Special Issue about Competing Risks and Multi-State Models

There is a clear growing interest, at least in the statistical literature, in competing risks and multi-state models. With the rising interest in competing risks and multi-state models a number of software packages have been developed for the analysis of such models. The present special issue of the Journal of Statistical Software introduces a selection of R packages devoted to competing risks and multi-state models. This introduction to the special issue contains some background and highlights the contents of the contributions.

Special Issue about Competing Risks and Multi-State Models

There is a clear growing interest, at least in the statistical literature, in competing risks and multi-state models. With the rising interest in competing risks and multi-state models a number of software packages have been developed for the analysis of such models. The present special issue of the Journal of Statistical Software introduces a selection of R packages devoted to competing risks and multi-state models. This introduction to the special issue contains some background and highlights the contents of the contributions

Efficient estimation of Banach parameters in semiparametric models

Consider a semiparametric model with a Euclidean parameter and an infinite-dimensional parameter, to be called a Banach parameter. Assume: (a) There exists an efficient estimator of the Euclidean parameter. (b) When the value of the Euclidean parameter is known, there exists an estimator of the Banach parameter, which depends on this value and is efficient within this restricted model. Substituting the efficient estimator of the Euclidean parameter for the value of this parameter in the estimator of the Banach parameter, one obtains an efficient estimator of the Banach parameter for the full semiparametric model with the Euclidean parameter unknown. This hereditary property of efficiency completes estimation in semiparametric models in which the Euclidean parameter has been estimated efficiently. Typically, estimation of both the Euclidean and the Banach parameter is necessary in order to describe the random phenomenon under study to a sufficient extent. Since efficient estimators are asymptotically linear, the above substitution method is a particular case of substituting asymptotically linear estimators of a Euclidean parameter into estimators that are asymptotically linear themselves and that depend on this Euclidean parameter. This more general substitution case is studied for its own sake as well, and a hereditary property for asymptotic linearity is proved.Comment: Published at http://dx.doi.org/10.1214/009053604000000913 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

mstate: An R Package for the Analysis of Competing Risks and Multi-State Models

Multi-state models are a very useful tool to answer a wide range of questions in survival analysis that cannot, or only in a more complicated way, be answered by classical models. They are suitable for both biomedical and other applications in which time-to-event variables are analyzed. However, they are still not frequently applied. So far, an important reason for this has been the lack of available software. To overcome this problem, we have developed the mstate package in R for the analysis of multi-state models. The package covers all steps of the analysis of multi-state models, from model building and data preparation to estimation and graphical representation of the results. It can be applied to non- and semi-parametric (Cox) models. The package is also suitable for competing risks models, as they are a special category of multi-state models. This article offers guidelines for the actual use of the software by means of an elaborate multi-state analysis of data describing post-transplant events of patients with blood cancer. The data have been provided by the EBMT (the European Group for Blood and Marrow Transplantation). Special attention will be paid to the modeling of different covariate effects (the same for all transitions or transition-specific) and different baseline hazard assumptions (different for all transitions or equal for some).

Maximum likelihood estimation in the additive hazards model

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We describe an efficient algorithm to find the maximum likelihood estimator. The method is contrasted with the ordinary least squares approach in a simulation study, and the method is illustrated on a realistic data set

Individual frailty excess hazard models in cancer epidemiology

Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We investigate the effects of unobserved individual heterogeneity in the context of excess hazard models, one of the main tools in cancer epidemiology. We propose an individual excess hazard frailty model to account for individual heterogeneity. This represents an extension of frailty modeling to the relative survival framework. In order to facilitate the inference on the parameters of the proposed model, we select frailty distributions which produce closed-form expressions of the marginal hazard and survival functions. The resulting model allows for an intuitive interpretation, in which the frailties induce a selection of the healthier individuals among survivors. We model the excess hazard using a flexible parametric model with a general hazard structure which facilitates the inclusion of time-dependent effects. We illustrate the performance of the proposed methodology through a simulation study. We present a real-data example using data from lung cancer patients diagnosed in England, and discuss the impact of not accounting for unobserved heterogeneity on the estimation of net survival. The methodology is implemented in the R package IFNS

SUrvival Control Chart EStimation Software in R: the success package

Monitoring the quality of statistical processes has been of great importance, mostly in industrial applications. Control charts are widely used for this purpose, but often lack the possibility to monitor survival outcomes. Recently, inspecting survival outcomes has become of interest, especially in medical settings where outcomes often depend on risk factors of patients. For this reason many new survival control charts have been devised and existing ones have been extended to incorporate survival outcomes. The R package success allows users to construct risk-adjusted control charts for survival data. Functions to determine control chart parameters are included, which can be used even without expert knowledge on the subject of control charts. The package allows to create static as well as interactive charts, which are built using ggplot2 (Wickham 2016) and plotly (Sievert 2020).Comment: 29 pages, 10 figures, guide for the R package success, see https://cran.r-project.org/package=succes

General tests of the Markov property in multi-state models

Multi-state models for event history analysis most commonly assume the process is Markov. This article considers tests of the Markov assumption that are applicable to general multi-state models. Two approaches using existing methodology are considered; a simple method based on including time of entry into each state as a covariate in Cox models for the transition intensities and a method involving detecting a shared frailty through a stratified Commenges-Andersen test. In addition, using the principle that under a Markov process the future rate of transitions of the process at times t > s should not be influenced by the state occupied at time s, a new class of general tests is developed by considering summaries from families of log-rank statistics where patients are grouped by the state occupied at varying initial time s. An extended form of the test applicable to models that are Markov conditional on observed covariates is also derived. The null distribution of the proposed test statistics are approximated by using wild bootstrap sampling. The approaches are compared in simulation and applied to a dataset on sleeping behaviour. The most powerful test depends on the particular departure from a Markov process, although the Cox-based method maintained good power in a wide range of scenarios. The proposed class of log-rank statistic based tests are most useful in situations where the non-Markov behaviour does not persist, or is not uniform in nature across patient time