostate cancer detection, it is however widely used by physicians due to lack of an alternative. Thus, the identification of a biomarker(s) that can complement or replace PSA represents a major goal for prostate cancer research. Screening complex biological specimens such as blood, urine, and tissue to identify protein biomarkers has become increasingly popular over the last decade thanks to advances in proteomic discovery methods. The completion of human genome sequence together with new development in mass spectrometry instrumentation and bioinformatics has been a major driving force in biomarker discovery research. Here we review the current state of proteomic applications as applied to various sample sources including blood, urine, tissue, and “secretome” for the purpose of prostate cancer biomarker discovery. Additionally, we review recent developments in validation of putative markers, efforts at systems biology approach, and current challenges of proteomics in biomarker discovery.     

Combined hypermethylation of APC and GSTP1 as a molecular marker for prostate cancer: quantitative pyrosequencing analysis

A total of 149 human prostate tissues obtained from our institute were assessed: 52 specimens of benign prostate hyperplasia (BPH) and 97 specimens of prostate cancer (PCa). The methylation status of the genes of Adenomatous polyposis coli (APC) and glutathione-S-transferase-P1 (GSTP1) was analyzed by quantitative pyrosequencing. A methylation score (M score) was calculated to capture the combined methylation level of both genes. The methylation level of each single gene and that of both genes combined was significantly higher in PCa specimens than in BPH (each p < 0.001). The value of APC methylation, GSTP1 methylation, and M score for predicting PCa was measured by the area under the receiver operating characteristic (ROC) curve and reached 0.954, 0.942, and 0.983, respectively. The sensitivity and specificity of the M score in discriminating between PCa and BPH reached 92.8% and 100.0%, respectively. The M score was positively associated with the serum prostate-specific antigen (PSA) level (p trend < 0.001). Our study demonstrates that the quantitative measurement of two methylation markers might drastically improve the ability to discriminate PCa from BPH.     

Diagnosis and prognosis potential of four gene promoter hypermethylation in prostate cancer

The current prostate special antigen (PSA) test causes the overtreatment of indolent prostate cancer (PCa). It also increases the risk of delayed treatment of aggressive PCa. DNA methylation aberrations are important events for gene expression dysregulation during tumorigenesis and have been suggested as novel candidate biomarkers for PCa. This may improve the diagnosis and prognosis of PCa. This study assessed the differential methylation and messenger RNA (mRNA) expression between normal and PCa samples. Correlation between promoter methylation and mRNA expression was estimated using Pearson's correlation coefficients. Moreover, the diagnostic potential of candidate methylation markers was estimated by the receiver operating characteristic (ROC) curve using continuous beta values. Survival and Cox analysis was performed to evaluate the prognostic potential of the candidate methylation markers. A total of 359 hypermethylated sites 3435 hypomethylation sites, 483 upregulated genes, and 1341 downregulated genes were identified from The Cancer Genome Atlas database. Furthermore, 17 hypermethylated sites (covering 13 genes), including known genes associated with hypermethylation in PCa (e.g., AOX1 and C1orf114), showed high discrimination between adjacent normal tissues and PCa samples with the area under the ROC curve from 0.88 to 0.94. Notably, ANXA2, FGFR2, HAAO, and KCNE3 were identified as valuable prognostic markers of PCa through the Kaplan–Meier analysis. Using gene methylation as a continuous variable, four promoter hypermethylation was significantly associated with disease-free survival in univariate Cox regression and multivariate Cox regression. This study identified four novel diagnostic and prognostic markers for PCa. The markers provide important strategies for improving the timely diagnosis and prognosis of PCa.     

