title: Bounding the per-protocol effect in randomized trials: an application to colorectal cancer screening.
abstract: BACKGROUND
  The per-protocol effect is the effect that would have been observed in a randomized trial had everybody followed the protocol. Though obtaining a valid point estimate for the per-protocol effect requires assumptions that are unverifiable and often implausible, lower and upper bounds for the per-protocol effect may be estimated under more plausible assumptions. Strategies for obtaining bounds, known as "partial identification" methods, are especially promising in randomized trials.
  
  
  RESULTS
  We estimated bounds for the per-protocol effect of colorectal cancer screening in the Norwegian Colorectal Cancer Prevention trial, a randomized trial of one-time sigmoidoscopy screening in 98,792 men and women aged 50-64 years. The screening was not available to the control arm, while approximately two thirds of individuals in the treatment arm attended the screening. Study outcomes included colorectal cancer incidence and mortality over 10 years of follow-up. Without any assumptions, the data alone provide little information about the size of the effect. Under the assumption that randomization had no effect on the outcome except through screening, a point estimate for the risk under no screening and bounds for the risk under screening are achievable. Thus, the 10-year risk difference for colorectal cancer was estimated to be at least -0.6 % but less than 37.0 %. Bounds for the risk difference for colorectal cancer mortality (-0.2 to 37.4 %) and all-cause mortality (-5.1 to 32.6 %) had similar widths. These bounds appear helpful in quantifying the maximum possible effectiveness, but cannot rule out harm. By making further assumptions about the effect in the subpopulation who would not attend screening regardless of their randomization arm, narrower bounds can be achieved.
  
  
  CONCLUSIONS
  Bounding the per-protocol effect under several sets of assumptions illuminates our reliance on unverifiable assumptions, highlights the range of effect sizes we are most confident in, and can sometimes demonstrate whether to expect certain subpopulations to receive more benefit or harm than others.
  
  
  BACKGROUND
  Clinicaltrials.gov identifier NCT00119912 (registered 6 July 2005).
authors.affiliation: Department of Epidemiology, Erasmus Medical Center, PO Box 2040, 3000, CA, Rotterdam, The Netherlands. sswanson@hsph.harvard.edu.|Department of Epidemiology, Harvard TH Chan School of Public Health, Boston, MA, USA. sswanson@hsph.harvard.edu.
authors.forename: Sonja A
authors.initials: SA
authors.lastname: Swanson
authors.affiliation: Institute of Health and Society, University of Oslo, Oslo, Norway. oyvind.holme@medisin.uio.no.|Sørlandet Hospital Kristiansand, Kristiansand, Norway. oyvind.holme@medisin.uio.no.
authors.forename: Øyvind
authors.initials: Ø
authors.lastname: Holme
authors.affiliation: Institute of Health and Society, University of Oslo, Oslo, Norway. magnus.loberg@medisin.uio.no.|Oslo University Hospital, Oslo, Norway. magnus.loberg@medisin.uio.no.
authors.forename: Magnus
authors.initials: M
authors.lastname: Løberg
authors.affiliation: Department of Epidemiology, Harvard TH Chan School of Public Health, Boston, MA, USA. mkalager@hsph.harvard.edu.|Institute of Health and Society, University of Oslo, Oslo, Norway. mkalager@hsph.harvard.edu.|Telemark Hospital, Skien, Norway. mkalager@hsph.harvard.edu.
authors.forename: Mette
authors.initials: M
authors.lastname: Kalager
authors.affiliation: Department of Epidemiology, Harvard TH Chan School of Public Health, Boston, MA, USA. michael.bretthauer@medisin.uio.no.|Institute of Health and Society, University of Oslo, Oslo, Norway. michael.bretthauer@medisin.uio.no.|Oslo University Hospital, Oslo, Norway. michael.bretthauer@medisin.uio.no.
authors.forename: Michael
authors.initials: M
authors.lastname: Bretthauer
authors.affiliation: Institute of Health and Society, University of Oslo, Oslo, Norway. Geir.Hoff@kreftregisteret.no.|Telemark Hospital, Skien, Norway. Geir.Hoff@kreftregisteret.no.|Cancer Registry of Norway, Oslo, Norway. Geir.Hoff@kreftregisteret.no.
authors.forename: Geir
authors.initials: G
authors.lastname: Hoff
authors.affiliation: Institute of Health and Society, University of Oslo, Oslo, Norway. eline.aas@medisin.uio.no.
authors.forename: Eline
authors.initials: E
authors.lastname: Aas
authors.affiliation: Department of Epidemiology, Harvard TH Chan School of Public Health, Boston, MA, USA. miguel_hernan@post.harvard.edu.|Department of Biostatistics, Harvard TH Chan School of Public Health, Boston, MA, USA. miguel_hernan@post.harvard.edu.|Harvard-MIT Division of Health Sciences and Technology, Boston, MA, USA. miguel_hernan@post.harvard.edu.
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Hernán
mesh_terms: D002985:Clinical Protocols; D015179:Colorectal Neoplasms / Q000401:mortality / Q000473:pathology*; D003627:Data Interpretation, Statistical; D055088:Early Detection of Cancer / Q000379:methods* / Q000706:statistics & numerical data; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D009664:Norway; D018579:Patient Selection; D011237:Predictive Value of Tests; D011379:Prognosis; D012107:Research Design; D018570:Risk Assessment; D012307:Risk Factors; D012812:Sigmoidoscopy / Q000706:statistics & numerical data; D013997:Time Factors