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Background: Prostate cancer (PCa) is among the most common cancers in men and its diagnosis requires the histopathological evaluation of biopsies by human experts. While several recent artificial intelligence-based (AI) approaches have reached human expert-level PCa grading, they often display significantly reduced performance on external datasets. This reduced performance can be caused by variations in sample preparation, for instance the staining protocol, section thickness, or scanner used. Another limiting factor of contemporary AI-based PCa grading is the prediction of ISUP grades, which leads to the perpetuation of human annotation errors., Methods: We developed the prostate cancer aggressiveness index (PCAI), an AI-based PCa detection and grading framework that is trained on objective patient outcome, rather than subjective ISUP grades. We designed PCAI as a clinical application, containing algorithmic modules that offer robustness to data variation, medical interpretability, and a measure of prediction confidence. To train and evaluate PCAI, we generated a multicentric, retrospective, observational trial consisting of six cohorts with 25,591 patients, 83,864 images, and 5 years of median follow-up from 5 different centers and 3 countries. This includes a high-variance dataset of 8,157 patients and 28,236 images with variations in sample thickness, staining protocol, and scanner, allowing for the systematic evaluation and optimization of model robustness to data variation. The performance of PCAI was assessed on three external test cohorts from two countries, comprising 2,255 patients and 9,437 images., Findings: Using our high-variance datasets, we show how differences in sample processing, particularly slide thickness and staining time, significantly reduce the performance of AI-based PCa grading by up to 6.2 percentage points in the concordance index (C-index). We show how a select set of algorithmic improvements, including domain adversarial training, conferred robustness to data variation, interpretability, and a measure of credibility to PCAI. These changes lead to significant prediction improvement across two biopsy cohorts and one TMA cohort, systematically exceeding expert ISUP grading in C-index and AUROC by up to 22 percentage points., Interpretation: Data variation poses serious risks for AI-based histopathological PCa grading, even when models are trained on large datasets. Algorithmic improvements for model robustness, interpretability, credibility, and training on high-variance data as well as outcome-based severity prediction gives rise to robust models with above ISUP-level PCa grading performance., Competing Interests: Competing interests FW, PF, AD, PS, PW, CB, EB, and SB work part time for Spearpoint Analytics AB, a company developing AI-based digital pathology solutions. The authors declare no other conflicts of interest.