In high-risk stage II-III melanoma, RFS appeared to be a valid surrogate end point for OS for adjuvant randomized studies assessing interferon or a checkpoint inhibitor. In future similar adjuvant studies, a hazard ratio for RFS of 0.77 or less would predict a treatment impact on OS.

In this paper, we develop a simple diagnostic test for the random-effects distribution in mixed models. The test is based on the gradient function, a graphical tool proposed by Verbeke and Molenberghs to check the impact of assumptions about the random-effects distribution in mixed models on inferences. Inference is conducted through the bootstrap. The proposed test is easy to implement and applicable in a general class of mixed models. The operating characteristics of the test are evaluated in a simulation study, and the method is further illustrated using two real data analyses.

Joint modeling of various longitudinal sequences has received quite a bit of attention in recent times. This paper proposes a so-called marginalized joint model for longitudinal continuous and repeated time-to-event outcomes on the one hand and a marginalized joint model for bivariate repeated time-to-event outcomes on the other. The model has several appealing features. It flexibly allows for association among measurements of the same outcome at different occasions as well as among measurements on different outcomes recorded at the same time. The model also accommodates overdispersion. The time-to-event outcomes are allowed to be censored. While the model builds upon the generalized linear mixed model framework, it is such that model parameters enjoy a direct marginal interpretation. All of these features have been considered before, but here we bring them together in a unified, flexible framework. The model framework's properties are scrutinized using a simulation study. The models are applied to data from a chronic heart failure study and to a so-called comet assay, encountered in preclinical research. Almost surprisingly, the models can be fitted relatively easily using standard statistical software.

Generalized linear mixed models (GLMM) are commonly used to analyze hierarchical data. Unlike linear mixed models, they do not automatically provide parametric marginal regression functions, while such functions are needed for population-averaged inferences. This issue has received considerable attention and here three approaches to address it are reviewed, expanded, and compared: (1) the closed-form expressions of the marginal moments and distributions for a variety of GLMMs, derived by Molenberghs et al. (2010), as well as an extension that accommodates overdispersion; (2) the marginalized multilevel models of Heagerty (1999); (3) the bridge distribution of Wang and Louis (2003), a form for the random-effects distribution that allows the conditional and hierarchical mean to be described by the same link function. Our derivations are for the identity link function, the log link, and a collection of links for binary data. We highlight a number of useful connections: (a) it is shown that the bridge distribution for data with a mean on the unit interval is unique; (b) the three approaches are different for unit-interval data with the logit link, but are connected for the probit link; for the latter, there exist closed forms; (c) further results are derived for the bridge distribution in the case of unit-interval data and a Student's t link; (d) in contrast to the unit-interval case, it is shown how large classes of distributions act as bridge distributions when an identity or a logarithmic link is adopted; (e) for these links, the three approaches are either identical or closely connected; (f) it is underscored for a random-intercepts model and logarithmic link, that the data contain no information about the particular distribution for the random intercept, given that the same fit to the data can be ascribed to an entire class of random-intercept distribution; (g) the implications of the difference between the unit-interval case on the one hand and the identity and logarithmic cases on the other, regarding sensitivity to model assumptions, are discussed.

This paper presents, extends, and studies a model for repeated, overdispersed time-to-event outcomes, subject to censoring. Building upon work by Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs et al. (2010), gamma and normal random effects are included in a Weibull model, to account for overdispersion and between-subject effects, respectively. Unlike these authors, censoring is allowed for, and two estimation methods are presented. The partial marginalization approach to full maximum likelihood of Molenberghs et al. (2010) is contrasted with pseudo-likelihood estimation. A limited simulation study is conducted to examine the relative merits of these estimation methods. The modeling framework is employed to analyze data on recurrent asthma attacks in children on the one hand and on survival in cancer patients on the other.