Background: Solid evidence of the safety and effectiveness of retinoblastoma (RB) conservative treatment using thermotherapy and systemic chemotherapy with long-term follow-up is scarce, especially in low-resource countries. Aims: This study examined the outcomes of this treatment and associated predictors in Vietnam to strengthen the current RB treatment protocol focusing on preserving eye and vision in low-resource settings. Methods and results: A prospective cohort study was conducted at Ho Chi Minh City Eye Hospital in Vietnam from 2005 to 2019. All eligible patients with bilateral RB (one eye already removed and another eye classified as group A or B) and without previous treatment were recruited. All patients received thermotherapy and six cycles of systemic three-agent chemotherapy repeated every 4 weeks. A standardized questionnaire was used to collect information on study participants' age, symptoms, tumor characteristics, treatment, and outcomes. Among 50 eyes of all 50 patients with a median age of 9 (4–20) months, 34 eyes were in group B (68%). The median follow-up time was 60 (60–84) months. All 139 preserved tumors regressed mostly to type 4 (70.4%) and type 3 (23.7%) scars. Kaplan–Meier analysis found the overall globe-salvage rate at 5 years of 91.9% (95% CI: 80.1%–97.7%). Most eyes (41/50, 82%, 95% CI: 69.2%–90.2%) had a final visual acuity ≥0.1. The visual acuity is higher when tumors regressed to a type 4 scar (p =.007, AOR = 8.098, 95% CI: 1.79–36.53) which also shows less enucleation than a type 3 scar (p =.002, AOR = 0.06, 95% CI: 0.01–0.37%). Gender effect on visual acuity after treatment was significant and may be due to discrimination. No major complications were recorded. Conclusion: Conservative treatment of early-stage RB is safe and effective. Long-term, thorough follow-ups of patients post-treatment are needed. The regression patterns of scars could be a useful indicator of treatment failure.

Purpose:It remains unclear whether preoperative central graft thickness (CGT) contributes to visual outcomes of Descemet stripping automated endothelial keratoplasty (DSAEK). This retrospective cohort study examined the ability of preoperative and postoperative CGT to predict 12-month best spectacle-corrected visual acuity (BSCVA) after DSAEK for Fuchs endothelial corneal dystrophy/moderate pseudophakic bullous keratopathy/second graft.Methods:All consecutive patients who underwent DSAEK in 2015 to 2018 were included. The primary end point was 12-month BSCVA. DSAEK-CGT was measured preoperatively and 6 times between postoperative day 8 and month 12. Eyes were divided according to preoperative CGT 130 m (ultrathin-DSAEK threshold) or 6-month postoperative CGT 100 m (mean 6-month postoperative DSAEK-CGT). The t test assessed CGT evolution of the 4 groups over time. Multivariate analyses examined whether preoperative CGT or 6-month CGT categories predicted 12-month BSCVA. Multivariate analysis assessed the preoperative/perioperative factors that predicted 6-month CGT.Results:A total of 108 eyes (68 patients) underwent DSAEK. Preoperative CGT was >130 and ≤130 m in 87 and 21 eyes, respectively. Postoperative CGT was >100 and ≤100 m in 50 and 58 eyes, respectively. Thin 6-month postoperative grafts thinned significantly more relative to preoperative thickness than thick grafts (P < 0.001). Preoperative CGT subgroups did not show this difference. Six-month postoperative CGT (P = 0.01), but not preoperative CGT, predicted 12-month BSCVA. Preoperative CGT strongly predicted 6-month CGT (P = 0.0003).Conclusions:Postoperative, but not preoperative, DSAEK-CGT predicted 6-month BSCVA. The correlation between preoperative and postoperative CGT and interstudy variation in preoperative CGT measurement accuracy may explain literature disparities regarding the importance of preoperative CGT in DSAEK outcomes.

This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on (Formula presented.), as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available. Supplementary materials for this article are available online.

Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map g, called density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of g are then proposed, by M-estimation, simulation-based inference, or by an iterative procedure available in the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method.

We study the weak convergence of conditional empirical copula processes indexed by general families of conditioning events that have non zero probabilities. Moreover, we also study the case where the conditioning events are chosen in a data-driven way. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general multivariate measures of association, possibly given some fixed or random conditioning events. By applying our theoretical results, we prove the asymptotic normality of the estimators of such measures. We illustrate our results with financial data.

