This review uses machine learning techniques to manage missing data in time-to-event analyses, particularly with censored data. Missing patient dropout data affects outcome variables and covariates, complicating analysis and inference accuracy. A comprehensive search was conducted across PubMed, Web of Knowledge, Scopus, and Embase for studies published between January 2010 and July 2024 that addressed approaches to managing missing data in survival analysis. The review emphasized machine learning (ML) methods for handling missing data. We reviewed 22 studies on missing data handling in survival analyses, including prevalence, mechanisms, censorship types, and software tools. Most studies (31.8%) were published in 2021, with 59.1% addressing missing at random data. Nearly 46% did not use simulations for imputation performance. K-nearest Neighbor (KNN) was the most common ML method (36.3%). Fourteen studies used R (63.6%), four used Python (18.8%), and others used SAS or MATLAB. All ML methods improved predictive performance based on criteria like C-index and bias. Despite guidelines, ML techniques in survival analysis with censored data are rarely applied. Many studies do not clearly describe missing data handling or assumptions. Our review highlights improved predictive performance when ML manages missing data.