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.

中文翻译：

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使用混合分类模型的轨迹聚类

轨迹分类在临床研究中变得频繁，以了解个体轨迹的异质性。轨迹的标准分类模型假设组内没有个体间差异。但是，这种假设往往并不恰当，可能会高估模型的误差方差，导致分类有偏差。因此，标准分类模型的两个扩展是通过混合模型开发的。第一个考虑组间相等的个体间方差，第二个考虑不相等的个体间方差。进行了模拟以评估这些考虑因素对分类的影响。模拟结果表明，在组内个体之间存在真实差异的情况下，第一个扩展模型给出的错误分类百分比（差异高达 50%）低于标准模型。当组间个体间方差不相等时，第二个模型与第一个模型相比降低了错误分类的百分比（高达 11%）。然而，这两个扩展需要大量重复测量才能正确调整。使用葡萄胎刮宫后的人绒毛膜促性腺激素轨迹，标准分类模型主要根据其水平对轨迹进行分类，而两个扩展模型则根据其模式对它们进行分类，从而提供了更多的临床相关组。综上所述，对于重复测量次数不可忽略的研究，首先使用考虑组间个体间方差相等的分类模型而不是标准分类模型似乎更合适。一个考虑不等个体间方差的模型可能会在此后找到它的位置。