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Inference for survival prediction under the regularized Cox model.

ABSTRACT: When a moderate number of potential predictors are available and a survival model is fit with regularization to achieve variable selection, providing accurate inference on the predicted survival can be challenging. We investigate inference on the predicted survival estimated after fitting a Cox model under regularization guaranteeing the oracle property. We demonstrate that existing asymptotic formulas for the standard errors of the coefficients tend to underestimate the variability for some coefficients, while typical resampling such as the bootstrap tends to overestimate it; these approaches can both lead to inaccurate variance estimation for predicted survival functions. We propose a two-stage adaptation of a resampling approach that brings the estimated error in line with the truth. In stage 1, we estimate the coefficients in the observed data set and in [Formula: see text] resampled data sets, and allow the resampled coefficient estimates to vote on whether each coefficient should be 0. For those coefficients voted as zero, we set both the point and interval estimates to [Formula: see text] In stage 2, to make inference about coefficients not voted as zero in stage 1, we refit the penalized model in the observed data and in the [Formula: see text] resampled data sets with only variables corresponding to those coefficients. We demonstrate that ensemble voting-based point and interval estimators of the coefficients perform well in finite samples, and prove that the point estimator maintains the oracle property. We extend this approach to derive inference procedures for survival functions and demonstrate that our proposed interval estimation procedures substantially outperform estimators based on asymptotic inference or standard bootstrap. We further illustrate our proposed procedures to predict breast cancer survival in a gene expression study.

SUBMITTER: Sinnott JA

PROVIDER: S-EPMC5031946 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundNarrowing a large set of features to a smaller one can improve our understanding of the main risk factors for in-hospital mortality in patients with COVID-19. This study aimed to derive a parsimonious model for predicting overall survival (OS) among re-infected COVID-19 patients using machine-learning algorithms.MethodsThe retrospective data of 283 re-infected COVID-19 patients admitted to twenty-six medical centers (affiliated with Shiraz University of Medical Sciences) from 10 June to 26 December 2020 were reviewed and analyzed. An elastic-net regularized Cox proportional hazards (PH) regression and model approximation via backward elimination were utilized to optimize a predictive model of time to in-hospital death. The model was further reduced to its core features to maximize simplicity and generalizability.ResultsThe empirical in-hospital mortality rate among the re-infected COVID-19 patients was 9.5%. In addition, the mortality rate among the intubated patients was 83.5%. Using the Kaplan-Meier approach, the OS (95% CI) rates for days 7, 14, and 21 were 87.5% (81.6-91.6%), 78.3% (65.0-87.0%), and 52.2% (20.3-76.7%), respectively. The elastic-net Cox PH regression retained 8 out of 35 candidate features of death. Transfer by Emergency Medical Services (EMS) (HR=3.90, 95% CI: 1.63-9.48), SpO2≤85% (HR=8.10, 95% CI: 2.97-22.00), increased serum creatinine (HR=1.85, 95% CI: 1.48-2.30), and increased white blood cells (WBC) count (HR=1.10, 95% CI: 1.03-1.15) were associated with higher in-hospital mortality rates in the re-infected COVID-19 patients.ConclusionThe results of the machine-learning analysis demonstrated that transfer by EMS, profound hypoxemia (SpO2≤85%), increased serum creatinine (more than 1.6 mg/dL), and increased WBC count (more than 8.5 (×109 cells/L)) reduced the OS of the re-infected COVID-19 patients. We recommend that future machine-learning studies should further investigate these relationships and the associated factors in these patients for a better prediction of OS.

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Inference for survival prediction under the regularized Cox model.

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