Methods
We simulated a population of 20,000 HIV-positive adults starting ART. We randomly assigned each individual an ART starting date, by sampling from a uniform distribution spanning the interval from January 1, 2003, to December 31, 2012. In our simulation, persons on ART are assumed to interrupt ART at an annual rate equal to
where T is time (in years) since the individual first started ART and the parameters θ and a have been set to 0.13 and 0.75, respectively, consistent with South African data. Persons who have interrupted ART are assumed to resume therapy at a rate of 0.6 treatment resumptions per year, consistent with the same South African data. Patients can interrupt and resume treatment multiple times. In treated individuals, the annual mortality rate is assumed to be
where s is the cumulative time (in years) spent on ART prior to the most recent resumption (0 if the patient has not previously interrupted ART) and t is the time (in years) spent on ART since the most recent ART resumption. Parameter B has been set to 0.28, consistent with the high rates of mortality observed in the first month of ART. Parameter c has been set to 0.75, reflecting residual benefit from previous ART exposure, and parameter d has been set to 0.05, consistent with South African mortality data. The same formula is used to determine mortality in persons who have interrupted ART, but with t set to 0. A more detailed description of the model is provided in Web Appendices 1 and 2 http://aje.oxfordjournals.org/content/180/12/1208/suppl/DC1 (available at http://aje.oxfordjournals.org/).
For each individual, a sequence of treatment interruptions and resumptions was simulated until the person either died or survived to mid-2013. LTFU was defined retrospectively, that is, based on whether the individual was considered to have been in care at the analysis closure date. LTFU was defined using a 6-month window: Patients were considered LTFU if they were not receiving any ART during the period from January 1, 2013, to mid-2013 and had not died while on ART (deaths occurring while off ART were included in the LTFU definition, as these deaths would not usually be reported to the ART program). For persons designated LTFU, the LTFU date was defined as the most recent date of ART interruption prior to the start of 2013. Patients were coded as deceased if they had died while on ART prior to January 1, 2013. All other individuals were censored at January 1, 2013 (the analysis closure date).
All patient outcomes were simulated in Excel and Visual Basic (Microsoft Corporation, Redmond, Washington), while survival analyses were performed using STATA 12.0 (StataCorp LP, College Station, Texas). The probability of being classified as LTFU was calculated using the cumulative incidence command, and in a sensitivity analysis the competing risk-adjusted estimate of the probability of LTFU was calculated. In an additional sensitivity analysis, a "prospective" definition of LTFU was considered, classifying individuals as LTFU at the time they first interrupted ART for more than 6 months. All software code used to simulate the patient data and perform the statistical analyses is available in the Web material http://aje.oxfordjournals.org/content/180/12/1208/suppl/DC1.