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Improving HIV testing among the populations at high risk is one of the first steps to achieving the Sustainable Development Goal target of ending AIDS by 2030. This study aims to develop multivariate statistical models to describe the HIV testing behavior of most at-risk populations. HIV testing data of 5667 Female Sex Workers (FSWs) registered with the National HIV Prevention Programme in 10 districts of Sri Lanka during 2016 and 2017 were modeled using univariate and multivariate survival analysis techniques. As the proportional hazard assumption was violated, the Prentice Williams &amp; Peterson (PWP) model was extended to include time-dependent covariates. The results show that the PWP gap time model and all univariate Cox Proportional Hazard Models generated consistent results. However, a higher number of effects of factors and their interactions were detected in the gap time model than in univariate models. The gap time model generated more precise estimates with lower standard errors compared to the total time model. The study concludes that the PWP model can be extended to handle time-dependent covariates. The PWP gap model is the more appropriate technique to model the time taken for HIV testing and subsequent clinic visit to uptake test results among Most at-risk Populations.

Modeling time taken to HIV testing and uptake of test results: extension of the PWP model to handle time-dependent covariates