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Table 4 Fitted multivariate and separate univariate joint models to the PBC data

From: joineRML: a joint model and software package for time-to-event and multivariate longitudinal outcomes

  joineRML (NR) joineRML (GN) Bootstrap joineR
  Estimate SE 95% CId Estimate SE 95% CId SE 95% CIe Estimate SE 95% CIe
β 0,1 0.5541 0.0858 (0.3859, 0.7223) 0.5549 0.0846 (0.3892, 0.7207) 0.0800 (0.4264, 0.7435) 0.5545 0.0838 (0.3802, 0.7031)
β 1,1 0.2009 0.0201 (0.1616, 0.2402) 0.2008 0.0201 (0.1614, 0.2402) 0.0204 (0.1669, 0.2468) 0.1808 0.0209 (0.1430, 0.2324)
β 0,2 3.5549 0.0356 (3.4850, 3.6248) 3.5546 0.0357 (3.4846, 3.6245) 0.0255 (3.4972, 3.5904) 3.5437 0.0333 (3.4418, 3.6095)
β 1,2 −0.1245 0.0101 (−0.1444, −0.1047) −0.1246 0.0101 (−0.1444, −0.1047) 0.0120 (−0.1489, −0.1063) −0.0997 0.0113 (−0.1256, −0.0773)
β 0,3 0.8304 0.0212 (0.7888, 0.8719) 0.8301 0.0210 (0.7888, 0.8713) 0.0196 (0.7953, 0.8638) 0.8233 0.0220 (0.7818, 0.8677)
β 1,3 −0.0577 0.0062 (−0.0699, −0.0456) −0.0577 0.0062 (−0.0698, −0.0455) 0.0057 (−0.0698, −0.0486) −0.0447 0.0052 (−0.0555, −0.0362)
γ v 0.0462 0.0151 (0.0166, 0.0759) 0.0462 0.0152 (0.0165, 0.0759) 0.0173 (0.0198, 0.0880) 0.0575a 0.0123a (0.0314, 0.0760)a
          0.0413b 0.0150b (0.0113, 0.0714)b
          0.0424c 0.0157c (0.0146, 0.0724)c
γ bil 0.8181 0.2046 (0.4171, 1.2191) 0.8187 0.2036 (0.4197, 1.2177) 0.2153 (0.5172, 1.4021) 1.2182 0.1654 (0.9800, 1.5331)
γ alb −1.7060 0.6181 (−2.9173, −0.4946) −1.6973 0.6163 (−2.9053, −0.4893) 0.7562 (−3.3862, −0.5188) −3.0770 0.6052 (−4.7133, −2.1987)
γ pro −2.2085 1.6070 (−5.3582, 0.9412) −2.2148 1.6133 (−5.3768, 0.9472) 1.6094 (−5.3050, 0.6723) −7.2078 1.2640 (−10.5247, −5.2616)
  1. Notation: SE = standard error; CI = confidence interval; NR = one-step Newton-Raphson update for γ; GN = one-step Gauss-Newton-like update for γ
  2. aSeparate model fit for serBilir
  3. bSeparate model fit for albumin
  4. cSeparate model fit for prothrombin
  5. dSEs are calculated from the inverse profile empirical information matrix, and confidence intervals are based on normal approximations of the type \(\hat {\boldsymbol {\theta }} \pm 1.96 \text {SE}(\hat {\boldsymbol {\theta }})\), where \(\hat {\boldsymbol {\theta }}\) denote the estimated maximum likelihood estimates
  6. eSEs and confidence intervals are derived from B=100 bootstrap samples, with confidence intervals based on the 2.5% and 97.5% percentiles. NB. one model failed to converge using joineRML within the maximum number of MC iterations, and so SEs and CIs are based on 99 bootstrap samples only