Landmark Prediction of Long Term Survival Incorporating Intermediate Event Information
Layla Parast, PhD
The Rand Corporation
Santa Monica, CA
In recent years, an increasing number of predictive markers have been identified as useful for risk prediction. When interest lies in predicting long term survival, it has often been argued that intermediate event information may be very helpful in improving the prediction. Most existing methods for incorporating potentially censored intermediate event information in predicting long term survival focus on modeling the disease process and are derived under restrictive parametric models in a multi-state survival setting. When such model assumptions fail to hold, the resulting prediction of long term survival may be invalid or inaccurate. We propose flexible landmark prediction modeling frameworks to incorporate intermediate event information and demonstrate that such frameworks could be very useful in two different settings. In the first setting where the overall goal is to predict long term survival at a landmark point, t_0, we demonstrate that a more accurate prediction can be achieved by incorporating intermediate event information up to t_0, along with baseline covariates, using a flexible varying-coefficient model. In the second setting where the goal is efficient estimation of long term survival, we demonstrate that efficiency can be gained via a semi-nonparametric two-stage estimation procedure by incorporating intermediate event information up to t_0 . We further derive a more powerful testing procedure based on these estimates to test for a treatment difference in a randomized clinical trial setting. Simulation studies suggest that the proposed procedures perform well in finite samples and demonstrate substantial potential gains in prediction accuracy and estimation efficiency in these two settings. We illustrate our proposed procedures using an AIDS Clinical Trial Protocol 175 dataset.