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Table 1 Summary statistics of baseline covariates, the estimated regression coefficients, and the estimated parameters of variance (Var) and covariance (Cov) from the univariate and bivariate mixed models for longitudinal mean deviation (MD) and visual acuity (VA)

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

Variables Mean ± SD or N (%) Estimated fixed and random effects ± standard errors
Univariate mixed model Bivariate mixed model
MD VA MD VA
Fixed effects:
 Intercept - −2.26 ± 0.34# 50.75 ± 1.03# −2.23 ± 0.34# 50.88 ± 1.00#
 Slope - −0.35 ± 0.04# −0.60 ± 0.11# −0.35 ± 0.04# −0.69 ± 0.11#
 Age (years) 65.7 ± 9.5 −0.49 ± 0.15# −3.45 ± 0.43# −0.43 ± 0.14# −3.07 ± 0.42#
 IOP (mmHg) 22.3 ± 6.2 −0.55 ± 0.16# −0.55 ± 0.47 −0.55 ± 0.16# −0.40 ± 0.45
 CCT (μm) 558.4 ± 37.8 0.35 ± 0.15* −0.07 ± 0.45 0.35 ± 0.15* −0.22 ± 0.44
 HCD 0.53 ± 0.19 0.20 ± 0.15 0.12 ± 0.44 0.20 ± 0.15 0.12 ± 0.44
 Male 150 (56%) 0.11 ± 0.29 0.77 ± 0.87 0.06 ± 0.29 1.01 ± 0.84
 African American 89 (33%) −0.57 ± 0.31 −2.13 ± 0.94* −0.58 ± 0.31 −2.15 ± 0.91*
 Observation group 158 (59%) −0.08 ± 0.32 −0.26 ± 0.94 −0.10 ± 0.32 −0.69 ± 0.92
Random effects:&
 Var(Ek)   2.03 ± 0.06# 19.15 ± 0.96# 2.02 ± 0.06# 19.19 ± 0.96#
 Var(Ik)   5.05 ± 0.51# 39.25 ± 4.69# 5.09 ± 0.51# 38.77 ± 4.63#
 Var(Sk)   0.29 ± 0.04# 1.35 ± 0.25# 0.29 ± 0.04# 1.35 ± 0.24#
 Cov(Ik, Sk)   0.62 ± 0.10# −1.23 ± 0.83 0.63 ± 0.10# −0.73 ± 0.79
 Cov(I1, I2)   - - - 3.88 ± 1.17#
 Cov(S1, S2)   - - - 0.37 ± 0.08#
 Cov(I1, S2)   - - - 1.16 ± 0.27#
 Cov(I2, S1)   - - - 0.67 ± 0.31*
  1. IOP intraocular pressure, CCT central corneal thickness, HCD horizontal cup-to-disc ratio
  2. &Ek, Ik, Sk: error term, random intercept, and random slope for MD (k = 1) and VA (k = 2)
  3. * p < 0.05, # p < 0.01