Based on the transition times, we assigned each simulated patient a viral load trajectory to determine their risk of HIV transmission over time (see Section 2.2, Supplemental Digital Content, http://links.lww.com/QAI/A493). We assumed that patients on virologically successful ART, including patients on irregular ART, had undetectable viral load. Two measures of transmission were estimated: cohort viral load (the sum of mean viral loads of each patient during a particular year,6 applying the concept of community viral load17 to a cohort of treated patients) and the expected number of transmissions, calculated from the individual viral load trajectories using a functional formula.5,6 We assumed that all patients were in consecutive 1-year partnerships and had 100 unprotected sex acts per year.5 HIV prevalence among partners at the beginning of the partnership was assumed to be 15%.18
Whenever possible, we used the results of our statistical analyses to estimate the parameters related to the patient's progression through different retention states (Table 2; see Table S5, Section 3, Supplemental Digital Content, http://links.lww.com/QAI/A493). Parameters related to virological and immunological progression were based on the findings of a previous study of 2 South African township cohorts.6
We simulated 4 scenarios. In the first scenario, “No LTFU,” we assumed all patients stay in care and on ART until death, and events (death, transfer) are correctly recorded. In the remaining 3 scenarios, we included all types of LTFU (unregistered deaths and transfers, irregular ART, and discontinuation of ART). A patient was considered LTFU if he or she missed a visit at the clinic (scheduled once a month) by 3 weeks. In the “No tracing” scenario, patients could return spontaneously to care, not as a result of tracing efforts. In the “Delayed tracing” scenario, patients were traced 6 months after LTFU. In the “Immediate tracing” scenario, patients were traced as soon as they were LTFU (3 weeks after the missed appointment).
We first describe the model's estimation of LTFU. To estimate the impact of retention in care on the preventive effect of ART, we then compare cohort viral load and transmission in scenarios with and without LTFU. Finally, we compare cohort viral load and transmission across the 3 scenarios in which patients LTFU are traced. Model outputs are presented as mean values over 100 model runs, with 95% prediction intervals (PrIs). We conducted 2 sensitivity analyses to account for uncertainty in selected parameters. In the first analysis, we modified the rates of discontinued and irregular ART. About one-third of the patients in the data set who were on irregular ART had gaps in ART intake and may therefore have had detectable viral load. We reduced the hazard of irregular ART by one-third and increased the hazard of ART discontinuation by the corresponding amount. In the second analysis, we decreased the rate of spontaneous return to one-third of the assumed rate we had assumed in the main analysis.
Table 3 shows model estimates for the number of patients LTFU for different reasons, number of patients traced, number of patients returning to care, total cohort viral load, and number of expected transmissions for the 3 strategies that included LTFU per 1000 patients over 5 years.
Rates of Loss to Follow-up
The model estimated that about 440 of 1000 simulated patients were LTFU in the first 5 years of ART (Table 3). About 160 patients were lost in the first year of ART, and between 50 and 90 in each of the following years. According to the model outputs, 23% of the patients LTFU had died. Discontinued treatment accounted for 37% of LTFU, changes to irregular ART for 26%, unregistered official transfers out for 8%, and self-transfers for 5%.
Effect of Loss to Follow-up on Transmission
In the absence of tracing, LTFU more than doubled cohort viral load over that of a cohort fully retained in care (Fig. 2A). The number of expected transmissions over 5 years increased from 33 to 54 per 1000 patients (Fig. 2B). In the first year of ART, the number of expected transmissions per 1000 patients was about 9 in the scenario without LTFU, and 11 in the scenario with LTFU. Annual transmissions in subsequent years decreased in the scenario without LTFU and stayed close to 6 from the second year on. In the scenario with LTFU and no tracing, transmissions per year were between 10 and 11.
