Robust statistical methods for analysis of biomarkers measured with batch/experiment-specific errors

Addressing heterogeneous sensitivity in biomarker screening with application in NanoString nCounter data

Biomarkers are measurable indicators of biological processes and have wide biomedical applications including disease screening and prognosis prediction. Candidate biomarkers can be screened in high-throughput settings, which allow simultaneous measurements of a large number of molecules. For binary biomarkers, the ability to detect a molecule may be hindered by the presence of background noise and the variable signal strength, which lower the sensitivity to a different extent for different target molecules in a sample-specific manner. This heterogeneity in detection sensitivity is often overlooked and leads to an inflated false positive rate. We propose a novel sensitivity adjusted likelihood-ratio test (SALT), which properly controls the false positives and is more powerful than the unadjusted approach. We show that sample-and-feature-specific detection sensitivity can be well estimated from NanoString nCounter data, and using the estimated sensitivity in SALT results in improved biomarker screening.

The emerging landscape of health research based on biobanks linked to electronic health records: Existing resources, statistical challenges, and potential opportunities

Biobanks linked to electronic health records provide rich resources for health-related research. With improvements in administrative and informatics infrastructure, the availability and utility of data from biobanks have dramatically increased. In this paper, we first aim to characterize the current landscape of available biobanks and to describe specific biobanks, including their place of origin, size, and data types. The development and accessibility of large-scale biorepositories provide the opportunity to accelerate agnostic searches, expedite discoveries, and conduct hypothesis-generating studies of disease-treatment, disease-exposure, and disease-gene associations. Rather than designing and implementing a single study focused on a few targeted hypotheses, researchers can potentially use biobanks' existing resources to answer an expanded selection of exploratory questions as quickly as they can analyze them. However, there are many obvious and subtle challenges with the design and analysis of biobank-based studies. Our second aim is to discuss statistical issues related to biobank research such as study design, sampling strategy, phenotype identification, and missing data. We focus our discussion on biobanks that are linked to electronic health records. Some of the analytic issues are illustrated using data from the Michigan Genomics Initiative and UK Biobank, two biobanks with two different recruitment mechanisms. We summarize the current body of literature for addressing these challenges and discuss some standing open problems. This work complements and extends recent reviews about biobank-based research and serves as a resource catalog with analytical and practical guidance for statisticians, epidemiologists, and other medical researchers pursuing research using biobanks.

Evaluation of Cerebrospinal Fluid Assay Variability in Alzheimer's Disease

Studies of cerebrospinal fluid (CSF) biomarkers in Alzheimer's disease (AD) have indicated that much of the variability observed in the biomarkers may be due to measurement error. Biomarkers are often obtained with measurement error, which may make the diagnostic biomarker appear less effective than it truly is. In the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, technical replicates of CSF biomarkers are available; the National Alzheimer's Coordinating Center database contains longitudinal replicates of CSF biomarkers. We focus on the area under the receiver operating characteristic curve (AUC) as the measure of diagnostic effectiveness for differentiating AD from normal cognition using CSF biomarkers and compare AUC estimates obtained by a more standard, naïve method (which uses a single observation per subject and ignores measurement error) to a maximum likelihood (ML) based method (which uses all replicates per subject and adjusts for measurement error). The choice of analysis method depends upon the noise to signal ratio (i.e., the magnitude of the measurement error variability relative to the true biomarker variability); moderate to high ratios may significantly bias the naïve AUC estimate, and the ML-based method would be preferred. The noise to signal ratios were low for the ADNI biomarkers but high for the tTau and pTau biomarkers in NACC. Correspondingly, the naïve and ML-based AUC estimates were nearly identical in the ADNI data but dissimilar for the tTau and pTau biomarkers in the NACC data. Therefore, using the naïve method is adequate for analysis of CSF biomarkers in the ADNI study, but the ML method is recommended for the NACC data.

Adjustment for measurement error in evaluating diagnostic biomarkers by using an internal reliability sample

Biomarkers are often measured with error due to imperfect lab conditions or temporal variability within subjects. Using an internal reliability sample of the biomarker, we develop a parametric bias-correction approach for estimating a variety of diagnostic performance measures including sensitivity, specificity, the Youden index with its associated optimal cut-point, positive and negative predictive values, and positive and negative diagnostic likelihood ratios when the biomarker is subject to measurement error. We derive the asymptotic properties of the proposed likelihood-based estimators and show that they are consistent and asymptotically normally distributed. We propose confidence intervals for these estimators and confidence bands for the receiver operating characteristic curve. We demonstrate through extensive simulations that the proposed approach removes the bias due to measurement error and outperforms the naïve approach (which ignores the measurement error) in both point and interval estimation. We also derive the asymptotic bias of naïve estimates and discuss conditions in which naïve estimates of the diagnostic measures are biased toward estimates produced when the biomarker is ineffective (i.e., when sensitivity equals 1 - specificity) or are anticonservatively biased. The proposed method has broad biomedical applications and is illustrated using a biomarker study in Alzheimer's disease. We recommend collecting an internal reliability sample during the biomarker discovery phase in order to adequately evaluate the performance of biomarkers with careful adjustment for measurement error.

Modeling clinical outcome using multiple correlated functional biomarkers: A Bayesian approach

In some biomedical studies, biomarkers are measured repeatedly along some spatial structure or over time and are subject to measurement error. In these studies, it is often of interest to evaluate associations between a clinical endpoint and these biomarkers (also known as functional biomarkers). There are potentially two levels of correlation in such data, namely, between repeated measurements of a biomarker from the same subject and between multiple biomarkers from the same subject; none of the existing methods accounts for correlation between multiple functional biomarkers. We propose a Bayesian approach to model a clinical outcome of interest (e.g. risk for colorectal cancer) in the presence of multiple functional biomarkers while accounting for potential correlation. Our simulations show that the proposed approach achieves good performance in finite samples under various settings. In the presence of substantial or moderate correlation, the proposed approach outperforms an existing approach that does not account for correlation. The proposed approach is applied to a study of biomarkers of risk for colorectal neoplasms and our results show that the risk for colorectal cancer is associated with two functional biomarkers, APC and TGF-α, in particular, with their values in the region between the proliferating and differentiating zones of colorectal crypts.

A conditional likelihood approach for regression analysis using biomarkers measured with batch-specific error

Measurement error is common in epidemiological and biomedical studies. When biomarkers are measured in batches or groups, measurement error is potentially correlated within each batch or group. In regression analysis, most existing methods are not applicable in the presence of batch-specific measurement error in predictors. We propose a robust conditional likelihood approach to account for batch-specific error in predictors when batch effect is additive and the predominant source of error, which requires no assumptions on the distribution of measurement error. Although a regression model with batch as a categorical covariable yields the same parameter estimates as the proposed conditional likelihood approach for linear regression, this result does not hold in general for all generalized linear models, in particular, logistic regression. Our simulation studies show that the conditional likelihood approach achieves better finite sample performance than the regression calibration approach or a naive approach without adjustment for measurement error. In the case of logistic regression, our proposed approach is shown to also outperform the regression approach with batch as a categorical covariate. In addition, we also examine a 'hybrid' approach combining the conditional likelihood method and the regression calibration method, which is shown in simulations to achieve good performance in the presence of both batch-specific and measurement-specific errors. We illustrate our method by using data from a colorectal adenoma study.