title: The time-dependent bias and its effect on extra length of stay due to nosocomial infection.
abstract: OBJECTIVE
  Many studies disregard the time dependence of nosocomial infection when examining length of hospital stay and the associated financial costs. This leads to the "time-dependent bias," which biases multiplicative hazard ratios. We demonstrate the time-dependent bias on the additive scale of extra length of stay.
  
  
  METHODS
  To estimate the extra length of stay due to infection, we used a multistate model that accounted for the time of infection. For comparison we used a generalized linear model assuming a gamma distribution, a commonly used model that ignores the time of infection. We applied these two methods to a large prospective cohort of hospital admissions from Argentina, and compared the methods' performance using a simulation study.
  
  
  RESULTS
  For the Argentina data the extra length of stay due to nosocomial infection was 11.23 days when ignoring time dependence and only 1.35 days after accounting for the time of infection. The simulations showed that ignoring time dependence consistently overestimated the extra length of stay. This overestimation was similar for different rates of infection and even when an infection prolonged or shortened stay. We show examples where the time-dependent bias remains unchanged for the true discharge hazard ratios, but the bias for the extra length of stay is doubled because length of stay depends on the infection hazard.
  
  
  CONCLUSIONS
  Ignoring the timing of nosocomial infection gives estimates that greatly overestimate its effect on the extra length of hospital stay.
authors.affiliation: Queensland University of Technology, Brisbane, Australia. a.barnett@qut.edu.au
authors.forename: Adrian G
authors.initials: AG
authors.lastname: Barnett
authors.forename: Jan
authors.initials: J
authors.lastname: Beyersmann
authors.forename: Arthur
authors.initials: A
authors.lastname: Allignol
authors.forename: Victor D
authors.initials: VD
authors.lastname: Rosenthal
authors.forename: Nicholas
authors.initials: N
authors.lastname: Graves
authors.forename: Martin
authors.initials: M
authors.lastname: Wolkewitz
mesh_terms: D000368:Aged; D001118:Argentina; D015982:Bias; D003198:Computer Simulation; D003428:Cross Infection / Q000191:economics* / Q000628:therapy*; D003657:Decision Making; D005260:Female; D017721:Hospital Costs; D006801:Humans; D017053:Infection Control / Q000191:economics* / Q000592:standards; D007362:Intensive Care Units / Q000191:economics / Q000706:statistics & numerical data; D007902:Length of Stay / Q000191:economics* / Q000706:statistics & numerical data; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D010343:Patient Admission / Q000191:economics / Q000706:statistics & numerical data; D016016:Proportional Hazards Models; D011446:Prospective Studies; D013997:Time Factors