Systems dealing with confidential data may leak some information by their observable outputs. Quantitative information flow analysis provides a method for quantifying the amount of such information leakage. To avoid the high computational cost of exhaustive search, statistical analysis has been studied to estimate information leakage by analyzing only a small but representative subset of the system's behavior. In this paper we propose a new compositional statistical analysis method for quantitative information flow that combines multiple statistical analyses with static trace analysis. We use partial knowledge of the system's source code or specification, therefore improving both quality and cost of the analysis. The new method can optimize the use of weighted statistical analysis by performing it on components of the system and appropriately adapting their weights. We show this approach combined with the precision of trace analysis produces better estimates and narrower confidence intervals than the state of the art.