Table 3.
Summary of the results of simulation analyses to assess bias in the estimate of mean slope (β 1) when models that are simpler than the data‐generating process are applied in the presence of ‘missing at random’ censoring.
| RS+ME | RS+BM+ME | RS+fBM+ME | MVT: RS+fBM+ME | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Prop. cens. | n obs. | Failed | β 1 bias | Failed | β 1 bias | Failed | β 1 bias | Failed | β 1 bias | |
| (median (IQR)) | (median (IQR)) | (%) | (coverage) | (%) | (coverage) | (%) | (coverage) | (%) | (coverage) | |
| N=100, freq=1 | ||||||||||
| Uncensored | 0 (0–0) | 600 (600–600) | 0 | 0.013 (93.8) | 0.0 | 0.012 (94.6) | 2.6 | 0.011 (94.0) | 1.2 | 0.012 (96.0) |
| ART200 | 21 (18–24) | 573 (567–579) | 0 | −0.100 (88.2) | 0.4 | −0.021 (96.8) | 1.4 | 0.000 (95.3) | 0.2 | 0.008 (95.4) |
| ART350 | 51 (48–55) | 505 (493–515) | 0 | −0.244 (73.0) | 1.2 | −0.071 (95.1) | 2.6 | −0.001 (96.5) | 1.4 | 0.000 (95.9) |
| ART500 | 77 (75–80) | 400 (388–413) | 0 | −0.384 (72.0) | 2.4 | −0.146 (94.9) | 5.2 | −0.022 (94.3) | 1.0 | −0.019 (93.5) |
| N=100, freq=3 | ||||||||||
| Uncensored | 0 (0–0) | 1600 (1600–1600) | 0 | 0.000 (95.4) | 0.0 | −0.001 (97.0) | 4.0 | −0.002 (96.0) | 2.0 | −0.001 (96.7) |
| ART200 | 30 (27–34) | 1414 (1386–1441) | 0 | −0.161 (84.4) | 0.8 | −0.054 (95.8) | 4.8 | −0.009 (96.0) | 3.4 | −0.004 (96.1) |
| ART350 | 63 (60–66) | 1095 (1060–1131) | 0 | −0.289 (71.8) | 0.4 | −0.125 (95.0) | 7.0 | −0.002 (97.8) | 2.6 | −0.002 (97.9) |
| ART500 | 85 (82–87) | 724 (687–761) | 0 | −0.322 (84.6) | 2.2 | −0.270 (92.0) | 9.8 | −0.025 (94.5) | 3.0 | −0.027 (94.2) |
| N=200, freq=1 | ||||||||||
| Uncensored | 0 (0–0) | 1200 (1200–1200) | 0 | 0.004 (94.6) | 0.0 | 0.005 (94.4) | 1.0 | 0.004 (93.7) | 0.0 | 0.001 (94.4) |
| ART200 | 22 (20–24) | 1144 (1136–1152) | 0 | −0.106 (82.4) | 0.2 | −0.019 (95.4) | 1.2 | 0.000 (94.1) | 0.6 | 0.000 (95.0) |
| ART350 | 52 (49–54) | 1008 (993–1023) | 0 | −0.234 (56.0) | 0.4 | −0.057 (95.8) | 2.4 | 0.007 (95.3) | 0.8 | 0.005 (95.2) |
| ART500 | 78 (76–80) | 799 (780–816) | 0 | −0.360 (56.2) | 0.4 | −0.118 (92.6) | 6.8 | 0.007 (94.6) | 1.6 | −0.001 (94.5) |
| N=200, freq=3 | ||||||||||
| Uncensored | 0 (0–0) | 3200 (3200–3200) | 0 | −0.002 (94.6) | 0.0 | −0.001 (95.6) | 2.4 | −0.001 (94.7) | 0.4 | 0.000 (92.2) |
| ART200 | 30 (28–32) | 2840 (2804–2874) | 0 | −0.161 (66.6) | 0.2 | −0.054 (93.0) | 2.2 | −0.012 (94.5) | 0.8 | −0.005 (92.1) |
| ART350 | 62 (60–65) | 2197 (2142–2244) | 0 | −0.300 (44.6) | 0.4 | −0.127 (88.0) | 4.4 | −0.014 (96.2) | 2.4 | −0.007 (96.1) |
| ART500 | 84 (83–86) | 1454 (1404–1508) | 0 | −0.337 (70.2) | 1.0 | −0.243 (86.3) | 12.4 | −0.004 (93.8) | 5.8 | −0.017 (93.8) |
Bias is calculated as the mean estimate of β 1 minus the true value, and is presented with coverage of nominal 95% confidence intervals in parentheses. For each combination of number of simulated patients (N) and annual frequency of observation (freq), 500 cohorts were generated and analysed under different censoring regimes, corresponding to treatment initiation at CD4 cut‐offs of 200 (ART200), 350 (ART350) or 500 (ART500). All cohorts were simulated with a follow‐up of 5 years, including an observation at time zero for each patient. Data were generated according to a multivariate‐t distribution (MVT) incorporating a fractional Brownian motion (fBM) process and measurement error (ME) and, alongside a model of the correct form, normal linear mixed models were fit with a random slopes (RS) structure alone and with RS in combination with Brownian motion (BM) and fBM processes. Model fitting was considered to have failed when parameter estimates were not returned or when the covariance matrix of parameter estimates was not positive‐definite. IQR, interquartile range; n obs., total observations included in analysis per simulated cohort; Prop. cens., proportion of patients in simulated cohort subject to censoring before 5years.