title: Immortal time bias in observational studies of time-to-event outcomes.
abstract: The purpose of the study is to show, through simulation and example, the magnitude and direction of immortal time bias when an inappropriate analysis is used.
  
  
  
  We compare 4 methods of analysis for observational studies of time-to-event outcomes: logistic regression, standard Cox model, landmark analysis, and time-dependent Cox model using an example data set of patients critically ill with influenza and a simulation study.
  
  
  
  For the example data set, logistic regression, standard Cox model, and landmark analysis all showed some evidence that treatment with oseltamivir provides protection from mortality in patients critically ill with influenza. However, when the time-dependent nature of treatment exposure is taken account of using a time-dependent Cox model, there is no longer evidence of a protective effect of treatment. The simulation study showed that, under various scenarios, the time-dependent Cox model consistently provides unbiased treatment effect estimates, whereas standard Cox model leads to bias in favor of treatment. Logistic regression and landmark analysis may also lead to bias.
  
  
  
  To minimize the risk of immortal time bias in observational studies of survival outcomes, we strongly suggest time-dependent exposures be included as time-dependent variables in hazard-based analyses.
authors.affiliation: School of Public Health, University of Queensland, Brisbane, QLD, Australia. Electronic address: m.jones@sph.uq.edu.au.
authors.forename: Mark
authors.initials: M
authors.lastname: Jones
authors.affiliation: Sunnybrook Health Sciences Centre, Toronto, ON, Canada. Electronic address: Rob.Fowler@sunnybrook.ca.
authors.forename: Robert
authors.initials: R
authors.lastname: Fowler
mesh_terms: D000998:Antiviral Agents / Q000627:therapeutic use*; D015982:Bias; D003198:Computer Simulation; D016638:Critical Illness; D006801:Humans; D053118:Influenza A Virus, H1N1 Subtype; D007251:Influenza, Human / Q000188:drug therapy* / Q000401:mortality; D016015:Logistic Models; D064887:Observational Studies as Topic; D053139:Oseltamivir / Q000627:therapeutic use*; D016016:Proportional Hazards Models; D016019:Survival Analysis; D013997:Time Factors
chemical_list: D000998:Antiviral Agents; D053139:Oseltamivir
keywords: Immortal time bias; Survival analysis; Time-dependent exposure