As most adaptive clinical trial designs are implemented in stages, well-understood methods of sequential trial monitoring are needed. In the frequentist paradigm, examples of sequential monitoring methodologies include the p-value combination tests, conditional error, conditional power, and alpha spending approaches. Within the Bayesian framework, posterior and predictive probabilities are used as monitoring criteria, with the latter being analogous to the conditional power approach. In a placebo or active-contolled dose response clinical trial, we are interested in achieving two objectives: selecting the best therapeutic dose and confirming this selected dose. Traditional approach uses the parallel group design with Dunnett's adjustment. Recently, some two- stage Seamless II/III designs have been proposed. The drop-the-losers design considers selecting the dose with the highest empirical mean after the first stage, while another design assumes a dose-response model to aid dose selection. These designs however do not consider prioritizing the doses and adaptively inserting new doses. We propose an adaptive staggered dose design for a normal endpoint that makes minimal assumption regarding the dose response and sequentially adds doses to the trial. An alpha spending function is applied in a novel way to monitor the doses across the trial. Through numerical and simulation studies, we confirm that optimistic alpha spending coupled with informative dose ordering jointly produce some desirable operating characteristics when compared to drop-the-losers and model-based Seamless designs. In addition, we show how the design parameters can be flexibly varied to further improve its performance and how it can be extended to binary and survival endpoints. In a biosimilarity trial, we are interested in establishing evidence of comparable efficacy between a follow-on biological product and a reference innovator product. So far, no standard method for biosimilarity has been endorsed by regulatory agency. We propose a Bayesian hierarchical bias model and a non-inferiority hypothesis framework to prove biosimilarity. A two-stage adaptive design using predictive probability as early stopping criterion is pro- posed. Through simulation study, the proposed design controls the type I error better than the frequentist approach and Bayesian power is superior when biosimilarity is plausible. Two-stage design further reduces the expected sample size.