Early phase clinical trials are conducted with limited time and patient resources. Despite design restrictions, patient safety must be prioritised and trial conclusions must be accurate; maximising a promising treatment’s chance of success in later largescale, long-term trials. Increasing the efficiency of early phase clinical trials, through utilising available data more effectively, can lead to improved decision making during, and as a result of, the trial. This thesis contains three distinct pieces of research; each of which proposes a novel, early phase clinical trial design with this overall objective. The initial focus of the thesis is on dose-escalation. In the single-agent setting, subgroups of the population, between which the reaction to treatment may differ, are accounted for in dose-escalation. This is achieved using a Bayesian model-based approach to dose-escalation with spike and slab priors in order to identify a recommended dose of the treatment (for use in later trials) in each subgroup. Accounting for a potential subgroup effect in a dose-escalation trial can yield safety benefits for patients within, and post- trial due to subgorup-specific dosing which should improve the benefit-risk ratio of the treatment.Dual-agent dose-escalation is considered next. In the dual-agent setting, singleagent data, including toxicity and pharmacokinetic exposure information, is available. This information is used to define escalation rules that combine the outputs of independent dose-toxicity and dose-exposure models which are fitted to emerging trial data. This solution is practical to implement and reduces the subjectivity that currently surrounds the use of exposure data in dose-escalation. In addition, escalation decisions and consistency of the final recommended dose-pair are improved. The focus of the third piece of research changes. In this work, Bayesian sample size calculations for single-arm and randomised phase II trials with time-to-event endpoints are considered. Calculation of the sample size required for a trial is based on a proportional hazards assumption and utilises historical data on the control (and experimental) treatments. The sample sizes obtained are consistent with those currently used in practice while better accounting for available information and uncertainty in parameter estimates of the time-to-event distribution. Investigating allocation ratio’s in the randomised setting provides a basis for deciding whether a control arm is indeed necessary. That is, in a randomised trial, whether it is necessary for any patients to be randomised to the control treatment arm.