Trajectory clustering using mixed classification models

Abstract

Trajectory classification has become frequent in clinical research to understand the heterogeneity of individual trajectories. The standard classification model for trajectories assumes no between-individual variance within groups. However, this assumption is often not appropriate, which may overestimate the error variance of the model, leading to a biased classification. Hence, two extensions of the standard classification model were developed through a mixed model. The first one considers an equal between-individual variance across groups, and the second one considers unequal between-individual variance. Simulations were performed to evaluate the impact of these considerations on the classification. The simulation results showed that the first extended model gives a lower misclassification percentage (with differences up to 50%) than the standard one in case of presence of a true variance between individuals inside groups. The second model decreases the misclassification percentage compared with the first one (up to 11%) when the between-individual variance is unequal between groups. However, these two extensions require high number of repeated measurements to be adjusted correctly. Using human chorionic gonadotropin trajectories after curettage for hydatidiform mole, the standard classification model classified trajectories mainly according to their levels whereas the two extended models classified them according to their patterns, which provided more clinically relevant groups. In conclusion, for studies with a nonnegligible number of repeated measurements, the use, in first instance, of a classification model that considers equal between-individual variance across groups rather than a standard classification model, appears more appropriate. A model that considers unequal between-individual variance may find its place thereafter.

Keywords: ECM algorithm; between-individual variance; classification; longitudinal data; mixed model; trajectories.