Estimation of Seroprevalence, Rape, and Homelessness in the United States Using a Social Network Approach

Abstract

The authors have developed and tested scale-up methods, based on a simple social network theory, to estimate the size of hard-to-count subpopulations. The authors asked a nationally representative sample of respondents how many people they knew in a list of 32 subpopulations, including 29 subpopulations of known size and 3 of unknown size. Using these responses, the authors produced an effectively unbiased maximum likelihood estimate of the number of people each respondent knows. These estimates were then used to back-estimate the size of the three populations of unknown size. Maximum likelihood values and 95% confidence intervals are found for seroprevalence, 800,000 +/- 43,000; for homeless, 526,000 +/- 35,000; and for women raped in the last 12 months, 194,000 +/- 21,000. The estimate for seroprevalence agrees strikingly with medical estimates, the homeless estimate is well within the published estimates, and the authors' estimate lies in the middle of the published range for rape victims.

Two interpretations of reports of knowledge of subpopulation sizes

“…This simple model thus predicts that the mean number known rises from about 290 (for our original model, cf. Killworth et al, 1998b) to 365, and there is a chance of about 0.1% of a respondent believing that any network member is in any given subpopulation when in fact the member is not. This model predicts a linear variation with p; Fig.…”

“…Clearly, salience has a strong effect for respondents within this subpopulation. However, there are only about 800,000 seropositive individuals in the US (Killworth et al, 1998b) so that seropositive respondents would contribute to a number of people known who have AIDS by an amount (800,000/250 million) times 52.5, or 0.16, which is only one-third of the national average number of AIDS victims known anyway.…”

“…Some estimates of this distribution are given in Killworth et al (1998b). If a respondent recalls members of a subpopulation based on a power law, the survey-average response involves passing this power law through two averaging processes: (a) across the distribution of possible responses by respondents knowing c, and (b) across the range of c itself.…”

“…The pattern of responses by a single respondent concerning subpopulations of known size enables us to make a maximum likelihood estimate of the number of people in that respondent's network. Then, the pattern of responses about subpopulations of unknown size, across respondents, together with the estimated sizes of their networks, enables a second maximum likelihood estimate to be made for the size of the subpopulation (Killworth et al, 1998b).…”

Estimating the size of a union of random subsets of fixed cardinality

“…This technique was originally suggested by Killworth, Johnson, McCarty, Shelley and Bernard in situations where a direct question might well lead to misleading results because of the stigmatizing character of the question as for example 'Are you infected with the AIDS-virus? ', see [1] and [2] for details. However, the mathematical model underlying their approach is far more complicated since they do not fix the number of 'friends' about which each person is asked.…”