The New England Journal of Statistics in Data Science

Cure models are gaining more and more popularity for modeling time-to-event data for different forms of cancer, for which a considerable proportion of patients are considered “cured.” Two types of cure models are widely used, the mixture cure model (MCM) and the promotion time cure model (PTCM). In this article, we propose a unified estimand Δ for comparing treatment and control groups under the survival models with cure fraction, which focuses on whether the treatment extends survival for patients. In addition, we introduce a general framework of Bayesian inference under the cure models. Simulation studies demonstrate that regardless of whether the model is correctly specified, the inference of the unified estimand Δ yields desirable empirical performance. We analyze the ECOG’s melanoma cancer data E1684 via the unified estimand Δ under different models to further demonstrate the proposed methodology.

The purpose of this paper is to develop a practical framework for the analysis of the linear mixed-effects models for censored or missing data with serial correlation errors, using the multivariate Student’s t-distribution, being a flexible alternative to the use of the corresponding normal distribution. We propose an efficient ECM algorithm for computing the maximum likelihood estimates for these models with standard errors of the fixed effects and likelihood function as a by-product. This algorithm uses closed-form expressions at the E-step, which relies on formulas for the mean and variance of a truncated multivariate Student’s t-distribution. In order to illustrate the usefulness of the proposed new methodology, artificial and a real dataset are analyzed. The proposed algorithm and methods are implemented in the R package ARpLMEC.

Categorical data are prevalent in almost all research fields and business applications. Their statistical analysis and inference often rely on probit/logistic regression models. For these common models, however, there is no universally adopted measure for performing goodness-of-fit analysis. To this end, [26] proposed a so-called surrogate ${R^{2}}$ that resembles the ordinary least square (OLS) ${R^{2}}$ for linear regression models. The surrogate ${R^{2}}$ used the notion of surrogacy, namely, generating a continuous response S and using it as a surrogate of the original categorical response Y [24, 25, 8]. In this paper, we develop an R package $\mathbf{SurrogateRsq}$ to implement the surrogate ${R^{2}}$ method [43]. The package is compatible with existing model fitting functions (e.g., glm(), polr(), clm(), and vglm()), and its features are exhibited in a wine rating analysis. Our package can be used jointly with other R packages developed for variable selection and model diagnostics so as to form a complete model development process. This process is summarized and demonstrated in a categorical-data-modeling workflow that practitioners can follow. To exemplify an extended utility of the surrogate-${R^{2}}$-based goodness-of-fit analysis, we also use this package to illustrate how to compare different empirical models trained from different samples in the wine rating analysis. The result suggests that the package allows us to evaluate comparability across multiple samples/models/studies that address the same or similar scientific or business questions.