title: Estimating a population cumulative incidence under calendar time trends.
abstract: The risk of a disease or psychiatric disorder is frequently measured by the age-specific cumulative incidence. Cumulative incidence estimates are often derived in cohort studies with individuals recruited over calendar time and with the end of follow-up governed by a specific date. It is common practice to apply the Kaplan-Meier or Aalen-Johansen estimator to the total sample and report either the estimated cumulative incidence curve or just a single point on the curve as a description of the disease risk.
  
  
  
  We argue that, whenever the disease or disorder of interest is influenced by calendar time trends, the total sample Kaplan-Meier and Aalen-Johansen estimators do not provide useful estimates of the general risk in the target population. We present some alternatives to this type of analysis.
  
  
  
  We show how a proportional hazards model may be used to extrapolate disease risk estimates if proportionality is a reasonable assumption. If not reasonable, we instead advocate that a more useful description of the disease risk lies in the age-specific cumulative incidence curves across strata given by time of entry or perhaps just the end of follow-up estimates across all strata. Finally, we argue that a weighted average of these end of follow-up estimates may be a useful summary measure of the disease risk within the study period.
  
  
  
  Time trends in a disease risk will render total sample estimators less useful in observational studies with staggered entry and administrative censoring. An analysis based on proportional hazards or a stratified analysis may be better alternatives.
authors.affiliation: Section for Biostatistics, Aarhus University, Bartholins Allé 2, Aarhus C, DK-8000, Denmark. stefanh@ph.au.dk.
authors.forename: Stefan N
authors.initials: SN
authors.lastname: Hansen
authors.affiliation: Section for Biostatistics, Aarhus University, Bartholins Allé 2, Aarhus C, DK-8000, Denmark.
authors.forename: Morten
authors.initials: M
authors.lastname: Overgaard
authors.affiliation: Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, Copenhagen K, DK-1014, Denmark.
authors.forename: Per K
authors.initials: PK
authors.lastname: Andersen
authors.affiliation: Section for Biostatistics, Aarhus University, Bartholins Allé 2, Aarhus C, DK-8000, Denmark.
authors.forename: Erik T
authors.initials: ET
authors.lastname: Parner
mesh_terms: D000293:Adolescent; D000328:Adult; D000465:Algorithms; D001289:Attention Deficit Disorder with Hyperactivity / Q000175:diagnosis / Q000453:epidemiology; D000067877:Autism Spectrum Disorder / Q000175:diagnosis / Q000453:epidemiology; D002648:Child; D003198:Computer Simulation; D003718:Denmark / Q000453:epidemiology; D005260:Female; D005387:Finland / Q000453:epidemiology; D006801:Humans; D015994:Incidence; D053208:Kaplan-Meier Estimate; D008297:Male; D001523:Mental Disorders / Q000175:diagnosis / Q000453:epidemiology*; D008875:Middle Aged; D008962:Models, Theoretical; D009771:Obsessive-Compulsive Disorder / Q000175:diagnosis / Q000453:epidemiology; D015995:Prevalence; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods / Q000706:statistics & numerical data*; D012307:Risk Factors; D013997:Time Factors; D005879:Tourette Syndrome / Q000175:diagnosis / Q000453:epidemiology; D055815:Young Adult
keywords: Cumulative incidence; Dependent censoring; Stratification; Time to event; Time trends