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.

“Footprinting” missing epidemiological data for cervical cancer: a case study in India

“…Moreover, it also helps to pinpoint geographical units that could be interesting for future data collection efforts. Secondly, we made use of a newly developed clustering method [21, 22] that is able to assess the similarities between age-specific patterns of cervical cancer incidence, which have not been considered by previous studies.…”

“…The statistical method employed in the Clustering step to cluster registry-specific cervical cancer incidence data was a Poisson-regression-based CEM clustering algorithm,[21, 22] described in detail in Appendix S1 . Briefly, clusters of age-specific cervical cancer incidence were obtained by likelihood-based optimization under Poisson regression model.…”

Clustering of trajectories with mixed effects classification model: Inference taking into account classification uncertainties

“…This method is classically used for models without random effects, but it was evaluated and validated for mixed effects models 5 . In the M step, the estimates of $$$ {\boldsymbol{\beta}}_{\boldsymbol{k}},{\boldsymbol{D}}_{\boldsymbol{k}}, $$$ and $$$ {\sigma}_k^2 $$$ can be obtained using classical algorithms for mixed effects models, such as the ones included in the lme function from the nlme R package 10 (R version 3.6.2).…”

“…The classification model applied to the dataset was defined as the model used for data simulation. The CEM algorithm was initialized from the true partition because the performances of the CEM algorithm were already evaluated in a previous paper 5 . Except for the sensitivity analyses on the number of SEM iterations, all simulations were performed with a number of SEM iterations equal to 100.…”

“…This article focuses on the classification model. In order to take into account the between‐individual variability within groups, it is possible to extend the classification model by incorporating random effects around the typical trajectories 5 …”