Tracing and Prevention of Transmission
Without tracing, 50% of the patients who discontinued or changed to irregular ART spontaneously returned to care within 5 years. Immediate tracing increased the probability of return to 68%. With delayed tracing after 6 months, 59% of the patients who were expected to return did so within the 5-year follow-up time. Tracing reduced transmission moderately from the second year onwards. Cohort viral load in the cohort of 1000 patients was about 9 million copies per milliliter during the first year for all 3 strategies (Fig. 2A). Cohort viral load remained on the same level without tracing over the following years, but declined gradually to 6 to 7 million copies per milliliter with tracing. The pattern for expected transmissions was similar (Fig. 2B). During the first year, the 1000 treated patients transmitted on average 11 new infections in all scenarios. Over the subsequent years, the number of expected transmissions remained close to 11 without tracing, and decreased gradually to about 9 per 1000 with tracing. Over the 5 first years of ART, immediate tracing prevented 3.6 (95% PrI, −3.3 to 12.8) new infections for each 1000 patients. Tracing after 6 months prevented 2.5 (95% PrI, −5.8 to 11.1) new infections. Immediate tracing was more efficient than delayed tracing: 116 patients had to be traced to prevent 1 infection when tracing was immediate; 142 patients had to be traced to prevent 1 infection when tracing was delayed.
In the first sensitivity analysis, we increased the rate of discontinuation and decreased the rate of changing to irregular ART. Among all LTFU cases, the proportion of patients who discontinued ART increased from 37% to 51%. The increase in the number of patients alive and not on ART also increased the cohort viral load and moderately raised expected transmissions above the number from the main analysis in the absence of tracing. However, immediate tracing was more efficient than in the main analysis, and prevented 5.1 (95% PrI, −3.6 to 13.4) infections. The number of patients who needed to be traced to prevent 1 infection decreased to 86, with immediate tracing (see Table S6, Supplemental Digital Content, http://links.lww.com/QAI/A493).
In the second sensitivity analysis, we decreased the rate of spontaneous return from 0.33 to 0.10, so that about 10% (instead of almost 30%) of patients outside care spontaneously returned to the clinic within a year. If tracing was not available, during the 5 years of follow-up, only 58 of the 138 patients expected back actually returned. In the main analysis, immediate tracing increased the proportion of patients returning to care by 37%. In this sensitivity analysis, the immediate tracing more than doubled the proportion of patients who returned. The higher return from tracing reduced HIV transmission: tracing with a 6-month delay prevented 3.7 infections, and immediate tracing prevented 5.5 infections. About 78 immediate tracing efforts were needed to prevent 1 new infection (see Table S7, Supplemental Digital Content, http://links.lww.com/QAI/A493).
This mathematical modeling study based on the 2 ART programs in Malawi found that tracing patients LTFU can slightly reduce transmission from the patients who started ART. If 1000 patients are in 1-year partnerships and engage in 100 sex acts per year, active tracing can prevent 1 to 5 infections in this cohort over the first 5 years of ART. This is only a fraction of the >20 infections transmitted by patients who discontinued or interrupted ART. The effect depends on the delay between missed visit and tracing and on assumptions about both the rate of spontaneous return and the virological suppression of patients on irregular treatment.
In our main analysis, we found that 120 patients needed to be traced to prevent 1 new infection. If 1 tracing clerk can trace 4–5 missing patients per day, preventing a single transmission would require a 1.5-month workload. We judge this a reasonable investment since a newly infected patient will need life-long treatment and care costing thousands of dollars, and HIV infection can cut short a patient's life. We made some conservative assumptions (a relatively high spontaneous return rate and a complete viral suppression for patients with irregular ART) in our main analysis, and so may have underestimated the efficacy of tracing as prevention. We used sensitivity analyses to test on these assumptions the dependency of the efficacy of tracing as prevention, and found that the number of patients who needed to be traced decreased to about 70 if we used assumptions more favorable to tracing.
Immediate tracing of patients LTFU compared with delayed tracing after 6 months increased the efficacy of the intervention. The rationale for delayed tracing is that it reduces the burden of tracing by giving the patient time to spontaneously return. The delay slightly decreased the number of necessary tracings, but did not prevent as many transmissions as immediate tracing, and was thus less efficient. When tracing was delayed, the number of tracing efforts needed to prevent 1 infection increased about 26%. Our results underline the necessity of tracing patients LTFU as soon as possible.
Patients who interrupted ART contributed almost 40% of transmissions from treated patients, but tracing prevented less than a fifth of these infections. Interventions to improve retention and prevent LTFU may be more effective in reducing transmissions although no dedicated modeling studies have been conducted. Studies from Malawi show LTFU rates are lower in health centers than in large referral hospitals, so decentralized ART care in smaller health care units is a promising strategy.19,20 Retention may also be improved by introducing rapid point-of-care diagnostic tests21 and increasing community support.22 Patients in care also contribute to transmission through poor adherence and treatment failure. Viral load monitoring can help to identify patients with detectable viral load and minimize the transmission from these patients. Viral load monitoring can prevent about 30% of transmissions from patients retained in care6 and is likely to prevent more infections than tracing.
