Anticancer combination therapy has been developed to increase efficacy by enhancing synergy. Patient-derived xenografts (PDXs) have emerged as reliable preclinical models to develop effective treatments in translational cancer research. However, most PDX combination study designs focus on single dose levels, and dose-response surface models are not appropriate for testing synergism. We propose a comprehensive statistical framework to assess joint action of drug combinations from PDX tumor growth curve data. We provide various metrics and robust statistical inference procedures that locally (at a fixed time) and globally (across time) access combination effects under classical drug interaction models. Integrating genomic and pharmacological profiles in non-small-cell lung cancer (NSCLC), we have shown the utilities of combPDX in discovering effective therapeutic combinations and relevant biological mechanisms. We provide an interactive web server, combPDX (https://licaih.shinyapps.io/CombPDX/), to analyze PDX tumor growth curve data and perform power analyses.