Dry powder inhalers (DPI), used as a means for pulmonary drug delivery, typically contain a combination of active pharmaceutical ingredients (API) and significantly larger carrier particles. The microsized drug particles-which have a strong propensity to aggregate and poor aerosolization performance-are mixed with significantly large carrier particles that cannot penetrate the mouth-throat region to deagglomerate and entrain the smaller API particles in the inhaled airflow. Therefore, a DPI's performance depends on the carrier-API combination particles' entrainment and the time and thoroughness of the individual API particles' deagglomeration from the carrier particles. Since DPI particle transport is significantly affected by particle-particle interactions, particle sizes and shapes present significant challenges to computational fluid dynamics (CFD) modelers to model regional lung deposition from a DPI. We employed the Particle-In-Cell method for studying the transport/deposition and the agglomeration and deagglomeration for DPI carrier and API particles in the present work. The proposed development will leverage CFD-PIC and sensitivity analysis capabilities from the Department of Energy laboratories: Multiphase Flow Interface Flow Exchange and Dakota UQ software. A data-driven framework is used to obtain the reliable low order statics of the particle's residence time in the inhaler. The framework is further used to study the effect of drug particle density, carrier particle density and size, fluidizing agent density and velocity, and some numerical parameters on the particles' residence time in the inhaler.