The broad objective of this research is to develop new statistical methods for several important and timely problems that arise in cancer and HIV/AIDS clinical research. Major efforts will be directed toward (1) lifetime medical cost analysis with incomplete follow-up data and (2) covariate measurement error in logistic and Cox regressions. Current development in these two areas is inadequate and substantial gaps of knowledge exist. In medical research cost evaluation is becoming an important component and has been integrated in many studies, as our health care system is increasingly constrained with limited resources. However, statistical methods for lifetime medical cost analysis with incomplete follow-up data have largely been lacking. This work will focus on developing semipararametric tests and regressions, which accommodate right-censored data. The second area of research concerns the situation that regression covariates are not accurately ascertainable, e.g. dietary intakes in cancer prevention studies or CD4 lymphocyte count and viral load in HIV/AIDS research. Parametric- and nonparametric-correction methods will be developed for widely-applied logistic and Cox regressions with various scenarios of available data. Despite the challenges of these long-standing problems, preliminary investigations have shown considerable promise for elegant and practical solutions. Large-sample properties of the proposed test statistics and estimators will be rigorously investigated by making use of marked point process theory, martingale theory, and modern empirical process theory. Extensive simulation studies will be performed to validate these proposals under practical sample sizes. The proposed methods will be applied to a number of cancer and HIV/AIDS clinical trials. User-friendly computer programs will be developed and made available to the research community.
