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Crit Care Med. 2009 Nov;37(11):2939-45. doi: 10.1097/CCM.0b013e3181b7fbbb.

Immortal time bias in critical care research: application of time-varying Cox regression for observational cohort studies.

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Department of Biostatistics, Division of Allergy, Pulmonary, and Critical Care Medicine, Vanderbilt University School of Medicine, Nashville, TN, USA.



To examine the bias introduced by using time-fixed methodology to analyze the effects of a time-varying exposure incurred in the intensive care unit.


Prospective cohort and Monte Carlo simulation studies.


Medical and coronary intensive care units in a university hospital.


A total of 224 mechanically ventilated patients.


Part I was a case study analyzing the association between delirium in the intensive care unit (exposure variable) and outcomes (intensive care unit length of stay and 6-mo mortality) in a prospective cohort study. Part II was a Monte Carlo simulation generating 16,000 data sets wherein the true associations between delirium and outcomes were known before analysis. In both parts, we assessed associations between delirium in the intensive care unit and outcomes (intensive care unit length of stay and mortality), using time-fixed vs. time-varying Cox regression methodology.


In the case study, delirium analyzed as a time-fixed variable was associated with a delayed intensive care unit discharge (adjusted hazard ratio = 1.9, 95% confidence interval, 1.3-2.7, p < .001), but no association was noted using a time-varying method (adjusted hazard ratio = 1.1, 95% confidence interval = 0.7-1.6, p = .70). Alternatively, delirium analyzed as a time-fixed variable was not associated with 6-mo mortality (adjusted hazard ratio = 2.9, 95% confidence interval, 0.9-5.0, p = .09), whereas delirium analyzed as a time-varying variable was associated with increased mortality (adjusted hazard ratio = 3.2, 95% confidence interval, 1.4-7.7, p = .008). In the simulation study, time-fixed methods produced erroneous results in 97.1% of the data sets with no true association; time-varying methods produced erroneous results in only 3.7%. Similarly, time-fixed methods produced biased results when a true association was present, whereas time-varying methods produced accurate results.


Studies using a time-fixed analytic approach to understand relationships between exposures and clinical outcomes can result in considerable bias when the variables overlap temporally in occurrence. Those conducting such studies, and clinicians reading them, should ensure that time-varying exposures are correctly analyzed to avoid biased conclusions.

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