Patients associated with multiple co-occurring health conditions often face aggravated complications and less favorable outcomes. Co-occurring conditions are especially prevalent among individuals suffering from kidney disease, an increasingly widespread condition affecting 13% of the general population in the US. This study aims to identify and characterize patterns of co-occurring medical conditions in patients employing a probabilistic framework. Specifically, we apply topic modeling in a non-traditional way to find associations across SNOMED-CT codes assigned and recorded in the EHRs of >13,000 patients diagnosed with kidney disease. Unlike most prior work on topic modeling, we apply the method to codes rather than to natural language. Moreover, we quantitatively evaluate the topics, assessing their tightness and distinctiveness, and also assess the medical validity of our results. Our experiments show that each topic is succinctly characterized by a few highly probable and unique disease codes, indicating that the topics are tight. Furthermore, inter-topic distance between each pair of topics is typically high, illustrating distinctiveness. Last, most coded conditions grouped together within a topic, are indeed reported to co-occur in the medical literature. Notably, our results uncover a few indirect associations among conditions that have hitherto not been reported as correlated in the medical literature.