The FDA is responsible for the approval of new drugs, biological products and medical devices in the United States. As part of the approval process, the FDA relies on advisory committees, which provide independent advice from outside experts. In this paper, we empirically study the process of collective learning and voting in FDA advisory committees, using data from transcripts of all meetings conducted between 2007 and 2020. To do this, we structurally estimate a dynamic model in which committee members with heterogeneous preferences and priors hear evidence presented to them, and strategically decide when to stop gathering information and vote. We use our estimates to quantify the probability of correct recommendations by the advisory panels, and compute counterfactual policy experiments to evaluate institutional changes to the decision-making process ruling approval of new products by the FDA.