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In studies of HIV, interval-censored data occur naturally. HIV infection time is not usually known exactly, only that it occurred before the survey, within some time interval or has not occurred at the time of the survey. Infections are often clustered within geographical areas such as enumerator areas (EAs) and thus inducing unobserved frailty. In this paper we consider an approach for estimating parameters when infection time is unknown and assumed correlated within an EA where dependency is modeled as frailties assuming a normal distribution for frailties and a Weibull distribution for baseline hazards. The data was from a household based population survey that used a multi-stage stratified sample design to randomly select 23,275 interviewed individuals from 10,584 households of whom 15,851 interviewed individuals were further tested for HIV (crude prevalence = 9.1%). A further test conducted among those that tested HIV positive found 181 (12.5%) recently infected. Results show high degree of heterogeneity in HIV distribution between EAs translating to a modest correlation of 0.198. Intervention strategies should target geographical areas that contribute disproportionately to the epidemic of HIV. Further research needs to identify such hot spot areas and understand what factors make these areas prone to HIV.

Analysis of Complex Correlated Interval-Censored HIV Data from Population Based Survey