Table 2.

Parameter estimation guidelines^*

Health Benefit Parameters
Discount factor: $D={\sum }_{t=1}^T\frac{1}{{(1+r)}^t}$   Treatment: a1 ≅ qtx + qIA(b1/D)   Prevention: ai ≅ qIA(σTεi + (bi/D)), i = 2, …, n
Estimation Guidelines
qtx	Net present number of QALYs a treated individual gains from receiving ART; estimates available in literature or can be estimated from existing models
qIA	Net present number of QALYs an individual gains from avoiding infection; estimates available in literature or can be estimated from existing models
σT	Chance that a person acquires HIV in T years   Stable epidemic: ${\sigma }_T\cong 1-{(\frac{\#\text{uninfected at end of year}}{\#\text{uninfected at start of year}})}^T$   Growing epidemic: ${\sigma }_T\cong \frac{1-{(\frac{\#\text{uninfected at end of year}j}{\#\text{uninfected at start of year}j})}^T+1-{(\frac{\#\text{uninfected at end of year}k}{\#\text{uninfected at start of year}k})}^T}{2}$
εtx	Efficacy of ART in reducing sexual infectivity in infected individuals; estimates available in literature
εi	Efficacy of prevention intervention i in reducing the chance of HIV acquisition; estimates available in literature
b1	Net present number of infections averted per person starting ART   Stable epidemic: $b_1\cong (\frac{\#\text{new infections per year}}{\#\text{untreated}+(1-{\epsilon }_{tx})\times \#\text{treated}}-\frac{\#\text{new infections per year}\times (1-{\epsilon }_{tx})}{\#\text{untreated}+(1-{\epsilon }_{tx})\times \#\text{treated}})\times D$   Growing epidemic: $b_1\cong \left[\right(\begin{array}{c}\hfill \frac{\#\text{new infections in year}j}{\#\text{untreated in year}j+(1-{\epsilon }_{tx})\times \#\text{treated in year}j}\hfill \\ \hfill +\frac{\#\text{new infections in year}k}{\#\text{untreated in year}k+(1-{\epsilon }_{tx})\times \#\text{treated in year}k}\hfill \end{array})-(\begin{array}{c}\hfill \frac{\#\text{new infections in year}j\times (1-{\epsilon }_{tx})}{\#\text{untreated in year}j+(1-{\epsilon }_{tx})\times \#\text{treated in year}j}\hfill \\ \hfill +\frac{\#\text{new infections in year}k\times (1-{\epsilon }_{tx})}{\#\text{untreated in year}k+(1-{\epsilon }_{tx})\times \#\text{treated in year}k}\hfill \end{array}\left)\right]\times \frac{1}{2}D$
bi	Net present number of infections averted per person starting prevention program i   Stable epidemic: $b_i\cong {\sigma }_T{\epsilon }_i(\frac{\#\text{new infections per year}}{\#\text{infected at start of year}})\times D$   Growing epidemic: $b_i\cong {\sigma }_T{\epsilon }_i\left(\text{min}\right((\frac{\#\text{new infections in year}j}{\#\text{infected at start of year}j}),(\frac{\#\text{new infections in year}k}{\#\text{infected at start of year}k})\left)\right)\times D$
Cost Parameters
Discount factor: $D={\sum }_{t=1}^T\frac{1}{{(1+r)}^t}$   Treatment: C1 ≅ c1 − sIA(b1/D)   Prevention: Ci ≅ ci − sIA(σTεi + (bi/D)), i= 2, …, n
Estimation Guidelines
c1	Difference in discounted lifetime healthcare costs for an infected individual receiving ART and an infected individual who never receives ART; estimates available in literature
ci	Net present cost of prevention program i for one person for T years; estimates available in literature or can be calculated based on program components
sIA	Difference in discounted lifetime healthcare costs for an infected individual and an uninfected individual; estimates available in literature

Note: ART = antiretroviral therapy; QALY = quality-adjusted life year

^*A number of simplifying assumptions are made in creating the parameter estimates. QALY gains from treatment (a₁) are estimated as the direct QALY gains to the individual being treated plus estimated secondary QALY gains accruing from other individuals in the population who thereby avoid infection. The net present QALY gains from prevention (a_i) are estimated as the direct QALY gains when the individual avoids infection plus estimated secondary QALY gains when other individuals thereby avoid infection. The chance a person acquires HIV in T years (σ_T) is a cumulative probability calculated without conditioning on whether the individual survives previous periods. The net present number of infections averted per person starting ART (b₁) is calculated as the difference in the number of infections caused per year by untreated individuals versus treated individuals, multiplied by the length of the time horizon and the discount factor. The net present number of infections averted per person starting prevention program i (b_i) is calculated assuming an average rate of new infections per year, multiplied by the annual chance a person acquires HIV infection, the efficacy of the prevention program, the length of the time horizon, and the discount factor. The net present per person cost of treatment (C₁) is calculated as the cost of treatment for the person who enrolls in treatment minus an estimate of averted treatment costs from individuals who thereby avoid infection. The net present per person cost of a prevention program (C_i) is calculated as the cost of the program minus an estimate of averted treatment costs from an individual who avoids infection and other individuals who thereby avoid infection.