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Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models
Fitting Cox models in a big data context -on a massive scale in terms of volume, intensity, and complexity exceeding the capacity of usual analytic tools-is often challenging. If some data are missing, it is even more difficult. We proposed algorithms that were able to fit Cox models in high dimensi...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Frontiers Media S.A.
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8591675/ https://www.ncbi.nlm.nih.gov/pubmed/34790895 http://dx.doi.org/10.3389/fdata.2021.684794 |
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author | Bertrand , Frédéric Maumy-Bertrand , Myriam |
author_facet | Bertrand , Frédéric Maumy-Bertrand , Myriam |
author_sort | Bertrand , Frédéric |
collection | PubMed |
description | Fitting Cox models in a big data context -on a massive scale in terms of volume, intensity, and complexity exceeding the capacity of usual analytic tools-is often challenging. If some data are missing, it is even more difficult. We proposed algorithms that were able to fit Cox models in high dimensional settings using extensions of partial least squares regression to the Cox models. Some of them were able to cope with missing data. We were recently able to extend our most recent algorithms to big data, thus allowing to fit Cox model for big data with missing values. When cross-validating standard or extended Cox models, the commonly used criterion is the cross-validated partial loglikelihood using a naive or a van Houwelingen scheme —to make efficient use of the death times of the left out data in relation to the death times of all the data. Quite astonishingly, we will show, using a strong simulation study involving three different data simulation algorithms, that these two cross-validation methods fail with the extensions, either straightforward or more involved ones, of partial least squares regression to the Cox model. This is quite an interesting result for at least two reasons. Firstly, several nice features of PLS based models, including regularization, interpretability of the components, missing data support, data visualization thanks to biplots of individuals and variables —and even parsimony or group parsimony for Sparse partial least squares or sparse group SPLS based models, account for a common use of these extensions by statisticians who usually select their hyperparameters using cross-validation. Secondly, they are almost always featured in benchmarking studies to assess the performance of a new estimation technique used in a high dimensional or big data context and often show poor statistical properties. We carried out a vast simulation study to evaluate more than a dozen of potential cross-validation criteria, either AUC or prediction error based. Several of them lead to the selection of a reasonable number of components. Using these newly found cross-validation criteria to fit extensions of partial least squares regression to the Cox model, we performed a benchmark reanalysis that showed enhanced performances of these techniques. In addition, we proposed sparse group extensions of our algorithms and defined a new robust measure based on the Schmid score and the R coefficient of determination for least absolute deviation: the integrated R Schmid Score weighted. The R-package used in this article is available on the CRAN, http://cran.r-project.org/web/packages/plsRcox/index.html. The R package bigPLS will soon be available on the CRAN and, until then, is available on Github https://github.com/fbertran/bigPLS. |
format | Online Article Text |
id | pubmed-8591675 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Frontiers Media S.A. |
record_format | MEDLINE/PubMed |
spelling | pubmed-85916752021-11-16 Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models Bertrand , Frédéric Maumy-Bertrand , Myriam Front Big Data Big Data Fitting Cox models in a big data context -on a massive scale in terms of volume, intensity, and complexity exceeding the capacity of usual analytic tools-is often challenging. If some data are missing, it is even more difficult. We proposed algorithms that were able to fit Cox models in high dimensional settings using extensions of partial least squares regression to the Cox models. Some of them were able to cope with missing data. We were recently able to extend our most recent algorithms to big data, thus allowing to fit Cox model for big data with missing values. When cross-validating standard or extended Cox models, the commonly used criterion is the cross-validated partial loglikelihood using a naive or a van Houwelingen scheme —to make efficient use of the death times of the left out data in relation to the death times of all the data. Quite astonishingly, we will show, using a strong simulation study involving three different data simulation algorithms, that these two cross-validation methods fail with the extensions, either straightforward or more involved ones, of partial least squares regression to the Cox model. This is quite an interesting result for at least two reasons. Firstly, several nice features of PLS based models, including regularization, interpretability of the components, missing data support, data visualization thanks to biplots of individuals and variables —and even parsimony or group parsimony for Sparse partial least squares or sparse group SPLS based models, account for a common use of these extensions by statisticians who usually select their hyperparameters using cross-validation. Secondly, they are almost always featured in benchmarking studies to assess the performance of a new estimation technique used in a high dimensional or big data context and often show poor statistical properties. We carried out a vast simulation study to evaluate more than a dozen of potential cross-validation criteria, either AUC or prediction error based. Several of them lead to the selection of a reasonable number of components. Using these newly found cross-validation criteria to fit extensions of partial least squares regression to the Cox model, we performed a benchmark reanalysis that showed enhanced performances of these techniques. In addition, we proposed sparse group extensions of our algorithms and defined a new robust measure based on the Schmid score and the R coefficient of determination for least absolute deviation: the integrated R Schmid Score weighted. The R-package used in this article is available on the CRAN, http://cran.r-project.org/web/packages/plsRcox/index.html. The R package bigPLS will soon be available on the CRAN and, until then, is available on Github https://github.com/fbertran/bigPLS. Frontiers Media S.A. 2021-11-01 /pmc/articles/PMC8591675/ /pubmed/34790895 http://dx.doi.org/10.3389/fdata.2021.684794 Text en Copyright © 2021 Bertrand and Maumy-Bertrand . https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. |
spellingShingle | Big Data Bertrand , Frédéric Maumy-Bertrand , Myriam Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models |
title | Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models |
title_full | Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models |
title_fullStr | Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models |
title_full_unstemmed | Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models |
title_short | Fitting and Cross-Validating Cox Models to Censored Big Data With Missing Values Using Extensions of Partial Least Squares Regression Models |
title_sort | fitting and cross-validating cox models to censored big data with missing values using extensions of partial least squares regression models |
topic | Big Data |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8591675/ https://www.ncbi.nlm.nih.gov/pubmed/34790895 http://dx.doi.org/10.3389/fdata.2021.684794 |
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