Modeling clinical endpoints as a function of change in antiretroviral therapy (ART) attempts to answer one simple but very challenging question: was the change in ART beneficial or not? We conceive a similar scientific question of interest in the current manuscript except that we are interested in modeling the time of ART regimen change rather than a comparison of two or more ART regimens. The answer to this scientific riddle is unknown and has been difficult to address clinically. Naturally, ART regimen change is left to a participant and his or her provider and so the date of change depends on participant characteristics. There exists a vast literature on how to address potential confounding and those techniques are vital to the success of the method here. A more substantial challenge is devising a systematic modeling strategy to overcome the missing time of regimen change for those participants who do not switch to second-line ART within the study period even after failing the initial ART. In this article, we adopt and apply a statistical method that was originally proposed for modeling infusion trial data, where infusion length may be informatively censored, and argue that the same strategy may be employed here. Our application of this method to therapeutic HIV/AIDS studies is new and interesting. Using data from the AIDS Clinical Trials Group (ACTG) Study A5095, we model immunological endpoints as a polynomial function of a participant's switching time to second-line ART for 182 participants who already failed the initial ART. In our analysis, we find that participants who switch early have somewhat better sustained suppression of HIV-1 RNA after virological failure than those who switch later. However, we also found that participants who switched very late, possibly censored due to the end of the study, had good HIV-1 RNA suppression, on average. We believe our scientific conclusions contribute to the relevant HIV literature and hope that the basic modeling strategy outlined here would be useful to others contemplating similar analyses with partially missing treatment length data.