Inference for Right Censored, and Right Censored Length Biased Data Through Inverse Weighting

In many medical studies, the outcome of interest may be the time from a starting point to a predefined specific event. A key feature of these data is that the complete event times may not be completely known for some subjects. When this occurs, the survival times are said to be censored. When observations are right censored, all that is known for such individuals is that their event time is greater than some given value. Analysis of variance has been one of the most powerful statistical tools for comparing mean continuous response across multiple groups. Use of classical ANOVA in time-to-event data is problematic because of the right censored nature of survival times. \ud In this dissertation, we propose a weighted analysis of variance approach to comparing mean continuous response between groups when the outcome is subject to right censoring. The method weights each observation by the inverse of the probability of being censored. We show that classical ANOVA methods such as decomposition of sums of squares and tests of contrasts follow in the weighted ANOVA setting. Simulation results show that the weighted ANOVA could be a comparable alternative to other methods of analyzing survival data. We apply our methods to a dataset from the North Central Cancer Treatment Group and another from the Radiation Therapy Oncology Group.\ud Length-Biased sampling is statistical artifact that occurs in survival analysis when the probability of an observation being included in the sample is proportional to a particular characteristic of that observation. When the length-biased data is subject to right censoring, the inference is biased if these key features of the data are not accounted for in the analysis.\ud In this dissertation, we propose an estimating equation approach to eliminate the bias introduced by censoring and the unequal probability of inclusion using inverse weighting. Simulation results show that the estimator is a simple and effective method of analyzing these types of survival data. We apply our methods to the Channing House data. \ud The mean survival time is often used as a measure of effectiveness in screening and other public health programs. When the data are right censored and/or length-biased, the mean survival time is a biased estimator of the population mean. This work is of important public health significance because it provides an effective method of comparing health populations using the mean survival time as the measure of effectiveness.\ud \u