This thesis presents three statistical projects on clinical trial design, climate projections and air pollution assessment. The first project is related to clinical trial phase I/II design. The objective is to find the optimal dose for treating patients. However, this quantity may differ according to the patient's individual characteristics. In this thesis, a novel Bayesian adaptive randomization design is introduced to evaluate the treatment effect for different levels of radiotherapy. This design is motivated by an ongoing lung cancel clinical trial, which classified patients in two subgroups based on their radiation susceptibility status. Patients in this trial experience tumor progression and normal tissue complication. The cause-specific hazard method is employed to model the two competing events. Simulation studies are conducted to show the good operating characteristics of this design under multiple scenarios.The second project is focused on climate projections. Decision making under climate change requires an accurate quantification of the uncertainty in the future climate. Physically constrained projections, in the presence of both observations and climate simulations, can be obtained by establishing an empirical relationship in the historical period, and use it to correct the bias of future simulations. Traditional bias correction approaches do not account for the uncertainty in the climate simulation and focus on regionally aggregated variables without spatial dependence. A new statistical model is proposed for bias correction of monthly surface temperatures with sparse and interpretable spatial structure and is used to obtain future projections with associated uncertainty, using only a small ensemble of global simulations.The last project deals with the connection between the ongoing COVID-19 pandemic and air pollution. Exposure to degraded air quality leads to increased premature mortality from cardiovascular and respiratory diseases. Among the far-reaching implications of the ongoing pandemic, a significant air quality improvement has been observed after the lockdowns imposed by many countries. We presented the first comprehensive study investigating the connection between interventions adopted to control a pandemic spread and subsequent effects on large-scale air quality and human health. We use fine particulate matter observations in Europe and China during 2016-2020 and integrate them with chemical transport model simulations as well as the latest epidemiological studies to quantify the health benefits during the pandemic.