Utilizing non-concurrent controls in the analysis of late-entering experimental arms in platform trials has recently received considerable attention, both on academic and regulatory levels. While incorporating this data can lead to increased power and lower required sample sizes, it might also introduce bias to the effect estimators if temporal drifts are present in the trial. Aiming to mitigate the potential calendar time bias, we propose various frequentist model-based approaches that leverage the non-concurrent control data, while adjusting for time trends. One of the currently available frequentist models incorporates time as a categorical fixed effect, separating the duration of the trial into periods, defined as time intervals bounded by any treatment arm entering or leaving the platform. In this work, we propose two extensions of this model. First, we consider an alternative definition of the time covariate by dividing the trial into fixed-length calendar time intervals. Second, we propose alternative methods to adjust for time trends. In particular, we investigate adjusting for autocorrelated random effects to account for dependency between closer time intervals and employing spline regression to model time with a smooth polynomial function. We evaluate the performance of the proposed approaches in a simulation study and illustrate their use by means of a case study.