Iván Díaz

Ivan Diaz, Mario Geiger, Richard Iain McKinley

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter sharing. These rotationally-equivariant convolutional layers have several advantages over standard convolutional layers, including increased robustness to unseen poses, smaller network size, and improved sample efficiency. Despite this, most segmentation networks used in medical image analysis continue to rely on standard convolutional kernels. In this paper, we present a new family of segmentation networks that use equivariant voxel convolutions based on spherical harmonics. These networks are robust to data poses not seen during training, and do not require rotation-based data augmentation during training. In addition, we demonstrate improved segmentation performance in MRI brain tumor and healthy brain structure segmentation tasks, with enhanced robustness to reduced amounts of training data and improved parameter efficiency. Code to reproduce our results, and to implement the equivariant segmentation networks for other tasks is available at http://github.com/SCAN-NRAD/e3nn_Unet

Richard Liu, Nicholas T. Williams, Kara E. Rudolph et al.

Causal mediation analyses investigate the mechanisms through which causes exert their effects, and are therefore central to scientific progress. The literature on the non-parametric definition and identification of mediational effects in rigourous causal models has grown significantly in recent years, and there has been important progress to address challenges in the interpretation and identification of such effects. Despite great progress in the causal inference front, statistical methodology for non-parametric estimation has lagged behind, with few or no methods available for tackling non-parametric estimation in the presence of multiple, continuous, or high-dimensional mediators. In this paper we show that the identification formulas for six popular non-parametric approaches to mediation analysis proposed in recent years can be recovered from just two statistical estimands. We leverage this finding to propose an all-purpose one-step estimation algorithm that can be coupled with machine learning in any mediation study that uses any of these six definitions of mediation. The estimators have desirable properties, such as $\sqrt{n}$-convergence and asymptotic normality. Estimating the first-order correction for the one-step estimator requires estimation of complex density ratios on the potentially high-dimensional mediators, a challenge that is solved using recent advancements in so-called Riesz learning. We illustrate the properties of our methods in a simulation study and illustrate its use on real data to estimate the extent to which pain management practices mediate the total effect of having a chronic pain disorder on opioid use disorder.

Vinzenz Uhr, Ivan Diaz, Christian Rummel et al.

Cortical thickness measurements from magnetic resonance imaging, an important biomarker in many neurodegenerative and neurological disorders, are derived by many tools from an initial voxel-wise tissue segmentation. White matter (WM) hypointensities in T1-weighted imaging, such as those arising from multiple sclerosis or small vessel disease, are known to affect the output of brain segmentation methods and therefore bias cortical thickness measurements. These effects are well-documented among traditional brain segmentation tools but have not been studied extensively in tools based on deep-learning segmentations, which promise to be more robust. In this paper, we explore the potential of deep learning to enhance the accuracy and efficiency of cortical thickness measurement in the presence of WM lesions, using a high-quality lesion filling algorithm leveraging denoising diffusion networks. A pseudo-3D U-Net architecture trained on the OASIS dataset to generate synthetic healthy tissue, conditioned on binary lesion masks derived from the MSSEG dataset, allows realistic removal of white matter lesions in multiple sclerosis patients. By applying morphometry methods to patient images before and after lesion filling, we analysed robustness of global and regional cortical thickness measurements in the presence of white matter lesions. Methods based on a deep learning-based segmentation of the brain (Fastsurfer, DL+DiReCT, ANTsPyNet) exhibited greater robustness than those using classical segmentation methods (Freesurfer, ANTs).

Iván Díaz

The consistency of doubly robust estimators relies on consistent estimation of at least one of two nuisance regression parameters. In moderate to large dimensions, the use of flexible data-adaptive regression estimators may aid in achieving this consistency. However, $n^{1/2}$-consistency of doubly robust estimators is not guaranteed if one of the nuisance estimators is inconsistent. In this paper we present a doubly robust estimator for survival analysis with the novel property that it converges to a Gaussian variable at $n^{1/2}$-rate for a large class of data-adaptive estimators of the nuisance parameters, under the only assumption that at least one of them is consistently estimated at a $n^{1/4}$-rate. This result is achieved through adaptation of recent ideas in semiparametric inference, which amount to: (i) Gaussianizing (i.e., making asymptotically linear) a drift term that arises in the asymptotic analysis of the doubly robust estimator, and (ii) using cross-fitting to avoid entropy conditions on the nuisance estimators. We present the formula of the asymptotic variance of the estimator, which allows computation of doubly robust confidence intervals and p-values. We illustrate the finite-sample properties of the estimator in simulation studies, and demonstrate its use in a phase III clinical trial for estimating the effect of a novel therapy for the treatment of HER2 positive breast cancer.