In today's healthcare, the prediction of time-to-onset of disease for a particular patient has important diagnostic value; it allows preventive and suitable treatment before symptoms of the disease occur. AI faces challenges in navigating uncertainties inherent in medical data and decision-making, especially in time-to-event predictions as time-to-event data pose challenges due to missingness, e.g. unknown time to event but healthy until last observation. Therefore, this research aims to tackle this challenge by integrating survival analysis data with uncertainty quantification in hybrid AI, ensuring reliable and interpretable time-to-event predictions. Combining these with clinical data and expert knowledge in the hybrid AI models will result in trustworthy solutions to empower the clinicians. Two use cases will exemplify this research. In the first use case, ICU infection management will be provided with dependable predictions for infections of multidrug-resistant organisms and commonly encountered hospital-acquired infections. The second use case will predict insightful prognosis for the manifestation of early chronic kidney disease in cats. However, the methodological advancements fostered by this research project hold the potential to become pioneering, transcending these applications to address a broader spectrum of health issues and even beyond the healthcare domain.