Beta-Binomial and Negative Binomial Models for the Analysis of Sexual Risk Behavior

Introduction: HIV-related sexual risk behavior has been associated with a variety of factors, including substance use, awareness of HIV positivity, sexual orientation, sex exchange, and various sociodemographics. Logistic regression of any unprotected intercourse is commonly used to identify such risk factors, but such methods fail to reveal whether changes in risk are due changes in the frequency of intercourse, changes in the odds of condom use, or changes in both. In contrast, beta-binomial regression for modelling condom use, in conjunction with negative binomial regression form modelling the frequency of intercourse, can provide a more nuanced understanding of how risk factors may influence the sexual transmission of HIV.

Methods: An application of these underutilized models is illustrated with data from the NIDA Cooperative Agreement, a publicly accessible multisite study of out-of-treatment injection drug users and crack users (n > 30,000). For each site, negative binomial regressions were used to model the frequency of unprotected intercourse and the frequency of intercourse and beta-binomial regression was used to model the probability of not using a condom when having intercourse. The multivariable models included a substance use and other predictors, and the findings were combined across sites through meta-analysis.

Results: Several types of substance use in the last 30 days were positively [or negatively] associated with the rate of intercourse (alcohol, marijuana, crack, speedball, amphetamine, [heroin]), but few were associated with failure to use a condom use when having intercourse (alcohol, amphetamine, injection drug use). Being female was associated with more intercourse and increasing age was associated with less intercourse, but neither was associated with condom use. Ever exchanging sex was associated with more frequent intercourse and with condom use, ever having had an STD was associated with more intercourse and with not using a condom, and being previously diagnosed HIV-positive was associated with less intercourse and with condom use.

Discussion: These analyses demonstrate that beta-binomial models in conjunction with negative binomial models can reveal important insights into sexual risk behavior that are not evident through more common approaches. For example, whereas substance use is often hypothesized to increase risk behavior through decreased condom use, these analyses reveal that the link between substance use and frequency of intercourse may be a major contributor to increased risk. This approach could be extended to intervention studies to understand whether experimental conditions reduce risk through decreased intercourse or increased condom use.