Renewable prediction of model averaging in the Cox proportional hazards model with streaming data

Survival predictions for individuals are increasingly crucial in both clinical practice and survival analysis. Recognizing the pivotal role of model averaging in enhancing prediction accuracy, we address the computational challenges posed by large streams of survival data. Traditional approaches become impractical as they necessitate access to all observations at each accumulation point. To overcome the issue, we introduce online updating model averaging methods tailored for predicting individual survival under the Cox proportional hazards model. We develop renewable estimation techniques for submodel parameters within the context of streaming survival data. Based on a penalized likelihood function, we propose online updating approaches to obtain the renewable estimators of weights. The log-ratio transformation technique is adopted to address the constraint problem of weights. Abundant simulation studies are conducted to illustrate the performance of our proposed renewable model averaging methods in terms of both computational efficiency and prediction accuracy in streaming survival data. Additionally, we demonstrate the superiority of the proposed methodologies by analyzing a substantial lung cancer dataset from the Surveillance, Epidemiology, and End Results program.