Abstract: In this paper, a tree-structured method is proposed to extend Classification and Regression Trees (CART) algorithm to multivariate survival data, assuming a proportional hazard structure in the whole tree. The method works on the marginal survivor distributions and uses a sandwich estimator of variance to account for the association between survival times. The Wald-test statistics is defined as the splitting rule and the survival trees are developed by maximizing between-node separation. The proposed method intends to classify patients into subgroups with distinctively different prognosis. However, unlike the conventional tree-growing algorithms which work on a subset of data at every partition, the proposed method deals with the whole data set and searches the global optimal split at each partition. The method is applied to a prostate cancer data and its performance is also evaluated by several simulation studies.
Abstract: Existing methods on sample size calculations for right-censored data largely assume the failure times follow exponential distribution or the Cox proportional hazards model. Methods under the additive hazards model are scarce. Motivated by a well known example of right-censored failure time data which the additive hazards model fits better than the Cox model, we proposed a method for power and sample size calculation for a two-group comparison assuming the additive hazards model. This model allows the investigator to specify a group difference in terms of a hazard difference and choose increasing, constant or decreasing baseline hazards. The power computation is based on the Wald test. Extensive simulation studies are performed to demonstrate the performance of the proposed approach. Our simulation also shows substantially decreased power if the additive hazards models is misspecified as the Cox proportional hazards model.
Abstract: Receiver operating characteristic (ROC) methodology is widely used to evaluate diagnostic tests. It is not uncommon in medical practice that multiple diagnostic tests are applied to the same study sample. A va riety of methods have been proposed to combine such potentially correlated tests to increase the diagnostic accuracy. Usually the optimum combina tion is searched based on the area under a ROC curve (AUC), an overall summary statistics that measures the distance between the distributions of diseased and non-diseased populations. For many clinical practitioners, however, a more relevant question of interest may be ”what the sensitivity would be for a given specificity (say, 90%) or what the specificity would be for a given sensitivity?”. Generally there is no unique linear combination superior to all others over the entire range of specificities or sensitivities. Under the framework of a ROC curve, in this paper we presented a method to estimate an optimum linear combination maximizing sensitivity at a fixed specificity while assuming a multivariate normal distribution in diagnostic tests. The method was applied to a real-world study where the accuracy of two biomarkers was evaluated in the diagnosis of pancreatic cancer. The performance of the method was also evaluated by simulation studies.