TABLE 2.
An illustration of the influence of immortal time bias (ITB) on associations between antifibrotic therapy and survival in simulated subjects with idiopathic pulmonary fibrosis (IPF) using four statistical methods.
| Antifibrotics users | Non–users | ||||||
| Person years* | Deaths | Person years* | Deaths | Crude HR (95% CI) | P-value | Difference (%)# | |
| (a) Time–fixed method | |||||||
| Immortal person–time | 483 | 0 | 0 | 0 | – | – | – |
| At risk person–time | 1,372 | 278 | 1,517 | 390 | – | – | – |
| Total | 1,855 | 278 | 1,517 | 390 | 0.55 (0.47, 0.64) | <0.001 | –41 |
| (b) Exclusion method | |||||||
| Immortal person–time | 0 | 0 | 0 | 0 | – | – | – |
| At risk person–time | 1,372 | 278 | 1,517 | 390 | – | – | – |
| Total | 1,372 | 278 | 1,517 | 390 | 0.79 (0.67, 0.92) | 0.003 | –15 |
| (c) Time–dependent method | |||||||
| Immortal person–time | 0 | 0 | 483 | 0 | – | – | – |
| At risk person–time | 1,372 | 278 | 1,517 | 390 | – | – | – |
| Total | 1,372 | 278 | 2,000 | 390 | 0.93 (0.79,1.09) | 0.391 | 0 |
| (d) 0.5 year landmark method | |||||||
| Immortal person–time | 483 | 0 | 0 | 0 | – | – | – |
| At risk person–time | 1,372 | 278 | 1,504 | 345 | – | – | – |
| Total | 1,855 | 278 | 1,504 | 345 | 0.61 (0.52, 0.71) | <0.001 | –34 |
| (e) 1 year landmark method | |||||||
| Immortal person–time | 483 | 0 | 0 | 0 | – | – | – |
| At risk person–time | 1,358 | 281 | 1,469 | 300 | – | – | – |
| Total | 1,841 | 281 | 1,469 | 300 | 0.69 (0.58, 0.81) | <0.001 | –26 |
| (f) 2 years landmark method | |||||||
| Immortal person–time | 414 | 0 | 0 | 0 | – | – | – |
| At risk person–time | 1,335 | 209 | 1,339 | 214 | – | – | – |
| Total | 1,749 | 209 | 1,339 | 214 | 0.69 (0.57, 0.84) | <0.001 | –26 |
Illustration models with methods of (a) time–fixed, (b) exclusion, (c) time–dependent, and (d)–(f) landmark. For the time–fixed method, the immortal time was ignored and incorporated in the treated group. For the exclusion method, the immortal time was excluded from the study. For the time–dependent method, the immortal time was switched into the control group, with an additional 483 subjects being added into the control group. For the landmark method, 0.5, 1, and 2 years landmarks excluded 45, 90, and 245 simulated subjects who had died prior to this time point, respectively. Immortal time was defined as the time from cohort entry to the initiation of antifibrotic therapy. Landmark time was defined as a fixed time point, which was the same for all subjects.
*Time from cohort entry until the occurrence of deaths.
#Difference in the effect estimates between the time-dependent methods and other methods.
ITB, immortal time bias; IPF, idiopathic pulmonary fibrosis; HR, hazard ratio; CI, confidence interval.