Variable selection in linear regression models: Choosing the best subset is not always the best choice.

We consider the question of variable selection in linear regressions, in the sense of identifying the correct direct predictors (those variables that have nonzero coefficients given all candidate predictors). Best subset selection (BSS) is often considered the "gold standard," with its use being restricted only by its NP-hard nature. Alternatives such as the least absolute shrinkage and selection operator (Lasso) or the Elastic net (Enet) have become methods of choice in high-dimensional settings. A recent proposal represents BSS as a mixed-integer optimization problem so that large problems have become computationally feasible. We present an extensive neutral comparison assessing the ability to select the correct direct predictors of BSS compared to forward stepwise selection (FSS), Lasso, and Enet. The simulation considers a range of settings that are challenging regarding dimensionality (number of observations and variables), signal-to-noise ratios, and correlations between predictors. As fair measure of performance, we primarily used the best possible F1-score for each method, and results were confirmed by alternative performance measures and practical criteria for choosing the tuning parameters and subset sizes. Surprisingly, it was only in settings where the signal-to-noise ratio was high and the variables were uncorrelated that BSS reliably outperformed the other methods, even in low-dimensional settings. Furthermore, FSS performed almost identically to BSS. Our results shed new light on the usual presumption of BSS being, in principle, the best choice for selecting the correct direct predictors. Especially for correlated variables, alternatives like Enet are faster and appear to perform better in practical settings.

No robust online effects of transcranial direct current stimulation on corticospinal excitability.

Transcranial direct current stimulation (tDCS) has been used for over twenty years to modulate cortical (particularly motor corticospinal) excitability both during (online) and outlasting (offline) the stimulation, with the former effects associated to the latter. However, tDCS effects are highly variable, partially because stimulation intensity is commonly not adjusted individually (in contrast to transcranial magnetic stimulation, TMS). In Experiment 1, we therefore explored an empirical approach of personalizing tDCS intensity for the primary motor cortex (M1) based on dose-response curves (DRCs), individually relating tDCS Intensity (in steps from 0.3 to 2.0 mA) and Polarity (anodal, cathodal) to the online modulation of concurrent TMS motor evoked potentials (MEP), assessing DRC reliability across two separate days. No robust DRCs could be observed, neither at the individual nor at the group level, with the only robust effect being a (paradoxical) MEP facilitation during cathodal tDCS at 2.0 mA, but no modulation at traditional intensities of or near 1 mA. In Experiment 2, we therefore attempted to replicate the classical bidirectional online MEP modulation during 1 mA tDCS that had been reported by several of the early seminal tDCS papers. We either closely recreated stimulation parameters and temporal protocol of these original studies (Experiment 2A) or slightly modernized them according to current standards (Experiment 2B). In neither experiment did we observed any significant online MEP modulation. We conclude that an empirical titration of individually effective tDCS intensities may not be feasible as online tDCS effects do not appear to be sufficiently robust.

Non-contrast-enhanced MR-angiography (MRA) of lower extremity peripheral arterial disease at 3 tesla: Examination time and diagnostic performance of 2D quiescent-interval single-shot MRA vs. 3D fast spin-Echo MRA.

PURPOSE: Non-contrast enhanced MRA is a promising diagnostic alternative to contrast-enhanced (CE-) MRA or CT in patients with lower extremity peripheral arterial disease (PAD) but potentially associated with prolonged examination times and inferior diagnostic performance. We aimed to compare examination times and diagnostic performance of non-contrast enhanced quiescent-interval slice-selective (QISS)-MRA and fast-spin-echo (FSE)-MRA at 3.0 T. MATERIALS AND METHODS: Forty-five patients with PAD were recruited for this IRB approved prospective study. Subjects underwent lower extremity MRA with 1) QISS-MRA, 2) FSE-MRA, and 3) CE-MRA (continuous table movement MRA and time-resolved MRA of the calf), which served as the standard of reference. Scan times for each examination step and total examination times for each of the three techniques was determined. Image quality and degree of stenosis were rated by two readers on a 5-point Likert scale. Sensitivity, specificity and diagnostic accuracy for relevant (>50%) stenosis were calculated. RESULTS: Median total examination time was 27:02 min for QISS-MRA (IQR, 25:13-31:01 min), 28:37 min for FSE-MRA (IQR, 25:51-33:12 min), and 31:22 min for CE-MRA (IQR, 26:41-33:23 min). Acquisition time for QISS-MRA was significantly longer compared to FSE-MRA and CE-MRA (p ≤ 0.0001), while time for localizers, scouts and planning of the MRA sequence was significantly shorter for QISS-MRA compared to FSE-MRA and CE-MRA (p ≤ 0.0001). QISS-MRA had significantly better image quality compared to FSE-MRA with less segments classified as non-diagnostic (Reader 1: 3% vs. 35%; Reader 2: 3% vs. 50%, p ≤ 0.0001). Overall, QISS-MRA showed significantly better diagnostic performance than FSE-MRA (sensitivity, 85% vs. 54%; specificity, 90% vs. 47%, diagnostic accuracy, 89% vs. 48%; p ≤ 0.0001). CONCLUSION: Total examination time of QISS-MRA and FSE-MRA was comparable with a conventional CE-MRA protocol. QISS-MRA showed significantly higher diagnostic performance than FSE-MRA.

Clone temporal centrality measures for incomplete sequences of graph snapshots.

BACKGROUND: Different phenomena like the spread of a disease, social interactions or the biological relation between genes can be thought of as dynamic networks. These can be represented as a sequence of static graphs (so called graph snapshots). Based on this graph sequences, classical vertex centrality measures like closeness and betweenness centrality have been extended to quantify the importance of single vertices within a dynamic network. An implicit assumption for the calculation of temporal centrality measures is that the graph sequence contains all information about the network dynamics over time. This assumption is unlikely to be justified in many real world applications due to limited access to fully observed network data. Incompletely observed graph sequences lack important information about duration or existence of edges and may result in biased temporal centrality values. RESULTS: To account for this incompleteness, we introduce the idea of extending original temporal centrality metrics by cloning graphs of an incomplete graph sequence. Focusing on temporal betweenness centrality as an example, we show for different simulated scenarios of incomplete graph sequences that our approach improves the accuracy of detecting important vertices in dynamic networks compared to the original methods. An age-related gene expression data set from the human brain illustrates the new measures. Additional results for the temporal closeness centrality based on cloned snapshots support our findings. We further introduce a new algorithm called REN to calculate temporal centrality measures. Its computational effort is linear in the number of snapshots and benefits from sparse or very dense dynamic networks. CONCLUSIONS: We suggest to use clone temporal centrality measures in incomplete graph sequences settings. Compared to approaches that do not compensate for incompleteness our approach will improve the detection rate of important vertices. The proposed REN algorithm allows to calculate (clone) temporal centrality measures even for long snapshot sequences.