When analysing time-to-event data it often happens that a certain fraction of the data corresponds to subjects that will never experience the event of interest. These event times are considered as infinite and the subjects are said to be cured. Survival models that take this feature into account are commonly referred to as cure models. This paper gives a review of the literature on cure regression models in which the event time (response) is subject to random right censoring and has a positive probability to be equal to infinity. Contents FACULTY OF ECONOMICS AND BUSINESS Naamsestraat 69 bus 3500 3000 LEUVEN, BELGIË tel.

In survival analysis, it often happens that a certain fraction of the subjects under study never experience the event of interest, that is, they are considered “cured.” In the presence of covariates, a common model for this type of data is the mixture cure model, which assumes that the population consists of two subpopulations, namely the cured and the non‐cured ones, and it writes the survival function of the whole population given a set of covariates as a mixture of the survival function of the cured subjects (which equals one), and the survival function of the non‐cured ones. In the literature, one usually assumes that the mixing probabilities follow a logistic model. This is, however, a strong modeling assumption, which might not be met in practice. Therefore, in order to have a flexible model which at the same time does not suffer from curse‐of‐dimensionality problems, we propose in this paper a single‐index model for the mixing probabilities. For the survival function of the non‐cured subjects we assume a Cox proportional hazards model. We estimate this model using a maximum likelihood approach. We also carry out a simulation study, in which we compare the estimators under the single‐index model and under the logistic model for various model settings, and we apply the new model and estimation method on a breast cancer data set.

Background Human milk oligosaccharides (HMOs) have important and diverse biological functions in early life. This study tested the safety and efficacy of a starter infant formula containing Limosilactobacillus (L.) reuteri DSM 17938 and supplemented with 2’-fucosyllactose (2’FL). Methods Healthy infants < 14 days old (n = 289) were randomly assigned to a bovine milk-based formula containing L. reuteri DSM 17938 at 1 × 107 CFU/g (control group; CG) or the same formula with added 1.0 g/L 2’FL (experimental group; EG) until 6 months of age. A non-randomized breastfed group served as reference (BF; n = 60). The primary endpoint was weight gain through 4 months of age in the formula-fed infants. Secondary endpoints included additional anthropometric measures, gastrointestinal tolerance, stooling characteristics, adverse events (AEs), fecal microbiota and metabolism, and gut immunity and health biomarkers in all feeding groups. Results Weight gain in EG was non-inferior to CG as shown by a mean difference [95% CI] of 0.26 [-1.26, 1.79] g/day with the lower bound of the 95% CI above the non-inferiority margin (-3 g/day). Anthropometric Z-scores, parent-reported stooling characteristics, gastrointestinal symptoms and associated behaviors, and AEs were comparable between formula groups. Redundancy analysis indicated that the microbiota composition in EG was different from CG at age 2 (p = 0.050) and 3 months (p = 0.052), approaching BF. Similarly, between sample phylogenetic distance (weighted UniFrac) for BF vs EG was smaller than for BF vs CG at 3-month age (p = 0.045). At age 1 month, Clostridioides difficile counts were significantly lower in EG than CG. Bifidobacterium relative abundance in EG tracked towards that in BF. Fecal biomarkers and metabolic profile were comparable between CG and EG. Conclusion L. reuteri-containing infant formula with 2’FL supports age-appropriate growth, is well-tolerated and may play a role in shifting the gut microbial pattern towards that of breastfed infants. Trial Registration The trial was registered on ClinicalTrials.gov (NCT03090360) on 24/03/2017.

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Summary Survival analysis relies on the hypothesis that, if the follow-up will be long enough, the event of interest will eventually be observed for all observations. This assumption, however, is often not realistic. The survival data then contain a cure fraction. A common approach to model and analyse this type of data consists in using cure models. Two types of information can therefore be obtained: the survival at a given time and the cure status, both possibly modelled as a function of the covariates. The cure status is often of interest for medical practitioners and one is usually interested in predicting it based on markers. The receiver operating characteristic, ROC, curves are one way to evaluate these predicting performances. However, the classical ROC curve method is not appropriate since the cure status is partially unobserved due to the presence of censoring in survival data. We propose a ROC curve estimator aiming to evaluate the cured/non-cured status classification performance from cure survival data. This estimator, which handles the presence of censoring, decomposes sensitivity and specificity by means of the definition of conditional probability, and estimates these two quantities by means of weighted empirical distribution functions. The mixture cure model is used to calculate the weights. Based on simulations, we demonstrate the good performance of the proposed method and compare it with the classical ROC curve nonparametric estimator that would be obtained if the cure status was fully observed. We also compare our proposed method with the ROC curves of Heagerty et al. (2000) for classical survival analysis. Finally, we illustrate the methodology on a breast cancer dataset.

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