Extracting scalar measures from functional data with applications to placebo response.

In controlled and observational studies, outcome measures are often observed longitudinally. Such data are difficult to compare among units directly because there is no natural ordering of curves. This is relevant not only in clinical trials, where typically the goal is to evaluate the relative efficacy of treatments on average, but also in the growing and increasingly important area of personalized medicine, where treatment decisions are optimized with respect to a relevant patient outcome. In personalized medicine, there are no methods for optimizing treatment decision rules using longitudinal outcomes, e.g., symptom trajectories, because of the lack of a natural ordering of curves. A typical practice is to summarize the longitudinal response by a scalar outcome that can then be compared across patients, treatments, etc. We describe some of the summaries that are in common use, especially in clinical trials. We consider a general summary measure (weighted average tangent slope) with weights that can be chosen to optimize specific inference depending on the application. We illustrate the methodology on a study of depression treatment, in which it is difficult to separate placebo effects from the specific effects of the antidepressant. We argue that this approach provides a better summary for estimating the benefits of an active treatment than traditional non-weighted averages.

Development and evaluation of a multimodal marker of major depressive disorder.

This study aimed to identify biomarkers of major depressive disorder (MDD), by relating neuroimage-derived measures to binary (MDD/control), ordinal (severe MDD/mild MDD/control), or continuous (depression severity) outcomes. To address MDD heterogeneity, factors (severity of psychic depression, motivation, anxiety, psychosis, and sleep disturbance) were also used as outcomes. A multisite, multimodal imaging (diffusion MRI [dMRI] and structural MRI [sMRI]) cohort (52 controls and 147 MDD patients) and several modeling techniques-penalized logistic regression, random forest, and support vector machine (SVM)-were used. An additional cohort (25 controls and 83 MDD patients) was used for validation. The optimally performing classifier (SVM) had a 26.0% misclassification rate (binary), 52.2 ± 1.69% accuracy (ordinal) and r = .36 correlation coefficient (p < .001, continuous). Using SVM, R2 values for prediction of any MDD factors were <10%. Binary classification in the external data set resulted in 87.95% sensitivity and 32.00% specificity. Though observed classification rates are too low for clinical utility, four image-based features contributed to accuracy across all models and analyses-two dMRI-based measures (average fractional anisotropy in the right cuneus and left insula) and two sMRI-based measures (asymmetry in the volume of the pars triangularis and the cerebellum) and may serve as a priori regions for future analyses. The poor accuracy of classification and predictive results found here reflects current equivocal findings and sheds light on challenges of using these modalities for MDD biomarker identification. Further, this study suggests a paradigm (e.g., multiple classifier evaluation with external validation) for future studies to avoid nongeneralizable results.

A method to identify differential expression profiles of time-course gene data with Fourier transformation.

BACKGROUND: Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. RESULTS: This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization.The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. CONCLUSIONS: Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be potentially used to identify genes which have the same patterns or biological processes, and help facing the present and forthcoming challenges of data analysis in functional genomics.

Robust fitting of [11C]-WAY-100635 PET data.

Fitting of a positron emission tomography (PET) time-activity curve is typically accomplished according to the least squares (LS) criterion, which is optimal for data having Gaussian distributed errors, but not robust in the presence of outliers. Conversely, quantile regression (QR) provides robust estimates not heavily influenced by outliers, sacrificing a little efficiency relative to LS when no outliers are present. Given these considerations, we hypothesized that QR would improve parameter estimate accuracy as measured by reduced intersubject variance in distribution volume (V(T)) compared with LS in PET modeling. We compare V(T) values after applying QR with those using LS on 49 controls studied with [(11)C]-WAY-100635. QR decreases the standard deviation of the V(T) estimates (relative improvement range: 0.08% to 3.24%), while keeping the within-group average V(T) values almost unchanged. QR variance reduction results in fewer subjects required to maintain the same statistical power in group analysis without additional hardware and/or image registration to correct head motion.