Joint Longitudinal-Survival Modelling of Childhood Leukemia Using EM Algorithm

Abstract

This Study aims to assess the impact of certain clinical factors on children with leukemia by employing The Joint Model for Longitudinal and survival data, using the Expectation–Maximization (EM) algorithm for parameter estimation. In this research, the longitudinal data are represented by repeated measurements of hemoglobin (Hb) levels over time, while the survival data correspond to the follow-up time until the realization of the event (death or censoring). The results revealed that Hb levels significantly decrease over time (p < 0.0001). Female patients had lower Hb levels compared to males (p=0.006), while older age was associated with slightly higher Hb values (p=0.0002). In the survival sub-model, the effects of age and sex were statistically insignificant (p > 0.05). Importantly, the negative and significant association parameter (γ, p=0.0001) indicated that higher Hb levels reduce the risk of death, highlighting the predictive value of longitudinal information in explaining survival outcomes. Based on the goodness-of-fit criteria (AIC and RMSE), the EM algorithm demonstrated high efficiency in estimating the parameters of the joint model and achieving strong agreement between predicted and observed values. Therefore, the joint model provides a powerful and effective tool for integrating longitudinal and survival information in the study of childhood leukemia, enhancing estimation accuracy and enabling more reliable conclusions about the factors influencing disease progression.