前列腺PI-RADS V2.1评分联合血清PSA相关指标对灰区前列腺癌的诊断价值研究

摘要 目的：探讨前列腺影像报告和数据系统第2.1版（PI-RADS V2.1）评分联合血清前列腺特异抗原（PSA）相关指标对灰区前列腺癌的诊断价值。方法：回顾性分析2016年1月至2019年12月的187例经病理证实且PSA为灰区（4-10 ng/mL）的前列腺癌或前列腺增生患者资料。根据病理结果分为前列腺癌（PCa）组与前列腺增生组（BPH）组。由两名经验丰富的MRI诊断医师通过盲法对所有患者MRI图像进行PI-RADS V2.1评分,统计并计算血清PSA相关指标：总前列腺特异抗原（t-PSA）、游离前列腺特异抗原（f-PSA）、游离前列腺特异抗原与总前列腺特异抗原比值（f-PSA/t-PSA）、前列腺特异抗原密度（PSAD）。采用t检验比较各项指标在两组间的差异性,并使用受试者工作曲线（ROC）分析各项指标对灰区前列腺癌的诊断效能。结果：PI-RADS V2.1评分与PSAD在PCa与BPH组之间的差异具有统计学意义（P＜0.05）,而t-PSA、f-PSA、f-PSA/t-PSA在PCa与BPH组之间的差异均无统计学意义（P＞0.05）。根据ROC曲线分析,PI-RADS V2.1评分、PSAD、PI-RADS V2.1评分联合PSAD诊断灰区前列腺癌的曲线下面积（AUC）分别为0.814、0.671及0.838,且PI-RADS V2.1评分联合PSAD的AUC显著高于单独应用PI-RADS V2.1评分（Z=1.989,P＜0.05）与PSAD（Z=3.174,P＜0.05）。结论：PI-RADS V2.1评分与PSAD对诊断灰区前列腺癌具有较高诊断效能,且联合PI-RADS V2.1评分与PSAD能进一步提高诊断效能。     

Measurement of aberrant glycosylation of prostate specific antigen can improve specificity in early detection of prostate cancer

Introduction

We previously identified prostate cancer (PCa)-associated aberrant glycosylation of PSA, where α2,3-linked sialylation is an additional terminal N-glycan on free PSA (S2,3PSA). We then developed a new assay system measuring S2,3PSA using a magnetic microbead-based immunoassay. We compared the diagnostic accuracy of conventional PSA and percent-free PSA (%fPSA) tests.

Methods

We used MagPlex beads to measure serum S2,3PSA levels using anti-human fPSA monoclonal antibody (8A6) for capture and anti-α2,3-linked sialic acid monoclonal antibody (HYB4) for detection. We determined the cutoff values in a training test and measured serum S2,3PSA levels in 314 patients who underwent biopsy, including 138 PCa and 176 non-PCa patients with PSA of <10.0 ng/ml. Serum S2,3PSA levels were presented as mean fluorescence intensity (MFI). Receiver operating characteristic curves were used to evaluate the diagnostic accuracy of total PSA, %fPSA, and S2,3PSA.

Results

We determined an MFI cutoff value of 1130 with a sensitivity of 95.0% and specificity of 72.0% for the diagnosis of PCa in the training test. In the validation study, the area under the curve for the detection of PCa with S2,3PSA was 0.84, which was significantly higher than that with PSA or %fPSA.

Conclusions

Although the present study is small and preliminary, these results suggest that the measurement of serum S2,3PSA using a magnetic microbead-based immunoassay may improve the accuracy of early detection of PCa and reduce unnecessary prostate biopsy.     

Time-dependent ROC curves for censored survival data and a diagnostic marker

ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.     

An interpretation for the ROC curve and inference using GLM procedures

The accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic (ROC) curve. This paper puts forth an interpretation for each point on the ROC curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject. This interpretation gives rise to new methods for making inference about ROC curves. It is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results, one component of the pair being from a diseased subject and the other from a nondiseased subject. Within the generalized linear model (GLM) binary regression framework, ROC curves can be estimated, and we highlight a new semiparametric estimator. Covariate effects can also be evaluated with the GLM models. The methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers. Asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters.     

On the use of partial area under the ROC curve for comparison of two diagnostic tests

Evaluation of diagnostic performance is typically based on the receiver operating characteristic (ROC) curve and the area under the curve (AUC) as its summary index. The partial area under the curve (pAUC) is an alternative index focusing on the range of practical/clinical relevance. One of the problems preventing more frequent use of the pAUC is the perceived loss of efficiency in cases of noncrossing ROC curves. In this paper, we investigated statistical properties of comparisons of two correlated pAUCs. We demonstrated that outside of the classic model there are practically reasonable ROC types for which comparisons of noncrossing concave curves would be more powerful when based on a part of the curve rather than the entire curve. We argue that this phenomenon stems in part from the exclusion of noninformative parts of the ROC curves that resemble straight‐lines. We conducted extensive simulation studies in families of binormal, straight‐line, and bigamma ROC curves. We demonstrated that comparison of pAUCs is statistically more powerful than comparison of full AUCs when ROC curves are close to a “straight line”. For less flat binormal ROC curves an increase in the integration range often leads to a disproportional increase in pAUCs’ difference, thereby contributing to an increase in statistical power. Thus, efficiency of differences in pAUCs of noncrossing ROC curves depends on the shape of the curves, and for families of ROC curves that are nearly straight‐line shaped, such as bigamma ROC curves, there are multiple practical scenarios in which comparisons of pAUCs are preferable.     

