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High‐dimensional multinomial regression models are very useful in practice but have received less research attention than logistic regression models, especially from the perspective of statistical inference. In this work, we analyze the estimation and prediction error of the contrast‐based ‐penalized multinomial regression model and extend the debiasing method to the multinomial case, providing a valid confidence interval for each coefficient and value of the individual hypothesis test. We also examine cases of model misspecification and non‐identically distributed data to demonstrate the robustness of our method when some assumptions are violated. We apply the debiasing method to identify important predictors in the progression into dementia of different subtypes. Results from extensive simulations show the superiority of the debiasing method compared to other inference methods. 

Abstract Early diagnosis of Alzheimer’s disease plays a pivotal role in patient care and clinical trials. In this study, we have developed a new approach based on 3D deep convolutional neural networks to accurately differentiate mild Alzheimer’s disease dementia from mild cognitive impairment and cognitively normal individuals using structural MRIs. For comparison, we have built a reference model based on the volumes and thickness of previously reported brain regions that are known to be implicated in disease progression. We validate both models on an internal held-out cohort from The Alzheimer's Disease Neuroimaging Initiative (ADNI) and on an external independent cohort from The National Alzheimer's Coordinating Center (NACC). The deep-learning model is accurate, achieved an area-under-the-curve (AUC) of 85.12 when distinguishing between cognitive normal subjects and subjects with either MCI or mild Alzheimer’s dementia. In the more challenging task of detecting MCI, it achieves an AUC of 62.45. It is also significantly faster than the volume/thickness model in which the volumes and thickness need to be extracted beforehand. The model can also be used to forecast progression: subjects with mild cognitive impairment misclassified as having mild Alzheimer’s disease dementia by the model were faster to progress to dementia over time. An analysis of the features learned by the proposed model shows that it relies on a wide range of regions associated with Alzheimer's disease. These findings suggest that deep neural networks can automatically learn to identify imaging biomarkers that are predictive of Alzheimer's disease, and leverage them to achieve accurate early detection of the disease. 

Brain age (BA), distinct from chronological age (CA), can be estimated from MRIs to evaluate neuroanatomic aging in cognitively normal (CN) individuals. BA, however, is a cross-sectional measure that summarizes cumulative neuroanatomic aging since birth. Thus, it conveys poorly recent or contemporaneous aging trends, which can be better quantified by the (temporal) pace P of brain aging. Many approaches to map P, however, rely on quantifying DNA methylation in whole-blood cells, which the blood–brain barrier separates from neural brain cells. We introduce a three-dimensional convolutional neural network (3D-CNN) to estimate P noninvasively from longitudinal MRI. Our longitudinal model (LM) is trained on MRIs from 2,055 CN adults, validated in 1,304 CN adults, and further applied to an independent cohort of 104 CN adults and 140 patients with Alzheimer’s disease (AD). In its test set, the LM computes P with a mean absolute error (MAE) of 0.16 y (7% mean error). This significantly outperforms the most accurate cross-sectional model, whose MAE of 1.85 y has 83% error. By synergizing the LM with an interpretable CNN saliency approach, we map anatomic variations in regional brain aging rates that differ according to sex, decade of life, and neurocognitive status. LM estimates of P are significantly associated with changes in cognitive functioning across domains. This underscores the LM’s ability to estimate P in a way that captures the relationship between neuroanatomic and neurocognitive aging. This research complements existing strategies for AD risk assessment that estimate individuals’ rates of adverse cognitive change with age.