The gold of biostatistical researches is to develop statistical tools that improves human health or increases understanding of human biology. One area of the studies focuses on designing clinical trials to find out if new drugs or treatments are efficacious. The other area focuses on studying diseases related variables, which gives better understanding of the diseases. The thesis explores these areas from both theoretical and practical points of views. In addition, the thesis develop statistical devices which improve the existing methods in these areas. Firstly, the thesis proposes a Bayesian decision-theoretic group sequential – adaptive randomization phase II clinical trial design. The design improves the trial efficiency by increasing statistical power and reducing required sample sizes. The design also increases patients’ individual benefit, because it enhances patients’ opportunities of receiving better treatments. Secondly, the thesis develops a semiparametric restricted moment model and a score imputation estimation for survival analysis. The method is more robust than the parametric alternatives. In addition to data analysis, the method is used to design a seamless phase II/III clinical trial. The seamless phase II/III clinical trial design shortens the durations between phase II and III studies, and improves the efficiency of the traditional designs by utilizing additional short term information for making decisions. Finally, the thesis develops a partial linear time varying semi-parametric single-index risk score model and a fused B-spline/kernel estimation for longitudinal data analysis. The method models confounder effects linearly. In addition, it uses a nonparametric nonlinear function, namely the single-index risk score, to model the effects of interests. The fused B-spline/kernel technique estimates both the parametric and nonparametric components consistently. The methodology is applied to study the onsite of Huntington’s disease in determining certain time varying covariate effects on the disease risk.