The Mizon-Richard encompassing test for the Cox and Aalen additive hazards models.

The Cox hazards model (Cox, 1972, Journal of the Royal Statistical Society, Series B34, 187-220) for survival data is routinely used in many applied fields, sometimes, however, with too little emphasis on the fit of the model. A useful alternative to the Cox model is the Aalen additive hazards model (Aalen, 1980, in Lecture Notes in Statistics-2, 1-25) that can easily accommodate time changing covariate effects. It is of interest to decide which of the two models that are most appropriate to apply in a given application. This is a nontrivial problem as these two classes of models are nonnested except only for special cases. In this article we explore the Mizon-Richard encompassing test for this particular problem. It turns out that it corresponds to fitting of the Aalen model to the martingale residuals obtained from the Cox regression analysis. We also consider a variant of this method, which relates to the proportional excess model (Martinussen and Scheike, 2002, Biometrika 89, 283-298). Large sample properties of the suggested methods under the two rival models are derived. The finite-sample properties of the proposed procedures are assessed through a simulation study. The methods are further applied to the well-known primary biliary cirrhosis data set.     

Explained variation in a fully specified model for data-grouped survival data

An additive hazards model may be used to quantify the effect of genetic and environmental predictors on flowering of sugar beet plants recorded as data-grouped time-to-event data. Estimated predictor effects have an intuitive interpretation rooted in the underlying time dynamics of the flowering process. However, agricultural experiments are often designed using several plots containing a large number of plants that are subsequently being monitored. In this article, we consider an additive hazards model with an additional plot structure induced by latent shared frailty variables. This approach enables us to derive a method to assess the quality of predictors in terms of how much plot variation they explain. We apply the method to a large data set exploring flowering of sugar beet and conclude that the genetic predictor biotype, which has a strong effect, also explains a substantial amount of the plot variation. The method is also applied to a data set from medical research concerning days to virus positivity of serum samples in AIDS patients.     

On cross-odds ratio for multivariate competing risks data

The cross-odds ratio is defined as the ratio of the conditional odds of the occurrence of one cause-specific event for one subject given the occurrence of the same or a different cause-specific event for another subject in the same cluster over the unconditional odds of occurrence of the cause-specific event. It is a measure of the association between the correlated cause-specific failure times within a cluster. The joint cumulative incidence function can be expressed as a function of the marginal cumulative incidence functions and the cross-odds ratio. Assuming that the marginal cumulative incidence functions follow a generalized semiparametric model, this paper studies the parametric regression modeling of the cross-odds ratio. A set of estimating equations are proposed for the unknown parameters and the asymptotic properties of the estimators are explored. Non-parametric estimation of the cross-odds ratio is also discussed. The proposed procedures are applied to the Danish twin data to model the associations between twins in their times to natural menopause and to investigate whether the association differs among monozygotic and dizygotic twins and how these associations have changed over time.     

Confidence bands for multiplicative hazards models: Flexible resampling approaches

We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data.     

Comparing Reference Charts

Reference charts are valuable tools for clinicians in their daily work on pediatric clinics. Reference charts are often constructed by smoothing techniques, and in this paper we present a newly developed non-parametric test for comparing these charts. We illustrate the method by an example. The worked example compares cross-sectional data on height in children from two Danish studies from 1970 and 1990, respectively. The test compares the average height over the range of ages for the two groups.     

Predicting cumulative incidence probability by direct binomial regression

We suggest a new simple approach for estimation and assessmentof covariate effects for the cumulative incidence curve in thecompeting risks model. We consider a semiparametric regressionmodel where some effects may be time-varying and some may beconstant over time. Our estimator can be implemented by standardsoftware. Our simulation study shows that the estimator workswell and has finite-sample properties comparable with the subdistributionapproach. We apply the method to bone marrow transplant dataand estimate the cumulative incidence of death in complete remissionfollowing a bone marrow transplantation. Here death in completeremission and relapse are two competing events.