Amyotrophic lateral sclerosis (ALS) is a neurodegenerative condition characterized by the progressive deterioration of motor neurons in the cortex and spinal cord. Using an automated robotic microscope platform that enables the longitudinal tracking of thousands of single neurons, we examine the effects a large library of compounds on modulating the survival of primary neurons expressing a mutation known to cause ALS. The goal of our analysis is to identify the few potentially beneficial compounds among the many assayed, the vast majority of which do not extend neuronal survival. This resembles the large-scale simultaneous inference scenario familiar from microarray analysis, but transferred to the survival analysis setting due to the novel experimental setup. We apply a three-component mixture model to censored survival times of thousands of individual neurons subjected to hundreds of different compounds. The shrinkage induced by our model significantly improves performance in simulations relative to performing treatment-wise survival analysis and subsequent multiple testing adjustment. Our analysis identified compounds that provide insight into potential novel therapeutic strategies for ALS.