Patient- and population-level health consequences of discontinuing antiretroviral therapy in settings with inadequate HIV treatment availability

Background In resource-limited settings, HIV budgets are flattening or decreasing. A policy of discontinuing antiretroviral therapy (ART) after HIV treatment failure was modeled to highlight trade-offs among competing policy goals of optimizing individual and population health outcomes. Methods In settings with two available ART regimens, we assessed two strategies: (1) continue ART after second-line failure (Status Quo) and (2) discontinue ART after second-line failure (Alternative). A computer model simulated outcomes for a single cohort of newly detected, HIV-infected individuals. Projections were fed into a population-level model allowing multiple cohorts to compete for ART with constraints on treatment capacity. In the Alternative strategy, discontinuation of second-line ART occurred upon detection of antiretroviral failure, specified by WHO guidelines. Those discontinuing failed ART experienced an increased risk of AIDS-related mortality compared to those continuing ART. Results At the population level, the Alternative strategy increased the mean number initiating ART annually by 1,100 individuals (+18.7%) to 6,980 compared to the Status Quo. More individuals initiating ART under the Alternative strategy increased total life-years by 15,000 (+2.8%) to 555,000, compared to the Status Quo. Although more individuals received treatment under the Alternative strategy, life expectancy for those treated decreased by 0.7 years (−8.0%) to 8.1 years compared to the Status Quo. In a cohort of treated patients only, 600 more individuals (+27.1%) died by 5 years under the Alternative strategy compared to the Status Quo. Results were sensitive to the timing of detection of ART failure, number of ART regimens, and treatment capacity. Although we believe the results robust in the short-term, this analysis reflects settings where HIV case detection occurs late in the disease course and treatment capacity and the incidence of newly detected patients are stable. Conclusions In settings with inadequate HIV treatment availability, trade-offs emerge between maximizing outcomes for individual patients already on treatment and ensuring access to treatment for all people who may benefit. While individuals may derive some benefit from ART even after virologic failure, the aggregate public health benefit is maximized by providing effective therapy to the greatest number of people. These trade-offs should be explicit and transparent in antiretroviral policy decisions.


Linear programming model
The linear programming model is specified formally in Equation A1, below. ), which seeks to maximize accumulated life-years for multiple cohorts of newlydetected, HIV infected individuals, including those who are not treated; a treatment capacity constraint ensuring that the number of available treatment "slots" in each period is not exceeded by the number of people on active treatment (Equation A1.a); a non-negativity constraint (Equation A1.b) ensuring that implemented levels of each strategy do not fall below 0%; and an implementation constraint (Equation A1.c) ensuring that the sum of the proportion of persons assigned to strategies within each period does not exceed 100%. For the steady state analysis, we assume that d c =d and x p =x, where d and x are constants (Equation A1.a). The population-level analysis was implemented in Microsoft Excel using Solver (Frontline Systems) software, which relies on the simplex method [10,11].

Linear programming model framework
We choose to employ a mathematical programming model not only to provide information on optimal implementation of alternative treatment strategies but also to do so by explicitly accounting for treatment-related resource constraints [11,12]. The method also holds the capability of implementing mixed solutions (i.e., partial implementation of 2 or more strategies) [13,14]. We chose to employ a particular class of mathematical programming models, the linear programming model, although we explored the option of employing an integer programming model. In Equation 1a, the decision variable (f i ), which represents the fraction of individuals receiving each treatment strategy, is multiplied by the number of patients seeking treatment (d). This multiplication could lead to fractional numbers of patients receiving treatment. Because individuals are not technically divisible, this suggests use of an integer programming model. However, given the computational complexities associated with solving integer programming problems and given large population sizes, the errors introduced by ignoring this integer constraint are likely to be small [15]. Therefore, we chose a linear programming model for its computational effectiveness and efficiency.

