Resistance to therapy remains a significant challenge in cancer treatment, often due to the presence of a stem-like cell population that drives tumor recurrence post-treatment. Moreover, many anticancer therapies induce plasticity, converting initially drug-sensitive cells to a more resistant state, e.g. through epigenetic processes and de-differentiation programs. Understanding the balance between therapeutic anti-tumor effects and induced resistance is critical for identifying treatment strategies. In this study, we present a robust statistical framework leveraging multi-type branching process models to characterize the evolutionary dynamics of tumor cell populations. This approach enables the detection and quantification of therapy-induced resistance using high-throughput drug screening data involving total cell counts, without requiring information on subpopulation counts. The framework is validated using both simulated (in silico) and recent experimental (in vitro) datasets, demonstrating its ability to generate meaningful predictions.