Machine Learning at the Service of Survival Analysis: Predictions Using Time-to-Event Decomposition and Classification Applied to a Decrease of Blood Antibodies against COVID-19

Abstract

The Cox proportional hazard model may predict whether an individual belonging to a given group would likely register an event of interest at a given time. However, the Cox model is limited by relatively strict statistical assumptions. In this study, we propose decomposing the time-to-event variable into “time” and “event” components and using the latter as a target variable for various machine-learning classification algorithms, which are almost assumption-free, unlike the Cox model. While the time component is continuous and is used as one of the covariates, i.e., input variables for various classification algorithms such as logistic regression, naïve Bayes classifiers, decision trees, random forests, and artificial neural networks, the event component is binary and thus may be modeled using these classification algorithms. Moreover, we apply the proposed method to predict a decrease or non-decrease of IgG and IgM blood antibodies against COVID-19 (SARS-CoV-2), respectively, below a laboratory cut-off, for a given individual at a given time point. Using train-test splitting of the COVID-19 dataset (n=663 individuals), models for the mentioned algorithms, including the Cox proportional hazard model, are learned and built on the train subsets while tested on the test ones. To increase robustness of the model performance evaluation, models’ predictive accuracies are estimated using 10-fold cross-validation on the split dataset. Even though the time-to-event variable decomposition might ignore the effect of individual data censoring, many algorithms show similar or even higher predictive accuracy compared to the traditional Cox proportional hazard model. In COVID-19 IgG decrease prediction, multivariate logistic regression (of accuracy 0.811), support vector machines (of accuracy 0.845), random forests (of accuracy 0.836), artificial neural networks (of accuracy 0.806) outperform the Cox proportional hazard model (of accuracy 0.796), while in COVID-19 IgM antibody decrease prediction, neither Cox regression nor other algorithms perform well (best accuracy is 0.627 for Cox regression). An accurate prediction of mainly COVID-19 IgG antibody decrease can help the healthcare system manage, with no need for extensive blood testing, to identify individuals, for instance, who could postpone boosting vaccination if new COVID-19 variant incomes or should be flagged as high risk due to low COVID-19 antibodies.