Strengths and Limitations
Our model was parameterized with routine data from 2 typical African public-sector ART programs in Lilongwe, Malawi, where patients present with low CD4 counts and symptoms of advanced disease, and the majority of patients are women (see Table S2, Supplemental Digital Content, http://links.lww.com/QAI/A493). Our results should be applicable to many African settings, but are affected by our assumptions, and we must acknowledge several limitations. We found that the rate of LTFU remained high even after tracing. We assumed the same proportion of different outcomes among patients who remained LTFU after tracing as among patients who were found. This might not be accurate because the outcome can influence the probability of finding the patient; for example, a patient who has moved to another region is probably harder to trace and also more likely to have transferred to another ART clinic than a patient who stays at the same address. Moreover, we could not estimate some parameters such as the rate of spontaneous return and the infectiousness of patients who dropped out of care, from the data.
One advantage of cohort viral load is that it does not depend on assumptions about the sexual behavior of patients. The disadvantage is that it cannot estimate the reduction in the absolute number of infections and can only approximate relative benefit. However, the expected number of transmissions is easily understood, but also sensitive to the frequency of sex acts and changes of partners. In our model, all patients had 100 unprotected acts per year and changed partners each year. The absolute numbers of new infections that we present are therefore specific to this scenario. Because of the low per-act probability of transmission, the number of transmissions is approximately proportional to the frequency of acts, and the effect of partner change rate is negligible.6 Therefore, the relative reduction in transmissions due to tracing will remain stable across the different risk behavior scenarios. If we however assume, for example, 25 sex acts per year, then it would take 400–500 tracings to prevent 1 infection.
Mathematical modeling has been widely used to compare management strategies for HIV-infected patients and to identify the optimal strategy,3,6,23–25 but most modeling studies have not compared model outputs to observed data. One reason for this is that the outputs of models are not necessarily directly comparable with observed data. The proportions of true outcomes among patients LTFU in our model did not exactly match the corresponding proportions in the source data. This is mainly because of the differences in censoring between the data and model; in the model everyone is followed up for exactly 5 years, whereas in the data set the follow-up time varied considerably, ranging from no follow-up to 10 years. Some of the difference can be attributed to the model; patients cannot return to earlier states and the number of events per patient is restricted in the model. In the real world, the same patient can become LTFU and return several times within a given follow-up period. This means that although the number of LTFU episodes predicted by the model is close to reality, the number of patients who survive the entire follow-up time is higher in the data than in the model. This makes it harder to compare the model with data, but it should not affect new infections, the main outcome of interest. Our model is also not a dynamic transmission model: we can estimate the potential transmission from the cohort but not evaluate the long-term effect on the transmission at the population level. The model we used has some important advantages. For example, time-to-event distributions are flexible and the model allows for time- and history-dependent hazards.
Some of the differences we observed may also be due to chance. We investigated the possibility of stochastic error by splitting the total cohorts into 10 subcohorts of 10,000 patients and compared the results. Consistent results from the subcohorts confirmed that cohorts of 100,000 simulated patients are large enough to provide reliable estimates of the true effect.
Until now, the focus of tracing has been on improving the patient's own health, on preventing mother-to-child transmission and on providing reliable estimates of cohort outcomes.7,26,27 Our analysis shows that tracing offers an additional benefit. Tracing patients LTFU may efficiently reduce HIV transmission in Malawi and similar settings. Although the number of prevented transmissions may be small, the associated workload is reasonable in light of the cost of each infection averted. Our findings support the inclusion of active tracing in guidelines of ART provision in low-income settings. However, most transmissions from patients who dropped out of care cannot be prevented by tracing alone. Interventions to keep patients in care and monitoring of adherence and treatment response accurately are likely to be of greater importance than tracing patients lost to follow-up.
The authors thank Kali Tal for commenting on and editing the article.
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antiretroviral therapy; transmission; lost to follow-up; mathematical model
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