Table 1. Simulation results for identification of at-risk multiple trajectories clusters associated with response outcomes.

Number of risk clusters associated with outcomes	Marginal method			Joint method PC-FPC
	j = 1	j = 2	j = 3
< 2	3.6%	5.0%	4.7%	0.0%
2	62.3%	83.0%	84.0%	9.6%
3	31.7%	11.5%	10.8%	59.8%
4	2.4%	0.5%	0.5%	30.6%

For 1000 Monte Carlo (MC) repetitions with sample size n = 1000, the numbers of risk clusters were identified by analysis of variance (ANOVA) and Tukey’s multiple comparisons with a family-wise significance level 0.05. At each repetition, we counted subgroups completely separated by Tukey’s post-hoc analysis. For example, we identify two clusters if all subgroups included in a cluster show significant differences in pairwise comparison (family-wise significance level 0.05) against the other cluster members. Percentages in each column of the table demonstrate how many clusters are detected through 1000 MC repetitions. For the comparison with the marginal method, we applied the same procedure, using the marginal trajectory information only for j = 1, 2, 3, respectively.