EM algorithm estimation of a structural equation model for the longitudinal study of the quality of life

Health-related quality of life (HRQoL) data are measured via patient questionnaires, completed by the patients themselves at different time points. We focused on oncology data gathered through the use of European Organization for Research and Treatment of Cancer questionnaires, which decompose HRQoL into several functional dimensions, several symptomatic dimensions, and the global health status (GHS). We aimed to perform a global analysis of HRQoL and reduce the number of analyses required by using a two-step approach. First, a structural equation model (SEM) was used for each time point; in these models, the GHS is explained by two latent variables. Each latent variable is a factor that summarizes, respectively, the functional dimensions and the symptomatic dimensions to the global measurement. This is achieved through the maximization of the likelihood of each SEM using the EM algorithm, which has the advantage of giving an estimation of the subject-specific factors and the influence of additional explanatory variables. Then, to consider the longitudinal aspect, the GHS variable and the two factors were concatenated for each patient visit at which the questionnaire was completed. The GHS and the two factors estimated in the first step can then be explained by additional explanatory variables using a linear mixed model.