title: Errors in reported degrees and respondent driven sampling: implications for bias.
abstract: BACKGROUND
  Respondent Driven Sampling (RDS) is a network or chain sampling method designed to access individuals from hard-to-reach populations such as people who inject drugs (PWID). RDS surveys are used to monitor behaviour and infection occurence over time; these estimations require adjusting to account for over-sampling of individuals with many contacts. Adjustment is done based on individuals' reported total number of contacts, assuming these are correct.
  
  
  METHODS
  Data on the number of contacts (degrees) of individuals sampled in two RDS surveys in Bristol, UK, show larger numbers of individuals reporting numbers of contacts in multiples of 5 and 10 than would be expected at random. To mimic these patterns we generate contact networks and explore different methods of mis-reporting degrees. We simulate RDS surveys and explore the sensitivity of adjusted estimates to these different methods.
  
  
  RESULTS
  We find that inaccurate reporting of degrees can cause large and variable bias in estimates of prevalence or incidence. Our simulations imply that paired RDS surveys could over- or under-estimate any change in prevalence by as much as 25%. These are particularly sensitive to inaccuracies in the degree estimates of individuals with who have low degree.
  
  
  CONCLUSIONS
  There is a substantial risk of bias in estimates from RDS if degrees are not correctly reported. This is particularly important when analysing consecutive RDS samples to assess trends in population prevalence and behaviour. RDS questionnaires should be refined to obtain high resolution degree information, particularly from low-degree individuals. Additionally, larger sample sizes can reduce uncertainty in estimates.
authors.affiliation: MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Dynamics, Imperial College London, St Mary's Hospital, Norfolk Place, London W2 1PG, UK. Electronic address: harriet.l.mills@gmail.com.
authors.forename: Harriet L
authors.initials: HL
authors.lastname: Mills
authors.affiliation: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
authors.forename: Samuel
authors.initials: S
authors.lastname: Johnson
authors.affiliation: School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol BS8 2PS, UK.
authors.forename: Matthew
authors.initials: M
authors.lastname: Hickman
authors.affiliation: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
authors.forename: Nick S
authors.initials: NS
authors.lastname: Jones
authors.affiliation: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
authors.forename: Caroline
authors.initials: C
authors.lastname: Colijn
mesh_terms: D015982:Bias; D006801:Humans; D015995:Prevalence; D012107:Research Design; D018401:Sample Size; D012494:Sampling Studies; D015819:Substance Abuse, Intravenous / Q000453:epidemiology*; D011795:Surveys and Questionnaires
keywords: At-risk populations; Contact network size; Respondent driven sampling