Phase II clinical trials aim to potentially screen out ineffective and identify effective therapies to move forward to randomized phase III trials. Single-arm studies remain the most utilized design in phase II oncology trials, especially in scenarios where a randomized design is simply not practical. Due to concerns regarding excessive toxicity or ineffective new treatment strategies, interim analyses are typically incorporated in the trial, and the choice of statistical methods mainly depends on the type of primary endpoints. For oncology trials, the most common primary objectives in phase II trials include tumor response rate (binary endpoint) and progression disease-free survival (time-to-event endpoint). Interim strategies are well-developed for both endpoints in single-arm phase II trials. The advent of molecular targeted therapies, often with lower toxicity profiles from traditional cytotoxic treatments, has shifted the drug development paradigm into establishing evidence of biological activity, target modulation and pharmacodynamics effects of these therapies in early phase trials. As such, these trials need to address simultaneous evaluation of safety as well as proof-of-concept of biological marker activity or changes in continuous tumor size instead of binary response rates. In this dissertation, we extend a predictive probability design for binary outcomes in the single-arm clinical trial setting and develop two interim designs for continuous endpoints, such as continuous tumor shrinkage or change in a biomarker over time. The two-stage design mainly focuses on the futility stopping strategies, while it also has the capacity of early stopping for efficacy. Both optimal and minimax designs are presented for this two-stage design. The multi-stage design has the flexibility of stopping the trial early either due to futility or efficacy. Due to the intense computation and searching strategy we adopt, only the minimax design is presented for this multi-stage design. The multi-stage design allows for up to 40 interim looks with continuous monitoring possible for large and moderate effect sizes, requiring an overall sample size less than 40. The stopping boundaries for both designs are based on predictive probability with normal likelihood and its conjugated prior distributions, while the design itself satisfies the pre-specified type I and type II error rate constraints. From simulation results, when compared with binary endpoints, both designs well preserve statistical properties across different effect sizes with reduced sample size. We also develop an R package, PPSC, and detail it in chapter four, so that both designs can be freely accessible for use in future phase II clinical trials with the collaborative efforts of biostatisticians. Clinical investigators and biostatisticians have the flexibility to specify the parameters from the hypothesis testing framework, searching ranges of the boundaries for predictive probabilities, the number of interim looks involved and if the continuous monitoring is preferred and so on.