title: Estimating time-varying exposure-outcome associations using case-control data: logistic and case-cohort analyses.
abstract: BACKGROUND
  Traditional analyses of standard case-control studies using logistic regression do not allow estimation of time-varying associations between exposures and the outcome. We present two approaches which allow this. The motivation is a study of vaccine efficacy as a function of time since vaccination.
  
  
  METHODS
  Our first approach is to estimate time-varying exposure-outcome associations by fitting a series of logistic regressions within successive time periods, reusing controls across periods. Our second approach treats the case-control sample as a case-cohort study, with the controls forming the subcohort. In the case-cohort analysis, controls contribute information at all times they are at risk. Extensions allow left truncation, frequency matching and, using the case-cohort analysis, time-varying exposures. Simulations are used to investigate the methods.
  
  
  RESULTS
  The simulation results show that both methods give correct estimates of time-varying effects of exposures using standard case-control data. Using the logistic approach there are efficiency gains by reusing controls over time and care should be taken over the definition of controls within time periods. However, using the case-cohort analysis there is no ambiguity over the definition of controls. The performance of the two analyses is very similar when controls are used most efficiently under the logistic approach.
  
  
  CONCLUSIONS
  Using our methods, case-control studies can be used to estimate time-varying exposure-outcome associations where they may not previously have been considered. The case-cohort analysis has several advantages, including that it allows estimation of time-varying associations as a continuous function of time, while the logistic regression approach is restricted to assuming a step function form for the time-varying association.
authors.affiliation: Department of Medical Statistics, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. ruth.keogh@lshtm.ac.uk.
authors.forename: Ruth H
authors.initials: RH
authors.lastname: Keogh
authors.affiliation: Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. punam.mangtani@lshtm.ac.uk.
authors.forename: Punam
authors.initials: P
authors.lastname: Mangtani
authors.affiliation: Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. laura.rogrigues@lshtm.ac.uk.
authors.forename: Laura
authors.initials: L
authors.lastname: Rodrigues
authors.affiliation: Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. patrick.nguipdop-djomo@lshtm.ac.uk.
authors.forename: Patrick
authors.initials: P
authors.lastname: Nguipdop Djomo
mesh_terms: D000465:Algorithms; D001500:BCG Vaccine / Q000008:administration & dosage*; D016022:Case-Control Studies; D015331:Cohort Studies; D006801:Humans; D016015:Logistic Models; D017063:Outcome Assessment, Health Care / Q000379:methods* / Q000706:statistics & numerical data; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D013997:Time Factors; D014376:Tuberculosis / Q000517:prevention & control*; D014611:Vaccination / Q000379:methods*
chemical_list: D001500:BCG Vaccine