Incorporating diagnostic accuracy into the estimation of discrete survival function

Empirical distribution function (EDF) is a commonly used estimator of population cumulative distribution function. Survival function is estimated as the complement of EDF. However, clinical diagnosis of an event is often subjected to misclassification, by which the outcome is given with some uncertainty. In the presence of such errors, the true distribution of the time to first event is unknown. We develop a method to estimate the true survival distribution by incorporating negative predictive values and positive predictive values of the prediction process into a product-limit style construction. This will allow us to quantify the bias of the EDF estimates due to the presence of misclassified events in the observed data. We present an unbiased estimator of the true survival rates and its variance. Asymptotic properties of the proposed estimators are provided and these properties are examined through simulations. We evaluate our methods using data from the VIRAHEP-C study.