Micro-ultrasound (micro-US) is a novel 29-MHz ultrasound technique that provides 3-4 times higher resolution than traditional ultrasound, delivering comparable accuracy for diagnosing prostate cancer to MRI but at a lower cost. Accurate prostate segmentation is crucial for prostate volume measurement, cancer diagnosis, prostate biopsy, and treatment planning. This paper proposes a deep learning approach for automated, fast, and accurate prostate segmentation on micro-US images. Prostate segmentation on micro-US is challenging due to artifacts and indistinct borders between the prostate, bladder, and urethra in the midline. We introduce MicroSegNet, a multi-scale annotation-guided Transformer UNet model to address this challenge. During the training process, MicroSegNet focuses more on regions that are hard to segment (challenging regions), where expert and non-expert annotations show discrepancies. We achieve this by proposing an annotation-guided cross entropy loss that assigns larger weight to pixels in hard regions and lower weight to pixels in easy regions. We trained our model using micro-US images from 55 patients, followed by evaluation on 20 patients. Our MicroSegNet model achieved a Dice coefficient of 0.942 and a Hausdorff distance of 2.11 mm, outperforming several state-of-the-art segmentation methods, as well as three human annotators with different experience levels. We will make our code and dataset publicly available to promote transparency and collaboration in research.
Correlated outcomes are common in many practical problems. Based on a decomposition of estimation bias into two types, within-subspace and against-subspace, we develop a robust approach to estimating the classification rule for the outcome of interest with the presence of auxiliary outcomes in high-dimensional settings. The proposed method includes a pooled estimation step using all outcomes to gain efficiency, and a subsequent calibration step using only the outcome of interest to correct both types of biases. We show that when the pooled estimator has a low estimation error and a sparse against-subspace bias, the calibrated estimator can achieve a lower estimation error than that when using only the single outcome of interest. An inference procedure for the calibrated estimator is also provided. Simulations and a real data analysis are conducted to justify the superiority of the proposed method.