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Information criteria for Firth's penalized partial likelihood approach in Cox regression models.

ABSTRACT: In the estimation of Cox regression models, maximum partial likelihood estimates might be infinite in a monotone likelihood setting, where partial likelihood converges to a finite value and parameter estimates converge to infinite values. To address monotone likelihood, previous studies have applied Firth's bias correction method to Cox regression models. However, while the model selection criteria for Firth's penalized partial likelihood approach have not yet been studied, a heuristic AIC-type information criterion can be used in a statistical package. Application of the heuristic information criterion to data obtained from a prospective observational study of patients with multiple brain metastases indicated that the heuristic information criterion selects models with many parameters and ignores the adequacy of the model. Moreover, we showed that the heuristic information criterion tends to select models with many regression parameters as the sample size increases. Thereby, in the present study, we propose an alternative AIC-type information criterion based on the risk function. A Bayesian information criterion type was also evaluated. Further, the presented simulation results confirm that the proposed criteria performed well in a monotone likelihood setting. The proposed AIC-type criterion was applied to prospective observational study data. Copyright © 2017 John Wiley & Sons, Ltd.

SUBMITTER: Nagashima K

PROVIDER: S-EPMC6084330 | biostudies-other | 2017 Sep

REPOSITORIES: biostudies-other

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Information criteria for Firth's penalized partial likelihood approach in Cox regression models.

Nagashima Kengo K Sato Yasunori Y

Statistics in medicine 20170612 21

In the estimation of Cox regression models, maximum partial likelihood estimates might be infinite in a monotone likelihood setting, where partial likelihood converges to a finite value and parameter estimates converge to infinite values. To address monotone likelihood, previous studies have applied Firth's bias correction method to Cox regression models. However, while the model selection criteria for Firth's penalized partial likelihood approach have not yet been studied, a heuristic AIC-type ...[more]

PMID: 28608396

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Project 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.

Dataset Information

Information criteria for Firth's penalized partial likelihood approach in Cox regression models.

Publications

Information criteria for Firth's penalized partial likelihood approach in Cox regression models.

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