title: Noncollapsibility in studies based on nonrepresentative samples.
abstract: BACKGROUND
  It is common to use nonrepresentative samples in observational epidemiologic studies, but there has been debate about whether this introduces bias. In this article, we consider the consequences on noncollapsibility of a sample selection related to a relevant outcome-risk factor.
  
  
  METHODS
  We focused on the odds ratio and defined the noncollapsibility effect as the difference between the marginal and the conditional (with respect to the outcome-risk factor) exposure-outcome association. We consider a situation in which the aims of the study require the estimate of a conditional effect.
  
  
  RESULTS
  Using a classical numerical example, which assumes that all variables are binary and that the outcome-risk factor is not an effect modifier, we illustrate that in the selected sample the noncollapsibility effect can either be larger or smaller than in the population-based study, according to whether the selection moves the prevalence of the risk factor closer to or away from 50%. When the outcome-risk factor is also a confounder, the magnitude of the noncollapsibility effect in the selected sample depends on the effects of the selection on both noncollapsibility and confounding.
  
  
  CONCLUSIONS
  When a key outcome-risk factor is unmeasured, in presence of noncollapsibility neither a population-based nor a selected study can directly estimate the conditional effect; whether the computable marginal is closer to the conditional in the selected or in the population-based study depends on the underlying population and the selection process.
authors.affiliation: Cancer Epidemiology Unit, Department of Medical Sciences, University of Turin, Turin, Italy. Electronic address: costanza.pizzi@unito.it.
authors.forename: Costanza
authors.initials: C
authors.lastname: Pizzi
authors.affiliation: Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK; Centre for Public Health Research, Massey University, Wellington, New Zealand.
authors.forename: Neil
authors.initials: N
authors.lastname: Pearce
authors.affiliation: Cancer Epidemiology Unit, Department of Medical Sciences, University of Turin, Turin, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Richiardi
mesh_terms: D035843:Biomedical Research / Q000592:standards*; D000068598:Data Accuracy; D016021:Epidemiologic Studies; D006801:Humans; D016017:Odds Ratio; D012107:Research Design / Q000592:standards*; D012307:Risk Factors; D015983:Selection Bias
keywords: Cohort study; Odds ratios; Selection bias