In many clinical trials, patients are not followed continuously. This means their vital status may not be immediately recorded. In such cases, the results from the Kaplan-Meier estimator or the log rank test, popular methods used for survival analysis, may be biased or inconsistent. Hu and Tsiatis first produced a new estimator to estimate survival distribution for right-censored data with delayed ascertainment, Van der Laan and Hubbard modified their estimator. We investigate each of these proposed estimators and their properties. Using simulations, we compare these new estimators to each other and to the Kaplan-Meier estimator using different sample sizes, different failure rates, and different maximum delay times. The public health importance of this thesis is that we can partially alleviate the problem caused by delayed ascertainment in the analysis of right-censored time to event data by choosing the most accurate and consistent estimator that accounts for the delayed ascertainment. The reduction of bias in analyses of public health data ensures that such studies are reliable so that proper inference can be made and hence, potential public health policy can be based on an accurate decision making process
