| In clinical trials, statistical inference is preferably conducted with less stringent assumptions. This dissertation proposes a non-parametric method for dichotomous and ordinal missing data, and it proposes a structure for the hypothesis testing and estimation for innovative crossover designs.;When data missing not at random (MNAR) arise from randomized multi-visit, multi-center clinical trials, sensitivity analyses to address possibly informative missing are needed. We propose a closed form point and variance matrix estimation for dichotomized missing data by probabilistically redistributing missing counts, adjusting for a stratification factor and/or baseline covariables. The parameter estimates are computed via weighted least squares asymptotic regression through randomization based methods. We further extend the methods to sensitivity analyses for ordinal endpoints.;A novel crossover design, the sequential parallel comparison design (SPCD), where information from placebo responders in the second period are excluded, serves as a design for studies with high placebo response. Estimators for sources of comparison in the traditional SPCD design, as well as other sources of information that are available, are constructed with methods based on the randomization distribution of the observed population using the nonparametric mean and variance estimates under the null hypothesis, which control Type I error well in hypothesis testing. Baseline imbalance is adjusted by randomization-based ANCOVA. Simulations are performed to study the statistical properties of the proposed methods, which are compared to those of a repeated measures model proposed by Doros et al. (2013).;Point and confidence interval estimation is also addressed by assuming the study population comes from a simple random sample of an almost infinite population. A consistent covariance matrix estimator is constructed and properties of the proposed estimators are studied with simulations, particularly for coverage of confidence intervals. The nominal coverage level is achieved with a t distribution for the approximation to the asymptotic distribution when the sample size is not sufficiently large.;The methodologies are extended to the two-way enrichment design (TED) introduced by Ivanova and Tamura (2011), and to a related bilateral design that applies the four sequence group design to two sides of the same subject instead of two periods. |
