The objective of this research is to develop new statistical methods for a variety of problems that arise in AIDS clinical trials. In most AIDS clinical trials data are not complete and up-to-date during interim analyses. This lag in obtaining complete data may bias severely the results of a trial especially if the lag time is differential by response and by treatment. A comprehensive method for analyzing clinical trials data that accounts for the lag times and gives unbiased results will be derived. Sequential methods will be developed, also, in conjunction with these analytic techniques that allow for early stopping of the clinical trial when treatment differences become sufficiently large. The relationship of time-to-event data to covariates is biased if the covariates are measured with error. Accordingly, nonparametric likelihood methods will be used to obtain unbiased estimates of the regression parameters in the Cox proportional hazards model when the covariates are measured with error. This will be especially useful in allowing the user to evaluate properly whether certain biological variables that are measured with error, such as CD4 counts and viral RNA, are good surrogate markers for clinical progression. Quality adjusted life, a measure of both the quality and quantity of life, is being used increasingly to evaluate therapies in clinical trials. Statistical methods for analyzing this endpoint are not well developed and fail to properly account for censored observations. A comprehensive inferential approach will be developed for modeling quality adjusted life expectancy to covariates when the data are subject to censoring.
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