Semiparametric estimation of the covariate-specific ROC curve in presence of ignorable verification bias

Covariate-specific receiver operating characteristic (ROC) curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker, when the accuracy of the test is associated with certain covariates. In many large-scale screening tests, the gold standard is subject to missingness due to high cost or harmfulness to the patient. In this article, we propose a semiparametric estimation of the covariate-specific ROC curves with a partial missing gold standard. A location-scale model is constructed for the test result to model the covariates' effect, but the residual distributions are left unspecified. Thus the baseline and link functions of the ROC curve both have flexible shapes. With the gold standard missing at random (MAR) assumption, we consider weighted estimating equations for the location-scale parameters, and weighted kernel estimating equations for the residual distributions. Three ROC curve estimators are proposed and compared, namely, imputation-based, inverse probability weighted, and doubly robust estimators. We derive the asymptotic normality of the estimated ROC curve, as well as the analytical form of the standard error estimator. The proposed method is motivated and applied to the data in an Alzheimer's disease research.     

Nonparametric and semiparametric group sequential methods for comparing accuracy of diagnostic tests

SUMMARY: Comparison of the accuracy of two diagnostic tests using the receiver operating characteristic (ROC) curves from two diagnostic tests has been typically conducted using fixed sample designs. On the other hand, the human experimentation inherent in a comparison of diagnostic modalities argues for periodic monitoring of the accruing data to address many issues related to the ethics and efficiency of the medical study. To date, very little research has been done on the use of sequential sampling plans for comparative ROC studies, even when these studies may use expensive and unsafe diagnostic procedures. In this article we propose a nonparametric group sequential design plan. The nonparametric sequential method adapts a nonparametric family of weighted area under the ROC curve statistics (Wieand et al., 1989, Biometrika 76, 585-592) and a group sequential sampling plan. We illustrate the implementation of this nonparametric approach for sequentially comparing ROC curves in the context of diagnostic screening for nonsmall-cell lung cancer. We also describe a semiparametric sequential method based on proportional hazard models. We compare the statistical properties of the nonparametric approach with alternative semiparametric and parametric analyses in simulation studies. The results show the nonparametric approach is robust to model misspecification and has excellent finite-sample performance.     

Application of the time-dependent ROC curves for prognostic accuracy with multiple biomarkers

The rapid advancement in molecule technology has led to the discovery of many markers that have potential applications in disease diagnosis and prognosis. In a prospective cohort study, information on a panel of biomarkers as well as the disease status for a patient are routinely collected over time. Such information is useful to predict patients' prognosis and select patients for targeted therapy. In this article, we develop procedures for constructing a composite test with optimal discrimination power when there are multiple markers available to assist in prediction and characterize the accuracy of the resulting test by extending the time-dependent receiver operating characteristic (ROC) curve methodology. We employ a modified logistic regression model to derive optimal linear composite scores such that their corresponding ROC curves are maximized at every false positive rate. We provide theoretical justification for using such a model for prognostic accuracy. The proposed method allows for time-varying marker effects and accommodates censored failure time outcome. When the effects of markers are approximately constant over time, we propose a more efficient estimating procedure under such models. We conduct numerical studies to evaluate the performance of the proposed procedures. Our results indicate the proposed methods are both flexible and efficient. We contrast these methods with an application concerning the prognostic accuracies of expression levels of six genes.     

Order-restricted inference for clustered ROC data with application to fingerprint matching accuracy

Receiver operating characteristic (ROC) curve is commonly used to evaluate and compare the accuracy of classification methods or markers. Estimating ROC curves has been an important problem in various fields including biometric recognition and diagnostic medicine. In real applications, classification markers are often developed under two or more ordered conditions, such that a natural stochastic ordering exists among the observations. Incorporating such a stochastic ordering into estimation can improve statistical efficiency (Davidov and Herman, 2012). In addition, clustered and correlated data arise when multiple measurements are gleaned from the same subject, making estimation of ROC curves complicated due to within-cluster correlations. In this article, we propose to model the ROC curve using a weighted empirical process to jointly account for the order constraint and within-cluster correlation structure. The algebraic properties of resulting summary statistics of the ROC curve such as its area and partial area are also studied. The algebraic expressions reduce to the ones by Davidov and Herman (2012) for independent observations. We derive asymptotic properties of the proposed order-restricted estimators and show that they have smaller mean-squared errors than the existing estimators. Simulation studies also demonstrate better performance of the newly proposed estimators over existing methods for finite samples. The proposed method is further exemplified with the fingerprint matching data from the National Institute of Standards and Technology Special Database 4.