Collection of accurate and representative data from agricultural fields is required for efficient crop management. Since growers have limited available resources, there is a need for advanced methods to select representative points within a field in order to best satisfy sampling or sensing objectives. The main purpose of this work was to develop a data-driven method for selecting locations across an agricultural field given observations of some covariates at every point in the field. These chosen locations should be representative of the distribution of the covariates in the entire population and represent the spatial variability in the field. They can then be used to sample an unknown target feature whose sampling is expensive and cannot be realistically done at the population scale. An algorithm for determining these optimal sampling locations, namely the multifunctional matching (MFM) criterion, was based on matching of moments (functionals) between sample and population. The selected functionals in this study were standard deviation, mean, and Kendall's tau. An additional algorithm defined the minimal number of observations that could represent the population according to a desired level of accuracy. The MFM was applied to datasets from two agricultural plots: a vineyard and a peach orchard. The data from the plots included measured values of slope, topographic wetness index, normalized difference vegetation index, and apparent soil electrical conductivity. The MFM algorithm selected the number of sampling points according to a representation accuracy of 90% and determined the optimal location of these points. The algorithm was validated against values of vine or tree water status measured as crop water stress index (CWSI). Algorithm performance was then compared to two other sampling methods: the conditioned Latin hypercube sampling (cLHS) model and a uniform random sample with spatial constraints. Comparison among sampling methods was based on measures of similarity between the target variable population distribution and the distribution of the selected sample. MFM represented CWSI distribution better than the cLHS and the uniform random sampling, and the selected locations showed smaller deviations from the mean and standard deviation of the entire population. The MFM functioned better in the vineyard, where spatial variability was larger than in the orchard. In both plots, the spatial pattern of the selected samples captured the spatial variability of CWSI. MFM can be adjusted and applied using other moments/functionals and may be adopted by other disciplines, particularly in cases where small sample sizes are desired.

Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We assume a regression-type relationship between conditional Kendall's tau and some covariates, in a parametric setting with a large number of transformations of a small number of regressors. This model may be sparse, and the underlying parameter is estimated through a penalized criterion and a two-step inference procedure. We prove non-asymptotic bounds with explicit constants that hold with high probabilities. We derive the consistency of the latter estimator, its asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper.

We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic pointwise and uniform bounds, that hold with high probabilities. We provide "direct proofs" of the consistency and the asymptotic law of conditional Kendall's tau. A simulation study evaluates the numerical performance of such nonparametric estimators. An application to the dependence between energy consumption and temperature conditionally to calendar days is finally provided.

It is shown how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (value of −1) conditionally on some covariates. The consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators is proven, including the equivalent of the logit and probit regressions in our framework. Specific algorithms are detailed, adapting usual machine learning techniques, including nearest neighbors, decision trees, random forests and neural networks, to the setting of the estimation of conditional Kendall's tau. Finite sample properties of these estimators and their sensitivities to each component of the data-generating process are assessed in a simulation study. Finally, all these estimators are applied to a dataset of European stock indices.

Extending the results of Bellec, Lecué and Tsybakov [1] to the setting of sparse high-dimensional linear regression with unknown variance, we show that two estimators, the Square-Root Lasso and the Square-Root Slope can achieve the optimal minimax prediction rate, which is (s/n) log (p/s), up to some constant, under some mild conditions on the design matrix. Here, n is the sample size, p is the dimension and s is the sparsity parameter. We also prove optimality for the estimation error in the l_q-norm, with q ∈ [1, 2] for the Square-Root Lasso, and in the l₂ and sorted l₁ norms for the Square-Root Slope. Both estimators are adaptive to the unknown variance of the noise. The Square-Root Slope is also adaptive to the sparsity s of the true parameter. Next, we prove that any estimator depending on s which attains the minimax rate admits an adaptive to s version still attaining the same rate. We apply this result to the Square-root Lasso. Moreover, for both estimators, we obtain valid rates for a wide range of confidence levels, and improved concentration properties as in [1] where the case of known variance is treated. Our results are non-asymptotic.

We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.