Tissue microarrays (TMAs) are a new high-throughput tool for the study of protein expression patterns in tissues and are increasingly used to evaluate the diagnostic and prognostic importance of biomarkers. TMA data are rather challenging to analyze. Covariates are highly skewed, non-normal, and may be highly correlated. We present statistical methods for relating TMA data to censored time-to-event data. We review methods for evaluating the predictive power of Cox regression models and show how to test whether biomarker data contain predictive information above and beyond standard pathology covariates. We use nonparametric bootstrap methods to validate model fitting indices such as the concordance index. We also present data mining methods for characterizing high risk patients with simple biomarker rules. Since researchers in the TMA community routinely dichotomize biomarker expression values, survival trees are a natural choice. We also use bump hunting (patient rule induction method), which we adapt to the use with survival data. The proposed methods are applied to a kidney cancer tissue microarray data set.