Immortal time bias
In a discussion of biases involving observational studies, if one wants to achieve a meaningful conclusion from survival analysis result from let’s say a retrospective data, the immortal time bias should be accounted for. The concept of immortal time bias occurs when the survival analysis assumes that the start time for controls and treated groups from subject’s time entering the study to the time of intervention are considered equal, which can impact the evaluation of treatment group efficacy.
Treatment group: Study start———————Intervention—–event
^^^^
(immortal time)
Control group: Study start————–event
Stata code
use http://www.stata-press.com/data/r8/stanford, clear
stset stime, id(id) failure(died)
stcox transplant
HR: .2674327 95% CI .1657774 – .4314233
As seen above, the immortal time which is the time from treatment arm subject start time to to intervention time gets ignored from the calculation and renders that either treatment ineffective or in other situations ignores patients who do not make it to the intervention. The most drastic outcome is that the results may inflate the effect of the treatment.
One simple method to is to use time of origin for controls and treatment groups which can minimize the immortal time but does not completely resolve the issue.
Stata code
gen landmark=10
stset stime, id(id) failure(died) origin(landmark)
stcox transplant
HR: .3656466 .1040087 95% CI .2093804 – .6385383
The other method is to use time-varying approach, by which we split the person-times before the intervention and add it to the control, and it will be censored.
Stata code
stset stime, id(id) failure(died)
replace wait=10000 if wait==0
stsplit posttransplant, at(0) after(wait)
stcox posttransplant
HR: 1.111523 95% CI .6193088 – 1.994939
References:
https://journals.sagepub.com/doi/pdf/10.1177/1536867X0400400212
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