Adaptive platform trials allow treatments to be added or dropped during the study, meaning that the control arm may be active for longer than the experimental arms. This leads to nonconcurrent controls, which provide nonrandomized information that may increase efficiency but may introduce bias from temporal confounding and other factors. Various methods have been proposed to control confounding from nonconcurrent controls, based on adjusting for time period. We demonstrate that time adjustment is insufficient to prevent bias in some circumstances where nonconcurrent controls are present in adaptive platform trials, and we propose a more general analytical framework that accounts for nonconcurrent controls in such circumstances. We begin by defining nonconcurrent controls using the concept of a concurrently randomized cohort, which is a subgroup of participants all subject to the same randomized design. We then use cohort adjustment rather than time adjustment. Due to flexibilities in platform trials, more than one randomized design may be in force at any time, meaning that cohort-adjusted and time-adjusted analyses may be quite different. Using simulation studies, we demonstrate that time-adjusted analyses may be biased while cohort-adjusted analyses remove this bias. We also demonstrate that the cohort-adjusted analysis may be interpreted as a synthesis of randomized and indirect comparisons analogous to mixed treatment comparisons in network meta-analysis. This allows the use of network meta-analysis methodology to separate the randomized and nonrandomized components and to assess their consistency. Whenever nonconcurrent controls are used in platform trials, the separate randomized and indirect contributions to the treatment effect should bepresented.