Modeling of treatment capacity
In developing and specifying the model, we chose to model the treatment capacity constraint in terms of treatment slots, defined in terms of numbers of individuals receiving ART annually. Treatment slots were chosen as a proxy for the myriad constraints faced by public sector antiretroviral programs, including financing, human resource capacity, health and social service constraints, and drug, technology, and personnel affordability [16][17][18]. While recent HIVrelated studies have modeled explicitly only funding constraints [19-21], we believe that financing reflects only one dimension of treatment capacity constraints. Therefore, we chose to characterize treatment capacity in terms of a single metric, available treatment "slots", which are limited based on a variety of factors.

Input parameters
The individual-level model produced several projections that were used as inputs to the population-level model. These included: (1) strategy-specific life expectancy estimates for the objective function parameter y c,i (Equation A1), and (2) the number receiving ART annually, which was used to derive strategy-specific annual probability of receiving ART (π n,c,i in Equation A1.a) and cohort and strategy-specific annual treatment need (i.e., π n,c,i d in Equation A1.a).

Multi-stage Modeling Approach
To highlight the tradeoffs associated with different treatment policies (in this case, discontinuation), this study was conducted using an integrated, or two-stage, modeling approach. While use of integrated modeling approaches has become more visible in the literature, few studies have evaluated HIV treatment policy using this method. Earnshaw and colleagues used output from a Markov model as inputs to a linear programming model in a resource allocation problem applied to diabetes prevention

Verification of Equilibrium for the Population-level Model
We conducted an analysis that was restricted to a hypothetical steady state (i.e., both detected cases and treatment capacity were constant). To produce a steady state, the simulation was partitioned into three periodsa burn-in period, analysis period, and censorship period. In the burn-in period, cohorts entered the model and individuals initiated and discontinued (due to a treatment policy or death) ART until the number of individuals entering and exiting treatment from year to year became constant. That is, the burn-in period continued until the model reached equilibrium. Once the model reached equilibrium, we used the analysis period to determine the optimal strategy or combination of strategies that would maximize life expectancy per member of each cohort over a defined timeframe. We also used this period to assess the number of individuals receiving treatment. Finally, rather than terminate the analysis at the end of the analysis period, we included an additional censorship period to account for the life years that would continue to accrue to individuals beyond the analytic timeframe.
We conducted a series of diagnostic evaluations to ensure that the model had reached a steady-state equilibrium. Figures A1 -A3 show three diagnostic and consistency checks for the population-level linear programming model. In Figure A1, we assessed percent change in life expectancy at the optimum across the periods: burn-in (periods 1-70), analysis (periods 71-80), and censorship (periods 81-100) periods. In the analysis period, we found that the percent change in life expectancy never exceeded 0·01% across the analysis period. In Figure A2, the percent difference at the optimum in the mean number initiating treatment across the analysis period remained relatively constant, never varying by more than 0·0008% between periods. Finally, Figure A3 shows that, beginning in the analysis period, the number of individuals remaining on treatment over time was similar across cohorts.

Sensitivity Analyses
Supplementary selected sensitivity analysis results are shown in Tables A1 -A4.  In the Status Quo, antiretroviral therapy (ART) is never discontinued. In the Alternative strategy, ART is discontinued when secondline ART failure is observed. In the base case, ART failure is defined as a 50% decrease in peak on-treatment CD4 count, CD4 count <100 cells/μL, CD4 count below pre-ART nadir, or a WHO stage III/IV event, excluding tuberculosis and severe bacterial infections [1]. On average, individuals who received no treatment lived approximately 1·9 years. † Results are for a 5-year analytic time horizon for a cohort of 30,000 newly detected infected individuals entering care annually. ‡ Treatment coverage is defined as the ratio of the number receiving treatment annually to the number qualifying for treatment annually. § In the base case, 15% were lost from care by 18 months. We assumed that 50% of those experiencing a WHO stage III/IV event after becoming lost would return to treatment and care.