A Hard EM algorithm for prediction of the cured fraction in survival data

• Published in: Computational statistics Vol. 37; no. 2; pp. 817 - 835
• Main Authors: Kosovalić, Nemanja, Barui, Sandip
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022; Springer Nature B.V
• Subjects: Algorithms; Asymptotic properties; Drug development; Economic Theory/Quantitative Economics/Mathematical Methods; Industrial development; Mathematics and Statistics; Missing data; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Survival; Survival analysis; Missing data; Survival analysis; Hard EM algorithm; PU learning; Cutaneous melanoma; Binary classification
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-021-01140-0

In clinical studies, survival analysis is a well known technique to analyze time to event data with the assumption that every subject in the study will encounter the event of interest. With recent advancements in the drug development industry, a fraction of subjects may not face the event and are considered as immune or cured. However, due to the finite study period, full knowledge of subjects who are immune is usually not known and hence, can be considered as missing. We develop a novel semi-parametric algorithm to address this problem by minimizing a suitable loss function, which incorporates the missing data and generates cure indicators for the censored individuals. We prove the existence of a global minimizer for the loss function and establish some asymptotic properties, demonstrate via numerical experiments that under appropriate circumstances, our approach performs better than simpler alternatives, and use this algorithm to estimate lifetime parameters and the overall survivor function.