Methodology (stat.ME)

Abstract: Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.

Abstract: Ranked data is commonly used in research across many fields of study including medicine, biology, psychology, and economics. One common statistic used for analyzing ranked data is Kendall's {\tau} coefficient, a non-parametric measure of rank correlation which describes the strength of the association between two monotonic continuous or ordinal variables. While the mathematics involved in calculating Kendall's {\tau} is well-established, there are relatively few graphing methods available to visualize the results. Here, we describe a visualization method for Kendall's {\tau} which uses a series of rigid Euclidean transformations along a Cartesian plane to map rank pairs into discrete quadrants. The resulting graph provides a visualization of rank correlation which helps display the proportion of concordant and discordant pairs. Moreover, this method highlights other key features of the data which are not represented by Kendall's {\tau} alone but may nevertheless be meaningful, such as the relationship between discrete pairs of observations. We demonstrate the effectiveness of our approach through several examples and compare our results to other visualization methods.

Abstract: A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an autoregressive representation and the Laplace functional. Moreover, these results are used to derive the moment, predictive, and pair correlation measures of the proposed shot noise Cox process. The model is flexible but still tractable and allows for capturing persistence, global trends, and latent spatial and temporal factors. A Bayesian inference approach is adopted, and an efficient Markov Chain Monte Carlo procedure based on conditional Sequential Monte Carlo is proposed. An application to georeferenced wildfire data illustrates the properties of the model and inference.