Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.

Summary: Phenotypic plasticity can have strong impacts on predator–prey interactions. Although much work has examined the effects of inducible defences, less understood is how inducible offences in predators affect predator–prey interactions and predator and prey phenotypes. Here, we examine the impacts of an inducible offence on the interactions and life histories of a cohort of predatory Hynobius retardatus salamander larvae and their prey, Rana pirica tadpoles. We examined larval (duration, survival) and post‐metamorphic (size) traits of both species after manipulating the presence/absence of tadpoles and salamanders with offensive (broadened gape width) or non‐offensive phenotypes in pond enclosures. Offensive phenotype salamanders reduced tadpole survival and metamorph emergence by 58% compared to tadpole‐only treatments, and by over 30% compared to non‐offensive phenotypes. Average time to metamorphosis of frogs was delayed by 30% in the presence of salamanders, although this was independent of salamander phenotype. Thus, offensive phenotype salamanders reduced the number of tadpoles remaining in the pond over time by reducing tadpole survival, not by altering patterns of metamorph emergence. Offensive phenotypes also caused tadpoles to metamorphose 19% larger than no salamander treatments and 6% larger than non‐offensive phenotype treatments. Pooled across salamander treatments, tadpoles caused salamanders to reach metamorphosis faster and larger. Moreover, in the presence of tadpoles, offensive phenotype salamanders metamorphosed 25% faster and 5% larger than non‐offensive phenotype salamanders, but in their absence, neither their size nor larval period differed from non‐offensive phenotype individuals. To our knowledge, this study is the first to demonstrate that inducible offences in predators can have strong impacts on predator and prey phenotypes across multiple life stages. Since early metamorphosis at a larger size has potential fitness advantages, the impacts of offensive phenotypes on frog and salamander life histories likely have significant consequences for individuals and populations. Furthermore, increased predation on tadpoles likely causes offensive phenotype individuals to have strong impacts on pond communities. Future studies should examine the fitness consequences of morphological and life‐history plasticity across multiple life stages and should address the population and community level consequences of offensive phenotypes.

Clinical risk prediction formulas for cancer patients can be improved by dynamically updating the formulas by intermediate events, such as tumor progression. The increased accessibility of individual patient data (IPD) from multiple studies has motivated the development of dynamic prediction formulas accounting for between-study heterogeneity. A joint frailty-copula model for overall survival and time to tumor progression has the potential to develop a dynamic prediction formula of death from heterogenous studies. However, the process of developing, validating, and publishing the prediction formula is complex, which has not been sufficiently described in the literature. In this article, we provide a tutorial in order to build a web-based application for dynamic risk prediction for cancer patients on the basis of the R packages joint.Cox and Shiny. We demonstrate the proposed methods using a dataset of breast cancer patients from multiple clinical studies. Following this tutorial, we demonstrate how one can publish web applications available online, which can be manipulated by any user through a smartphone or personal computer. After learning this tutorial, developers acquire the ability to build an online web application using their own datasets.