Super Learner for Survival Data Prediction

Abstract

Survival analysis is a widely used method to establish a connection between a time to event outcome and a set of potential covariates. Accurately predicting the time of an event of interest is of primary importance in survival analysis. Many different algorithms have been proposed for survival prediction. However, for a given prediction problem it is rarely, if ever, possible to know in advance which algorithm will perform the best. In this paper we propose two algorithms for constructing super learners in survival data prediction where the individual algorithms are based on proportional hazards. A super learner is a flexible approach to statistical learning that finds the best weighted ensemble of the individual algorithms. Finding the optimal combination of the individual algorithms through minimizing cross-validated risk controls for over-fitting of the final ensemble learner. Candidate algorithms may range from a basic Cox model to tree-based machine learning algorithms, assuming all candidate algorithms are based on the proportional hazards framework. The ensemble weights are estimated by minimizing the cross-validated negative log partial likelihood. We compare the performance of the proposed super learners with existing models through extensive simulation studies. In all simulation scenarios, the proposed super learners are either the best fit or near the best fit. The performances of the newly proposed algorithms are also demonstrated with clinical data examples.

Uncertainty in Lung Cancer Stage for Outcome Estimation via Set-Valued Classification

“…We select Kaplan-Meier estimation for simplicity and ease of exposition, but many alternative methods for survival outcome estimation could be used in practice, including standard parametric survival regression models, the Cox proportional hazards regression 22 , random survival forests 23 , and combinations of parametric, semi-parametric, and nonparametric approaches in a stacked survival model. 24,25,26 Using a Weibull distribution, we simulate right censored event times:…”

Conditional inspection and maintenance of a system with two interacting components

“…Badía et al [3] consider unrevealed failures for a stand-by multicomponent system assuming both economic interaction and dependence between times to failure of components. In, Golmakani and Moakedi [13] failures are stochastically dependent; however, the specification of the interaction is different, with a failure of one component increasing the failure rate of the other. In Wang et al [35] there exists economic dependence, where failure of one component is an opportunity to inspect others within the same subsystem, but not failure dependence.…”

“…For example, failures of secondary cooling systems can induce defects in primary systems that can in turn lead to failure. Electricity distribution systems (Golmakani and Moakedi,[13]), clutches in semi-automatic gearboxes (Scarf and Deara, [26]), manufacturing systems (Lai and Chen, [15]) provide other examples. Our model is motivated by the maintenance of an electro-mechanical clutch that is part of a guillotine whose function is to cut rebar mesh (steel lattice used to reinforce concrete).…”

“…We assume that a penalty cost is incurred while component 1 is in the failed state; this is modelled as a cost-rate (as in Golmakani and Moakedi [13] ) so that if component 1 is failed for time δ then the additional cost incurred is c d × δ, regardless of whether component 2 is good or defective. Our purpose is to determine T , the inspection interval,…”

“…Note that the expressions of E[D i ] and E[D p ] are given in (13) and (14) respectively. A similar reasoning follows to obtain the expected cost in a renewal cycle.…”