Sepsis is a devastating multi-stage health condition with a high mortality rate. Its complexity, prevalence, and dependency of its outcomes on early detection have attracted substantial attention from data science and machine learning communities. Previous studies rely on individual cellular and physiological responses representing organ system failures to predict health outcomes or the onset of different sepsis stages. However, it is known that organ systems' failures and dynamics are not independent events. In this study, we identify the dependency patterns of significant proximate sepsis-related failures of cellular and physiological responses using data from 12,223 adult patients hospitalized between July 2013 and December 2015. The results show that proximate failures of cellular and physiological responses create better feature sets for outcome prediction than individual responses. Our findings reveal the few significant proximate failures that play the major roles in predicting patients' outcomes. This study's results can be simply translated into clinical practices and inform the prediction and improvement of patients' conditions and outcomes.