Measures of discrimination and predictive accuracy for interval censored survival data

Medical researchers frequently make statements that one model predicts survival better than another, and are frequently challenged to provide rigorous statistical justification for these statements. In general, it is important to quantify how well the model is able to distinguish between high risk and low risk subjects (discrimination), and how well the model predicts the probability of having experienced the event of interest prior to a specified time t (predictive accuracy). For ordinary – right censored – survival data, the two most popular methods for discrimination and predictive accuracy are the concordance index, or c-index (Harrell et al. 1986) and the prediction error based on the Brier score (Graf et al. 1999). In the absence of censoring, it is straightforward to define and estimate these measures. Adaptations of these simple estimates for right censored survival data have been proposed and are now in common use. The novel part of this thesis is to develop methods for calculating/estimating the concordance index and the Brier score prediction error in the context of interval censored survival data. The starting point is that we have interval censored data of the form (Li, Ri] for subjects i = 1, ..., n, with Li < Ri(Li may be 0, Ri may be infinity to accommodate right censored data), and a given prediction model yielding a single (estimated) baseline hazard h0(t), one vector of (estimated) regression coefficients beta. From this prediction model, prognostic scores βxi, and predicted survival probabilities S(t|xi) = exp(−H0(t)βxi), may be calculated for each subject i. Methods to estimate the concordance index and the Brier score prediction error for exponential and Weibull baseline hazards are proposed and evaluated in a simulation study. An application to real data is also provided.