Advanced Methodology Developments in Mixture Cure Models

Modern medical treatments have substantially improved cure rates for many chronic diseases and have generated increasing interest in appropriate statistical models to handle survival data with non-negligible cure fractions. The mixture cure models are designed to model such data set, which assume that studied population is a mixture of being cured and uncured. In this dissertation, I will develop two programs named smcure and NPHMC in R. The first program aims to facilitate estimating two popular mixture cure models: the proportional hazards (PH) mixture cure model and accelerated failure time (AFT) mixture cure model. The second program focuses on designing the sample size needed in survival trial with and without cure fractions based on the PH mixture cure model and standard PH model. The two programs have been tested by comprehensive settings and real data analysis and are now available for download from R CRAN. The third project in my dissertation will focus on the development of a new estimation method for the PH mixture cure model with competing risk data. The performance of proposed method has been evaluated by extensive simulation studies

Mixture Cure Models: Simulation Comparisons of Methods in R and SAS

Typical survival methods have the assumption that every subject will eventually experience the event of interest, given enough follow-up time. However, there are some occasions in which a proportion of the population of interest will never experience the event of interest. Therefore, the incorporation of a “cure” fraction in a statistical model is necessary. In this thesis, I comprehensively evaluate mixture cure models in two different statistical software programs: the smcure package in R and the PSPMCM macro in SAS. Extensive simulation studies in R and SAS allow evaluation of the performance of these two models. An additional aspect of this thesis involves application of the mixture cure models in R and SAS to a new real data set of soft tissue sarcoma patients. The results from the models fitted to the sarcoma data set in R and in SAS will then be compared

On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility

[Abstract]: In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should be considered instead. This paper deals with the problem of adapting a machine learning approach for classical survival analysis to a situation when cure (i.e., not suffering the event) is a possibility. Specifically, a brief review of cure models and recent machine learning methodologies is presented, and an adaptation of machine learning approaches to account for cured individuals is introduced. In order to validate the proposed methods, we present an extensive simulation study in which we compare the performance of the adapted machine learning algorithms with existing cure models. The results show the good behavior of the semiparametric or the nonparametric approaches, depending on the simulated scenario. The practical utility of the methodology is showcased through two real-world dataset illustrations. In the first one, the results show the gain of using the nonparametric mixture cure model approach. In the second example, the results show the poor performance of some machine learning methods for small sample sizes.This project was funded by the Xunta de Galicia (Axencia Galega de Innovación) Research projects COVID-19 presented in ISCIII IN845D 2020/26, Operational Program FEDER Galicia 2014–2020; by the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union European Regional Development Fund (ERDF)-Galicia 2014–2020 Program, by grant ED431G 2019/01; and by the Spanish Ministerio de Economía y Competitividad (research projects PID2019-109238GB-C22 and PID2021-128045OA-I00). ALC was sponsored by the BEATRIZ GALINDO JUNIOR Spanish Grant from MICINN (Ministerio de Ciencia e Innovación) with code BGP18/00154. ALC was partially supported by the MICINN Grant PID2020-113578RB-I00 and partial support of Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14). We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C-2020-14Xunta de Galicia; IN845D 2020/2

Cure models to estimate time until hospitalization due to COVID-19

A short introduction to survival analysis and censored data is included in this paper. A thorough literature review in the field of cure models has been done. An overview on the most important and recent approaches on parametric, semiparametric and nonparametric mixture cure models is also included. The main nonparametric and semiparametric approaches were applied to a real time dataset of COVID-19 patients from the first weeks of the epidemic in Galicia (NW Spain). The aim is to model the elapsed time from diagnosis to hospital admission. The main conclusions, as well as the limitations of both the cure models and the dataset, are presented, illustrating the usefulness of cure models in this kind of studies, where the influence of age and sex on the time to hospital admission is shown.Comment: 14 pages, 8 figure

Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models

© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. This version of the article [López-Cheda, A., Cao, R., Jácome, M.A., Van Keilegom, I., 2017. Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models. Computational Statistics & Data Analysis 105, 144–165] has been accepted for publication in Computational Statistics & Data Analysis. The Version of Record is available online at https://doi.org/10.1016/j.csda.2016.08.002.[Abstract]: A completely nonparametric method for the estimation of mixture cure models is proposed. A nonparametric estimator of the incidence is extensively studied and a nonparametric estimator of the latency is presented. These estimators, which are based on the Beran estimator of the conditional survival function, are proved to be the local maximum likelihood estimators. An i.i.d. representation is obtained for the nonparametric incidence estimator. As a consequence, an asymptotically optimal bandwidth is found. Moreover, a bootstrap bandwidth selection method for the nonparametric incidence estimator is proposed. The introduced nonparametric estimators are compared with existing semiparametric approaches in a simulation study, in which the performance of the bootstrap bandwidth selector is also assessed. Finally, the method is applied to a database of colorectal cancer from the University Hospital of A Coruña (CHUAC).The first author’s research was sponsored by the Spanish FPU grant from MECD with reference FPU13/01371. The work of the first author has been partially carried out during a visit at the Université catholique de Louvain, financed by INDITEX, with reference INDITEX-UDC 2014. All the authors acknowledge partial support by the MINECO grant MTM2014-52876-R (EU ERDF support included). The first three authors’ research has been partially supported by MICINN Grant MTM2011-22392 (EU ERDF support included) and Xunta de Galicia GRC Grant CN2012/130. The research of the fourth author was supported by IAP Research Network P7/06 of the Belgian State (Belgian Science Policy), and by the contract “Projet d’Actions de Recherche Concertées” (ARC) 11/16-039 of the “Communauté française de Belgique” (granted by the “ Académie universitaire Louvain”). The authors would like to thank the Associate Editor and the three anonymous referees for their constructive and helpful comments, which have greatly improved the paper. The authors are grateful to Dr. Sonia Pértega and Dr. Salvador Pita, at the University Hospital of A Coruña, for providing the colorectal cancer data set.Xunta de Galicia; CN2012/13

Cure models to estimate time until hospitalization due to COVID-19

This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10489-021-02311-8[Abstract]: A short introduction to survival analysis and censored data is included in this paper. A thorough literature review in the field of cure models has been done. An overview on the most important and recent approaches on parametric, semiparametric and nonparametric mixture cure models is also included. The main nonparametric and semiparametric approaches were applied to a real time dataset of COVID-19 patients from the first weeks of the epidemic in Galicia (NW Spain). The aim is to model the elapsed time from diagnosis to hospital admission. The main conclusions, as well as the limitations of both the cure models and the dataset, are presented, illustrating the usefulness of cure models in this kind of studies, where the influence of age and sex on the time to hospital admission is shown.MPL activity was funded by the Science, Technology, and Innovation Plan of the Principality of Asturias (Spain) Ref: FC-GRUPIN-IDI/2018/000225, which is part-funded by the European Regional Development Fund (ERDF). ALC was sponsored by the BEATRIZ GALINDO JUNIOR Spanish Grant from MICINN (Ministerio de Ciencia, Innovación y Universidades) with reference BGP18/00154. RC and ALC acknowledge partial support by the MINECO grant MTM2017-82724-R, and by the Xunta de Galicia: Grupos de Referencia Competitiva ED431C-2020-14, Centro de Investigación del Sistema universitario de Galicia ED431G 2019/01, and Axencia Galega de Innovación (Ayudas proyectos de investigación COVID-19 presentados a la convocatoria del ISCIII IN845D 2020/26 - Programa Operativo FEDER Galicia 2014-2020), all of them through the ERDF.Gobierno del Principado de Asturias; FC-GRUPIN-IDI/2018/000225Xunta de Galicia; ED431C-2020-14Xunta de Galicia; ED431G 2019/0