Master protocol trials use a single overarching protocol to evaluate multiple interventions, diseases, or disease subtypes, where individuals are often randomized to different subsets of intervention arms based on individual characteristics, enrollment timing, and intervention availability. While offering increased flexibility, this constrained and non-uniform intervention assignment poses two fundamental inferential challenges: the precise definition of treatment effects and robust, efficient inference on these effects. These challenges arise primarily because some commonly used analysis approaches may target estimands defined on populations that inadvertently depend on the intervention allocation ratio, making them impossible to fully pre-specify, thereby undermining interpretability and opening the door to ambiguity, post-hoc decisions, and potential bias. This article, for the first time, presents a formal estimand framework for master protocol trials with precise specification of the population. The proposed entire concurrently eligible (ECE) trial population not only preserves the integrity of randomized comparisons but also remains invariant to the randomization ratio. Then, we develop weighting and post-stratification methods to estimate treatment effects under the same minimal assumptions used in traditional randomized trials. We also consider model-assisted covariate adjustment to fully unlock the efficiency potential of master protocol trials while maintaining robustness against model misspecification. The SIMPLIFY trial, a master protocol assessing continuation versus discontinuation of two common therapies in cystic fibrosis, is utilized to highlight the practical significance of this research. All analyses are conducted using the R package RobinCID.

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