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Table 5 Averages and 95% confidence intervals for correlations between random intercepts and correlation between random slopes based on simulated data, where data were generated under 3 different scenarios (Scenarios A: different proportions of progressive cases; Scenarios B: different magnitudes of deteriorating rates in progressive cases; Scenarios C: various strength of between-error correlations)

From: Estimating correlation between multivariate longitudinal data in the presence of heterogeneity

Simulation Scenarios Correlation between random intercepts Correlation between random slopes
True correlation (no heterogeneity) 0.145 0.111
Scenario A:
 5% 0.199 (0.070, 0.329) 0.522 (0.390, 0.654)a
 10% 0.246 (0.118, 0.373) 0.657 (0.562, 0.753)a
 15% 0.268 (0.153, 0.383)a 0.727 (0.651, 0.804)a
 20% 0.296 (0.178, 0.413)a 0.769 (0.698, 0.840)a
Scenario B:
 50% 0.200 (0.070, 0.329) 0.240 (0.051, 0.429)
 75% 0.207 (0.077, 0.336) 0.382 (0.223, 0.542)a
 100% 0.199 (0.070, 0.329) 0.522 (0.390, 0.654)a
 125% 0.205 (0.078, 0.332) 0.634 (0.532, 0.734)a
 150% 0.202 (0.078, 0.327) 0.706 (0.616, 0.795)a
Scenario C:
 0.0 0.199 (0.070, 0.329) 0.522 (0.390, 0.654)a
 0.2 0.232 (0.104, 0.361) 0.603 (0.479, 0.727)a
 0.4 0.273 (0.147, 0.398)a 0.686 (0.574, 0.797)a
 0.6 0.303 (0.180, 0.425)a 0.769 (0.664, 0.873)a
 0.8 0.334 (0.218, 0.450)a 0.853 (0.756, 0.949)a
  1. a95% confidence interval does not contain the true value