title: Definition and evaluation of the monotonicity condition for preference-based instruments.
abstract: BACKGROUND
  Preference-based instrumental variable methods are often used in comparative effectiveness research. Many instrumental variable studies estimate the local average treatment effect (ie, the effect in the "compliers") under the assumption of monotonicity, ie, no "defiers," and well-defined compliance types. However, the monotonicity assumption has not been empirically tested and the meaning of monotonicity itself is unclear.
  
  
  METHODS
  Here, we clarify the definition of local and global monotonicity and propose a novel study design to assess the monotonicity assumption empirically. Our design requires surveying physicians about their treatment plans and prescribing preferences for the same set of patients. We also discuss measures of monotonicity that can be calculated from this survey data. As an illustration, we conducted a pilot study in a survey of 53 physicians who reported treatment plans and prescribing preferences for hypothetical patients who were candidates for antipsychotic treatment.
  
  
  RESULTS
  In our study, nearly all patients exhibited some degree of monotonicity violations. In addition, patients could not be cleanly classified as compliers, defiers, always-takers, or never-takers.
  
  
  CONCLUSIONS
  We conclude that preference-based instrumental variable estimates should be interpreted cautiously because bias due to monotonicity violations is likely and because the subpopulation to which the estimate applies may not be well defined. Investigators using preference-based instruments may consider supplementing their study with a survey to empirically assess the magnitude and direction of bias due to violations of monotonicity.
authors.affiliation: From the aDepartment of Epidemiology, Harvard School of Public Health, Boston, MA; bDepartment of Health Science, Northeastern University, Boston, MA; cDepartment of Biostatistics, Harvard School of Public Health, Boston, MA; and dHarvard-MIT Division of Health Sciences and Technology, Boston, MA.
authors.forename: Sonja A
authors.initials: SA
authors.lastname: Swanson
authors.forename: Matthew
authors.initials: M
authors.lastname: Miller
authors.forename: James M
authors.initials: JM
authors.lastname: Robins
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Hernán
mesh_terms: D014150:Antipsychotic Agents / Q000627:therapeutic use; D057186:Comparative Effectiveness Research / Q000379:methods; D003627:Data Interpretation, Statistical; D006801:Humans; D010820:Physicians / Q000706:statistics & numerical data; D010865:Pilot Projects; D010818:Practice Patterns, Physicians' / Q000706:statistics & numerical data*; D011795:Surveys and Questionnaires
chemical_list: D014150:Antipsychotic Agents