The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

When analyzing time-to-event data, it often happens that a certain fraction of the data corresponds to subjects who 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 article reviews 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.

/pdf/cure-models-in-survival-analysis-1inwkzplv9.pdf

Cure Models in Survival Analysis

Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models

Farmland fragmentation and farmland consolidation are two sides of the same coin paradoxically viewed as farmland management tools. While there is a vast body of literature addressing the connections between farmland fragmentation and farmland consolidation on the one hand and agriculture production and crops diversification on the other hand, their relationship with variations in food security is still under-explored. This challenges policy makers about whether and how to devise policies in favor of fragmentation conservation or defragmentation. Therefore, drawing on the multiple secondary data and the deductive logical reasoning through an integrative concept-centric qualitative approach following the rationalist theory, this study critically reviews and analyses the existing body of literature to identify how farmland fragmentation versus defragmentation approaches relate to food security. The goal is to develop and derive an explicit model indicating when, where, how and why farmland fragmentation can be conserved or prevented and controlled for food security motives as a novel alternative comprehensive scientific knowledge generation, which could guide and inform the design of future research and policies about farmland fragmentation management. The findings show that both fragmentation and consolidation variously (positively and negatively) impact on food security at different (macro, meso and micro) levels. While farmland fragmentation is highly linked with food diversification (food quality), acceptability, accessibility, and sovereignty at the local (household and individual) levels, farmland consolidation is often associated with the quantity and availability of food production at the community, regional and national levels. Theoretically, the best management of farmland fragmentation for food security purposes can be achieved by minimizing the problems associated with physical and tenure aspects of farmland fragmentation along with the optimization of its potential benefits. In this regard, farmland consolidation, voluntary parcel exchange and on-field harvest sales, farmland realignment, and farmland use (crop) consolidation can be suitable for the control of physical fragmentation problems under various local conditions. Similarly, farmland banking and off-farm employment, restrictions about the minimum parcel sizes subdivision and absentee owners, joint ownership, cooperative farming, farmland use (crop) consolidation, agricultural land protection policies, and family planning measures can be suitable to prevent and minimize farmland tenure fragmentation problems. On the other hand, various agriculture intensification programs, agroecogical approaches, and land saving technologies can be the most suitable strategies to maximize the income from agriculture on fragmented plots under the circumstances of beneficial fragmentation. Moreover, in areas where both rational and defective fragmentation scenarios coexist, different specific strategies like localized and multicropping based land consolidation approaches in combination with or without agriculture intensification programs, can provide better and more balanced optimal solutions. These could simultaneously minimize the defective effects of fragmentation thereby optimizing or without jeopardizing its potential benefits with regard to food security under specific local conditions.

Farmland Fragmentation, Farmland Consolidation and Food Security: Relationships, Research Lapses and Future Perspectives

In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be “cured.” The population is thus a mixture of two subpopulations, one of cured subjects and one of “susceptible” subjects. We propose a novel approach to estimate a mixture cure model when covariates are present and the lifetime is subject to random right censoring. We work with a parametric model for the cure proportion, while the conditional survival function of the uncured subjects is unspecified. The approach is based on an inversion which allows us to write the survival function as a function of the distribution of the observable variables. This leads to a very general class of models which allows a flexible and rich modeling of the conditional survival function. We show the identifiability of the proposed model as well as the consistency and the asymptotic normality of the model parameters. We also consider in more detail the case where kernel estimators are used for the nonparametric part of the model. The new estimators are compared with the estimators from a Cox mixture cure model via simulations. Finally, we apply the new model on a medical data set.

/pdf/a-general-approach-for-cure-models-in-survival-analysis-4fv22853ts.pdf

A general approach for cure models in survival analysis

In lifetime data, like cancer studies, there may be long term survivors, which lead to heavy censoring at the end of the follow-up period. Since a standard survival model is not appropriate to handle these data, a cure model is needed. In the literature, covariate hypothesis tests for cure models are limited to parametric and semiparametric methods. We fill this important gap by proposing a nonparametric covariate hypothesis test for the probability of cure in mixture cure models. A bootstrap method is proposed to approximate the null distribution of the test statistic. The procedure can be applied to any type of covariate, and could be extended to the multivariate setting. Its efficiency is evaluated in a Monte Carlo simulation study. Finally, the method is applied to a colorectal cancer dataset.

/pdf/nonparametric-covariate-hypothesis-tests-for-the-cure-rate-1mrefcoibl.pdf

Nonparametric covariate hypothesis tests for the cure rate in mixture cure models

How do early socioeconomic circumstances impact inflammatory trajectories? Findings from Generation XXI.

Understanding the demand for hospital beds for COVID-19 patients is key for decision-making and planning mitigation strategies, as overwhelming healthcare systems has critical consequences for disease mortality. However, accurately mapping the time-to-event of hospital outcomes, such as the length-of-stay in the ICU, requires understanding patient trajectories while adjusting for covariates and observation bias, such as incomplete data. Standard methods, like the Kaplan-Meier estimator, require prior assumptions that are untenable given current knowledge. Using real-time surveillance data from the first weeks of the COVID-19 epidemic in Galicia (Spain), we aimed to model the time-to-event and event probabilities of patients hospitalized, without parametric priors and adjusting for individual covariates. We applied a nonparametric Mixture Cure Model and compared its performance in estimating hospital ward/ICU lengths-of-stay to the performances of commonly used methods to estimate survival. We showed that the proposed model outperformed standard approaches, providing more accurate ICU and hospital ward length-of-stay estimates. Finally, we applied our model estimates to simulate COVID-19 hospital demand using a Monte Carlo algorithm. We provided evidence that adjusting for sex, generally overlooked in prediction models, together with age is key for accurately forecasting ICU occupancy, as well as discharge or death outcomes.

/pdf/estimating-covid-19-hospital-demand-using-a-non-parametric-4fqxuwved5.pdf

Estimating COVID-19 hospital demand using a non-parametric model: a case study in Galicia (Spain)

Nonparametric Estimation in Mixture Cure Models [R package npcure version 0.1-5]

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